Mold filling simulation allows for verifying part design before mold tool steel is ever cut—ensuring that major revisions will not be necessary to either the part or the molds. Incorporating a CAD-embedded molding simulation software enables designers to make decisions to improve moldability early on and throughout the design process.

Figure 1. Fill analysis in SOLIDWORKS Plastics.

SOLIDWORKS Plastics is an add-in product for SOLIDWORKS that enables simulations for plastic injection molding and is available in three levels: ranging from Plastics Standard for predicting single part mold filling and common defects; Plastics Professional which allows analysis of the pack or “pressure hold” cycle, more complex materials and multi-cavity molds; to Plastics Premium, which enables molders and tool designers to simulate cooling channel design and predict warpage.

This article will examine some of the common molding defects that can be predicted and avoided using SOLIDWORKS Plastics—as well as the setup process required to perform an analysis.

Creating a Plastics Fill Study

Creating a Plastics study is a straightforward process, beginning with loading the SOLIDWORKS Plastics add-in.

Geometry Preparation

Geometry preparation involves making sure you are working in the SOLIDWORKS Part environment. For single parts there is no work required, but multi-cavity layouts may require conversion from assemblies into multi-body parts.

Note that for Plastics analysis the “positive” volume of the net molded part is required, rather than the negative shape of the mold cavity. If you are working from mold tooling and do not have the shape of the target part, it can easily be extracted using the Intersect feature in SOLIDWORKS.

The last task before beginning analysis setup is to define areas for the gate or injection locations where polymer will be injected into the cavity. This is commonly defined as a simple sketch point coincident with an edge or face of the model.

Study Setup

At this point a new study can be created. For most studies, the only choice the user needs to make is Solid or Shell mesh. We will explain meshing later in detail but the short version is that a Shell mesh allows rapid analysis of relatively constant wall thickness in thin-walled parts, while Solid mesh has an increased solve time but offers more rich results with less assumptions.

Figure 2 below illustrates the Plastics Study feature tree after mesh generation. The injection location was specified under boundary conditions and a sketch point was specified. The polymer was chosen inside the Injection Unit options.

Figure 2. Plastics study tree.

Starting with the 2020 version of SOLIDWORKS Plastics the user-interface was re-structured to match other SOLIDWORKS Simulation products more closely.

Like SOLIDWORKS Simulation and Flow Simulation, the study setup is stored on the part file and can take advantage of multiple configurations for analyzing geometry variations. Results files are saved in the same folder as the CAD files by default. 

The Injection Units settings let you specify the polymer as well as fill settings such as injection pressure, mold temperature and fill time, if known. In the absence of user-specified parameters here, Plastics will use data from the material specifications for mold temperature as well as automatically calculated values for fill time.

For a more detailed guide on how to set up a study in SOLIDWORKS Plastics check out this video: SOLIDWORKS Plastics: Simulation Setup Guide.

Interpreting Results

A variety of part-level defects can be identified easily with Plastics Standard, which has automatic checks and visualization for short shots (incomplete fills), weld (knit) lines, sink marks and air traps in the model. Therefore, most severe molding problems can be identified and mitigated early with a quick first-pass analysis, often set up and run in just a few minutes.

Machine selection can also be considered by predicting the clamp tonnage and pressure required to mold the part.

Cooling time is estimated at this stage and part design changes can be made to reduce cooling time or minimize knit lines or sink marks.

Testing Geometry Variations

Once the initial analysis has been performed, analyzing different geometry variations or polymers is as simple as clicking the “Duplicate Study” button to create a new SOLIDWORKS configuration and copied Plastics study.

Alternatively multiple geometry variations that are prepared in advance can be set up and batch solved through the Batch Manager.

Runner Balancing

Plastics Professional adds the ability to represent multi-cavity molds. Especially troublesome for molders are “family molds” (where multiple different parts are grouped together to save on tooling cost) which can suffer from unbalanced fill times. Observe Figure 3 below, where due to their different volumes the smaller part fills much more quickly. In the pack cycle, this may result in excessive flashing and other issues.

Figure 3. Family mold prior to runner balancing.

The process of “runner balancing” or resizing the runners is normally a manual undertaking to attempt to even out the flow between disparate parts. SOLIDWORKS Plastics Professional automates this process using a runner balancing wizard which iterates and attempts to automatically optimize runner and gate sizes until equal fill rates are achieved.

Runner systems in general can be quickly prototyped using single line sketches and assigning profiles and sizes, or they may be modeled in more detail by creating a solid body to represent the runner system and flagging it as part of the runner domain.

Figure 4. Runner system: sketch lines (left) vs solid body (right).

Modeling a solid body to represent the gate and runner is the preferred method to accurately represent localized gate effects and test different gate designs such as submarine gate, cashew gate, etc.

Solid Mesh

The examples thus far have featured a shell mesh—which is appropriate for initial predictions of fill performance on thin-walled parts.

For parts that may feature thin and thick regions, or out of desire for more accuracy and rich results, it may be desirable to utilize a solid mesh.

Figure 5. Solid mesh and boundary layer element closeup.

The shell meshes only the interior and exterior faces and performs extra calculations to interpolate what the flow front is doing through the thickness of the cavity.

The solid mesh generates boundary layer elements on the inner and outer skins of the model and then fills in the inside with tetrahedral elements, which allows it to calculate the flow front explicitly.

This means that in addition to ensuring accuracy, solid mesh enables additional results outputs.

Isosurface plots allow visualizing the 3D flow front of polymer, as visible in Figure 6 below.

Figure 6. Isosurface display for fill time plot with solid mesh.

The presence of “through thickness” elements also means that accurate cut plots can be created and data can be probed at any location internal to the part, which is practically a requirement for parts that feature thick wall sections.

Solid mesh functionality is available even in Plastics Standard but only for single body parts.

Solid Mesh Performance

Despite requiring many more elements, solid mesh solvers are very well multi-threaded. Despite the speed advantage shell mesh may have in terms of solve time on lower-end hardware, the gap in solve time can be reduced on hardware taking advantage of a high number of cores in the CPU and GPUs.

Overmolding

Figure 5 and Figure 6 also show an example of insert overmolding, a feature which requires Plastics Professional. The ability to specify multiple different domains makes it easy to separate the runner body, the insert and the part cavity itself.

By including the insert in the analysis, the appropriate material can be applied and more accurately represent the thermal effects in the mold.

Plastics Professional also supports multi-shot injection molding for plastic-on-plastic parts, as well as materials such as TPU and TPE for soft-touch overmolding.

Mold-level Analysis: Cool & Warp

At the high end of SOLIDWORKS Plastics simulation in Plastics Premium, mold-level analysis can be performed by representing the runners, cooling channels and a mold body around the cavity.

Figure 7 below shows the cooling channels, defined in this case using simple sketch lines. Flow rates and a fluid are input to the cooling channels, which will perform a fluid dynamics calculation to determine their heat removal performance.

Figure 7. Cooling channel and runner system defined in Plastics Premium.

Cooling channels can also be modeled using solid bodies to represent more complex cooling, such as conformal cooling channels.

Figure 8. Virtual mold mesh cross section.

Figure 8 shows a cross section of the virtual mold—a volume of metal to represent the mold body. The mold could be represented as separate solid bodies and inserts for more complex scenarios.

Including the detail of the mold and cooling channels allows a molder or tool designer to simulate the cooling portion of the mold cycle using Plastics Premium.

Mold Temperature Assumptions & Cooling Analysis

Note that all the analyses possible in Plastics Standard & Professional are predicated on a “uniform mold temperature” assumption—meaning that the mold temperature specified is assumed to be uniform throughout. This is usually a reasonable assumption for parts with uniform wall thickness but the more non-standard the part design the higher the odds that assumption is invalid.

In any case, running the cool analysis provides much more detail. The cool analysis can be performed up front (even before Fill or Pack) which makes for a convenient workflow if the tooling designer is simply trying to optimize cooling channels.

Figure 9. Cool results - mold temperature.

Once the cooling results are available, as visible in Figure 9 above, they will automatically be incorporated into subsequent calculations such as Flow, Pack and Warp, increasing their accuracy.

Running Cool/Flow/Pack/Warp provides the most rich results the software is able to offer. Warpage is predicted and contribution of thermal versus viscous effects can be evaluated.

Figure 10. Warpage result (exaggerated deformation).

An exaggerated warp deformation is visible in Figure 10 above. If it is not possible to correct the warp by improving the part or tooling design, the inverted shape of the warpage may be exported using the Reverse Warp option when creating a deformed body. This allows exporting a shape with “windage” with the intent of cutting the reverse-warped shape into the mold to help improve accuracy of the final part.

Conclusion

SOLIDWORKS Plastics add-in allows a mold filling simulation from within SOLIDWORKS. For part designers, Plastics Standard represents a great value and will typically make moldability problems obvious with a quick “first pass” analysis.  

Overmolding, family molds and an expanded range of molding processes are available in Plastics Professional. Plastics Premium adds the ability to represent cooling system design and the mold itself, as well as performing warpage analysis.

Aside from helping avoid costly tooling challenges, having a plastics simulation tool on hand is especially helpful whenever the part design veers from normal or known, tried and true existing designs. Plastics simulation allows for design innovation, rather than playing it safe, giving engineers confidence and security that approaches that of “tried and true” designs.

For more about the benefits of simulation, check out the whitepaper Enhancing Data Management Workflows Through CAD-Integrated Simulation.

You can’t run a simulation without meshing; it’s not possible. Meshing is to simulation what chicken is to chicken soup – the core building block. Meshing creates the finite elements that make up a finite element model so that you can do a finite element analysis, or FEA.

What do you have to know about meshing to run a FEA using SOLIDWORKS Simulation? Surprisingly little. But let’s suppose you want to run better simulations, or get the most accurate results.

It is the mesh that determines the accuracy of the results. Read on and you will find enough about meshing to get the most accurate results from your simulations.

What is Meshing?

Meshing is the process of breaking down your model into simple shapes called finite elements. Let’s define basic terms:

• Finite: a certain amount, as opposed to infinite.
• Element: A piece or block of a simple, predefined shape.

The elements are the basic components of the model. Meshing takes a complicated problem and breaks it down into a number of pieces (finite) of a shape that is easily calculated (elements).

Simulation software uses equations to solve for things such as stress on complicated shapes. But it breaks it down into thousands or hundreds of thousands of little pieces of a simpler shape. It works like this:

Creating the Mesh

Creating a mesh is easy in SOLIDWORKS Simulation. To get started, right click on the mesh icon in the Simulation Tree and click Create Mesh.

This will open the mesh interface. Think of meshing in SOLIDWORKS Simulation as having two levels: Level 1 we’ll call Quick Mesh and Level 2 is Advanced Mesh. This isn’t official SOLIDWORKS terminology, but rather the two ways to use the meshing interface.

Level 1: Quick Mesh – The Simplest Way to Mesh your Model

With a quick mesh, you don’t look at any options or even numbers. You only see a slider that controls the density or size of the elements. To the right is fine and to the left is coarse, referring to the element size. A fine mesh will have a greater number of smaller elements, while a coarse mesh will have fewer or larger elements.

You can change the average size of the elements in a part with a mesh slider. A powerful algorithm makes changing all the element sizes at once super easy. But when you create a mesh with the mesh slider, you are putting a lot of faith in its ability to give you a good mesh.

Level 2: Advanced Mesh – Have Control Over the Mesh

To take your mesh from quick to advanced we expand the options. Various options give you more control of your mesh than the mesh slider.

The first choice is the mesh algorithm you want to use. This defines the scheme used to build the mesh from the CAD geometry. There are three choices: standard, curvature-based, and blended curvature-based. As you can see, each one of these algorithms offers different settings.

Standard Mesh

This is the original meshing scheme of SOLIDWORKS Simulation and a good starting point. It works well for the simplest geometry.

Curvature-based Mesh

This offers the ability to specify a maximum and minimum element size. While this is great for geometry with a lot of small features, it can add unnecessary elements if used on simple geometry. It is very good at capturing changes in geometry from curved features to prismatic shapes.

Blended Curvature-based Mesh

Introduced to Simulation back in 2016, this is an extension of the Curvature-based mesh in that it offers a more advanced option to capture very small geometric features. This algorithm has one subtle difference, however: the option to “calculate minimum element size.” With this option you can capture small geometric features automatically.

Optional Level 3: Mesh Controls

With SOLIDWORKS Simulation, this is the closest you’ll get to manually building the mesh. Mesh controls are a way to locally define an element size in a particular region. This enables you to focus the resources on a specific area rather than the entire model.

This is especially useful if one area of the model has a small feature such as a radius, like that seen in the example below.

When working with a larger and more complicated models, mesh controls go from an optional step to a required one. In the example below of the industrial equipment, a simulation was done on the boom subassembly to ensure it could withstand the required forces during operation. With all the different components of various sizes, eight different mesh controls had to be used to get a mesh that captured all the geometry.

When working with just the one bracket part from the boom, no mesh controls were required because the geometry was simple—meaning it was consistent and uniform. However, the same could not be said when working with the entire boom assembly. The boom assembly contained many components of varying sizes—some small and others large—so mesh controls are required to get a good mesh. Without mesh controls, the mesh would have at worst completely failed to generate, or at best it would have been a bad mesh.

What’s a Good Mesh?

The secret of a good mesh can be hidden in the details, but SOLIDWORKS Simulation makes it easy to find them. Simply right click on “Mesh” and click “details.” You will be presented with a list from which we can determine the quality of the mesh:

• Maximum aspect ratio
• Percentage of elements with aspect ratio < 3
• Percentage of elements with aspect ratio > 10

What’s the Aspect Ratio?

The aspect ratio tells you the shape of the element. A value of 1 is optimum. The bigger the aspect ratio, the worse the shape of the element.

A good way to understand aspect ratio is to think of it as the element shape; however, the aspect ratio reported by Simulation is more than simply the shape. The simplest way to define the aspect ratio is by looking at the ratio of lines drawn normal from a face to the opposite vertex. As you can see, the higher the aspect ratio the more skewed the element.

How does this tell you if you have a good mesh? Since you know that a perfect element has an aspect ratio of 1, you would ideally want all your elements to have an aspect ratio of 1—but that just isn’t reasonable. The key is to make sure that your elements have low aspect ratios, so you look at the summary percentages; specifically, the percentage of elements with aspect ratio greater than 10 or less than 3. By looking at these values, you can know for sure you have a good mesh or if you need to improve on it.

Now you know how to create a mesh, improve the mesh with mesh controls and even determine if you have a good mesh. These are the three things that make up the foundation of meshing in SOLIDWORKS Simulation.

Learn more about using SOLIDWORKS for simulation with Design Through Analysis: Simulation-Driven Design Speeds System Level Design and Transition to Manufacturing.

Is This Crash Course in Simulation For You?

Do you use SOLIDWORKS? Then, yes, this crash course is most likely for you. Over recent years, Simulation has transitioned from being the final step in the design process to becoming the tool guiding you every step of the way throughout the entire design process. It’s not just a validation tool; rather, simulation is a design guide—your “GPS navigation” for CAD, providing step-by-step insight into your design.

Material Science Essentials: Knowing the Material Input and Understanding the Results of your Simulation.

Material Science is the one topic that gives you a good foundation for your simulation setup and how to understand the results. We will introduce the key topics needed so you’ll be ready to run SOLIDWORKS Simulation like a pro.

Please note that for the purposes of this article, when we say Simulation, we are referring specifically to linear static analysis in SOLIDWORKS Simulation. This means that the materials are linear, elastic and isotropic (but those are topics for another article). This article serves as an introduction to the engineering background needed to understand Simulation.

Material Science

Materials define exactly how the CAD model behaves in Simulation. Setting this up in Simulation is incredibly easy. You simply make your selection from the database to apply the material, just like you would at the CAD level. This is shown in the image below. It’s even easier If you apply your materials at the CAD level, because they’ll automatically be populated in Simulation.

Although the database is the same, it will look slightly different. Notice that from within Simulation you’ll see properties that are black, red and blue. These colors indicate what’s required for the study (red) and what might be required (blue) depending on the set up. As you can see in the image below, the line items are the same, but there is that added visual color cue indicating the required values for Simulation.

In my opinion, the three most important numbers for Simulation from the material library are:

1. Modulus of elasticity (Young’s modulus)
2. Yield strength
3. Poisson’s ratio

These are the three properties that you really need to run a Simulation. Here’s what they mean.

Modulus of Elasticity

The modulus of elasticity, also known as Young’s modulus, or E, defines a material’s inherent strength. What you would call a stronger material would have a higher modulus of elasticity. For example, steel has a higher modulus of elasticity than aluminum, which has a higher modulus of elasticity than rubber.

This number, or property, is important because it defines exactly how much stress a material undergoes after it is loaded in Simulation, just like in the real world. Stress is what most designers look to as an indicator of failure in their model. Too much stress is bad. How much stress is okay? We answer this question later. (Spoiler Alert! It has to do with the yield strength.)

When you consider this at the atomic level, this is the strength of the bonds between atoms. In the context of the modulus of elasticity, a material is stronger because the atoms hold on to each other better. It takes more force to separate the atoms from one another. This separation, or space between atoms, is what we see as deformation or the change in shape. In other words, when you pull on something, it stretches because the atoms are being separated.

You can think of the modulus of elasticity as the “spring” between the atoms, as illustrated in the image below. The larger the modulus of elasticity, the stronger the “spring,” which means a greater force is needed to stretch the spring or move the material.

Stress & Strain

Before we can continue with the modulus of elasticity, we need to introduce the concepts of stress and strain. Every material has a map that defines its behavior when loaded. This map is called the stress strain curve. We know exactly how much stress a material will see when it is “strained” or loaded.

In static Simulation the stress strain curve is linear. This line can be defined entirely by the modulus of elasticity. In other words, a material’s behavior in Simulation can be defined in large part by the modulus of elasticity. See the image showing a stress strain curve for a material. This outlines the material’s reaction to loadings through the relationship of stress and strain via the modulus of elasticity.

• Stress (σ) is what you, as a designer, want to know to determine part failure. It describes the intensity of the load on an object. It is literally the force over an area.

• Strain (ε) is what you can measure. It’s defined as the ratio of the change in shape of an object.

• Modulus of elasticity (E) is used to determine stress from strain. It’s the slope of the stress strain curve for a material (in a linear static analysis, especially in this article). The higher the slope, the stronger the material. This is shown in the graph below.

• Hooke’s Law is the equation relating it all together.

Yield Strength

The yield strength is used by designers as a measure of pass or fail for the design. Technically, the yield strength is a material property which marks the transition from the elastic deformation to plastic deformation. The difference between elastic and plastic is just temporary or permanent. Elastic deformation means it will go back to its original shape. Plastic deformation means its shape has been deformed too much and it will not go back to its original shape.

For a designer (in most circumstances), elastic deformation is okay, but plastic deformation is not—it’s considered a failure. Since the yield strength marks this transition, we use it to quantify pass or failure in terms of a value called the factor of safety.

The factor of safety is a number which relates the maximum stress to the yield strength. If this number is larger than 1 it passes; if it is less than 1 it is a failure.

A factor of safety plot can be easily shown in Simulation. The easiest way to use this plot is to have it indicate areas below a factor of safety of 1. This makes it obvious where there could be a failure. If you see any red, that’s where you need to focus your attention.

In Simulation, a stress result could be higher than the yield strength. However, it is important to note that this result is not accurate because beyond the yield strength the stress-Strain curve is no longer linear—meaning you need more than just the modulus of elasticity to get an accurate result. This is where a more advanced nonlinear simulation needs to be used. This is illustrated in the image below.

Poisson’s Ratio

Poisson’s ratio describes how a material changes shape. As the material is stretched in one direction, it needs to contract in another; this is known as Poisson’s effect. When a material deforms, you aren’t adding or reducing the mass, just changing its shape. Poisson’s ratio describes this change of shape. This is illustrated in the image below. As you apply a force to a material it will expand in the direction of the force, and contract perpendicular to the force.

The checkerboard started out as perfect squares. When it deformed from the force, it changed its shape to a rectangle. The edges in the direction of the force (longitudinal) are now longer, while the edges perpendicular to the force (transverse) are now smaller. The ratio of the change of shape, or strain, in the transverse direction to the longitudinal direction is the Poisson’s ratio.

Putting it All Together in Simulation

Now that you understand what these important terms mean, let’s take a simplified look at the steps for how they are used by Simulation to get results.

• Step 1: Run Simulation and see how the applied forces change the material shape based on its stiffness from the modulus of elasticity.
• Step 2: Determine the change in shape to then calculate strain.
• Step 3: Use Hooke’s Law and the calculated strain to calculate stress.
• Step 4: Check the factor of safety to see if the part will fail or not.

With a combination of these essential material properties, you can paint the picture of your model’s performance. Is your design strong enough? Will it break? These are all questions you can now answer with Simulation.

This article was just an introduction, meant to build a foundation of understanding for using Simulation. There are even more advanced foundational topics worth exploring such as meshing. But when it comes to materials in Simulation, there are many more advanced topics covering more advanced materials such as composites, hyperelastic and viscoelastic. There are even other material failure modes beyond yield, such as resonance and fatigue. But at the end of the day, you don’t need to know this to be successful with using Simulation to guide you through the design process.

People spend their entire careers and devote their life’s work to studying these topics. But that is not necessary to use and benefit from Simulation. Behind all the complexity of the numerical methods and engineering concepts in FEA lies a level of elegance and intuitiveness that make SOLIDWORKS Simulation a powerful tool in the hands of SOLIDWORKS designers.

Learn more with the whitepaper Design Through Analysis: Simulation-Driven Design Speeds System Level Design and Transition to Manufacturing.

Forces act on the rim of the wheel due to both the air pressure in the tire and the reaction force of the ground on the tire. The way that these forces are transferred through the tire into the rim have a significant impact on the stress in the wheel. Although it is possible to directly model the tire, this is generally unnecessary and will significantly increase the complexity of the model. There are, however, established analytical and empirical ways of simplifying the tire into a few boundary conditions that can be applied directly to the rim. The theory behind these is explained by Stearns et. al.

The Complexity of Modelling Tire-Rim Interaction

Firstly, let’s look at why we don’t want to model the actual tire using finite elements. There are a few reasons for this.

Firstly, as the toroidal shape of the tire makes contact with the planar ground surface, it must deform significantly to form a planar contact patch. This involves large deformations, which requires non-linear modeling. Secondly, a tire is not made up of a homogeneous isotropic solid material. Rather, a tire is a composite structure with a rubber matrix surrounding anisotropic textile casings and bead wires. Modeling all of this would require considerable pre-processing and solution times. Although tire interactions are modeled academically, it doesn’t make sense to do this type of work when designing a wheel.

Identifying the Forces Acting on the Rim

Before identifying the forces acting on the rim, the terminology used to refer to parts of the rim should be explained. The key parts of a rim and a tire are labeled below.

The tread is the part of the tire which contacts with the ground, the bead is a wire running around the edges of the tire which contact with the rim, and the sidewall is the vertical section of the tire connecting the bead to the tread.

The bead seats are the sections of the rim where the beads rest on the tire and vertical forces are transferred, and the rim flanges extend vertically to resist horizontal movement of the bead seat.

Forces act on the rim due to two primary sources: the air pressure within the tire, and the ground reaction forces. The air within the tire exerts a uniform pressure on all internal faces of the tire and rim; this is the inflation pressure, P. Where this pressure acts on the inside of the tread, it is contained by the tire casing and bead, causing internal hoop stresses in the tire but no reaction forces on the rim. However, where the inflation pressure acts on the side wall of the tire, it causes the beads to splay outwards. These sideways forces, Fs, are contained by the rim flange.

Calculating the force of the sidewall on the rim flange involves integrating the pressure over the area of the tire. The integration is quite simple because we’re only interested in the area of the sidewall projected onto the vertical plane. This area is given by π(r₂² - r₁²). The area is multiplied by the pressure P to give the total force acting on each side wall of the tire. The force acting on the rim flange is half of this because the bottom of the side wall is constrained by the rim while the top of the side wall is constrained by the tread of the tire itself. Therefore, these forces are given by the equation:

The other forces acting on the rim result from the ground reaction forces. These may be classified as vertical forces supporting the weight of the vehicle, torque resulting from acceleration and braking forces, and axial forces caused by cornering. These forces are transferred through the bead seat and rim flange, but they are not constant over the circumference of the rim. Instead, these forces act over a section of the rim, related to the tires contact patch and stiffness and given by the angle of loading, θ. The forces are distributed according to a cosine function over this region.

The loading angle depends on the combination of tire and rim, the tire pressure and the ground reaction force. In practice, it is not possible to determine this angle analytically, and an empirical method must be used. One approach is to run the simulation with several different loading angles and observe how this affects the stress in the wheel. It may then be possible to use a worst-case value. Alternatively, the results can be compared with experimental measurements to determine the actual loading angle.

Due to the rotation of the wheel and the periodic nature of the spokes, the stress in the wheel will cycle between two extreme states. In one state, the vertical ground reaction will be directly centered over the spoke and in the other it will fall halfway between the spokes. For every revolution of the wheel, each spoke will experience one cycle which should be taken into account for fatigue calculations.

Additional ground reaction forces also occur when cornering, braking or accelerating. Cornering results in an axial force which is transferred through the flange. This can also be expected to be sinusoidally distributed and act over a similar loading angle to the vertical reaction force.

In summary, there are five forces acting on the rim:

• Inflation pressure, P, acting uniformly on the internal faces of the rim not in contact with the tire.
• Side wall pressure reaction, Fs, acting on both rim flanges.
• Vertical ground reaction, Fv, distributed sinusoidally over both bead seats.
• Axial cornering reaction, F_A, distributed sinusoidally over one of the rim flanges depending on cornering direction.
• Tangential braking or cornering reaction, F_T, acts over the same region of the bead seats as the vertical ground reaction and is also sinusoidally distributed, with the tangential load transfer related to the normal force.

Simulating the Tire Loads in SOLIDWORKS

Before attempting to apply the tire forces to the rim, a few changes should be made to the solid model to simplify the analysis. Firstly, split lines must be added to the bead seats, so that the vertical ground reaction can be applied over the load angle. It also makes sense to cut the wheel in half so that symmetry can be used to simplify the model. Further defeaturing and the creation of surfaces for shell elements may also be desirable.

Here you can see the simple sketch containing a single line used with the Split Line command to split the bead seats, followed by the split lines in the two bead seats.

A static stress analysis is given as an example here. The following fixtures were used:

• Symmetry fixture on the three cut surfaces. This simply constrains all nodes on the surface so that they are able to move tangential to the surface, but no normal motion is allowed.
• Roller/Slider fixture on the inner face in contact with the hub.
• Foundation Bolts through the bolt holes to ground.

Next, the air pressure was applied to the rim. First, a uniform 50 psi pressure to the internal faces of the rim which were not in contact with the tire.

Next the side wall reaction force was calculated, using the equation for Fs described above. The radius of the inner face of the tire tread is 268 mm and the bead seat radius is 163 mm, resulting in an area of 142,173 mm². The inflation pressure of 50 psi is equal to 0.345 N/mm² halving the force on the sidewall gives a reaction force of 24,525 N, a surprisingly large force. Because of the symmetry in the model, this force is halved again and then separately applied to each sidewall, setting the direction normal to a reference plane.

Finally, the ground reaction force is added. Because this is sinusoidally distributed, the easiest way to apply it is using a Bearing Load. Before creating the bearing load, a coordinate system must be created with its z-axis on the axis of rotation for the wheel and the x axis through the center of the distribution.

The model can now be meshed and solved. A coarse mesh is shown, with local refinement after adaptive meshing. Although the polynomial solid elements in SOLIDWORKS Simulation cope reasonably well with thin walled sections, there is still an argument for meshing regions of this model with shell elements to efficiently obtain an accurate solution.

The simulation shows that the maximum von Mises stress is 146 MPa, occurring on the inner radius of the rim flange. This stress is almost entirely caused by the sideways force on the rim flange as the sidewalls attempt to spread outwards as a result of the inflation pressure. In fact, suppressing the ground reaction force produces no visible change in the stress distribution and only reduces the maximum stress by 3%. This shows the critical importance of properly considering boundary conditions when setting up a simulation.

Learn more about SOLIDWORKS with the whitepaper Understanding Nonlinear Analysis.

SOLIDWORKS simulation provides a wide range of tools to simulate stress in mechanical parts. As with any simulation, the results are only as good as the assumptions we make when setting up the model and analyzing the results. This article focuses on the way we interpret the calculated stress to determine whether a part will fail.

Before we get into determining whether your part will fail, it’s important remember that this is only one aspect of a good stress analysis. It’s also vital that the boundary conditions and mesh realistically simulate the loading of your part.

The first question to ask is whether the boundary conditions accurately represent the way the part will be loaded. The mesh must be of sufficient quality to provide numerically accurate calculations. Aspect ratio is one important measure of mesh quality, this means that the triangular faces of elements should be as close to equilateral triangles as possible. Very elongated elements with high aspect ratios over 3 will reduce the accuracy of the simulation. Similarly, distorted elements, as measured by the Jacobian, may cause the simulation to fail.

Selecting Mesh Details from the context menu of the element in the simulation tree brings up useful information to evaluate mesh quality. Geometry should be simplified, and mesh controls should be added to achieve a reasonable mesh quality.

Another important consideration for the mesh is whether it has sufficient detail to provide the actual maximum stress with stress concentrations.

There can be something of a trade-off here between removing features to improve mesh quality and maintaining the features that will actually affect the result. This is somewhere that the skill and experience of a stress analyst can be very valuable.

Simulation using finite elements usually isn’t actually the best way to determine the peak stress within stress concentrations. It’s much better to use the FEA to determine the stress field surrounding the stress concentration, and then determine the actual peak stress using an analytical method. Formulas for a wide range of features and loading conditions can be found in reference books such as Roark's Formulas for Stress and Strain, or Peterson's Stress Concentration Factors.

This is a very brief overview of what’s required to perform a good stress analysis. So, assuming you have accurately determined the stress in the part, how do you know whether it will fail?

Failure Criteria

Material failure may occur under static stress, fatigue or buckling. Under static stress conditions, materials generally fail in one of two ways, either by brittle failure (fracture) or by ductile failure (yield).

Mild steel is a typical example of a ductile material and ceramic is an example of a brittle material, although almost any material can behave in a brittle way under conditions such as very low temperature or highly cyclic loading. Similarly, most materials can be ductile at very high temperature. Over the full range of typical conditions, most materials can be considered to be either brittle or ductile. However, some materials, such as aluminium alloys, are a little less clear – a single large force is likely to result in yielding while a cyclic fatigue load will result in fracture.

The way that failure is defined may also vary according to the way a part is used. For example, if a shackle on a safety harness yields while arresting a fall, this probably doesn’t constitute a failure. In fact, it may be desirable for the shackle to yield, since this will dissipate some energy, protecting both inline equipment and the falling person from higher peak forces. [Hopefully, the shackle carries a warning that it should not be used after a fall, now that it has a shape different than its design shape. --Ed.]

In this case, a simple failure criterion could be when the average stress over its cross section exceeds the material’s ultimate tensile stress. However, if the same shackle was used as lifting gear, requiring repeated use, then yielding would be considered as a failure of the part. In this case, the same part, undergoing the same loading, can have different failure criteria – defined according to the usage requirements.

Some potential physical mechanisms for failure include yielding, fracture and buckling. A different analysis is required to check for each failure criteria.

For a part loaded in pure tension, the yield criterion is simply the yield stress for the material. However, most parts have more complex loadings, resulting in a three-dimensional combination of tension, compression and shear.

The simplest way to deal with this is to resolve the stresses into their principal directions, using Mohr’s circle. If these individual values are less than the material’s yield stress, this theory would assert that it shouldn’t fail. The principal stress approach is a simplification and other failure theories take a more sophisticated approach to determine when yield will occur. They consider the micro-mechanics of materials, involving atoms slipping within the crystal lattice and grain boundaries moving over each other.

Different approaches should, therefore, be used for ductile and brittle materials. They typically assume that a material is ductile and isotropic, meaning it has the same strength and stiffness in all directions. Metals can generally be considered to be isotropic, while wood and composites cannot.

The most common failure criteria used for static stress are von Mises, Tresca and maximum normal stress. They all involve first calculating principal stresses and then combining them into a single stress value that represents the stress at a point in the 3D solid. If this combined stress is less than the tensile yield stress for the material, it should not yield.

Von Mises and Tresca are used for ductile materials, while maximum normal stress is used for brittle materials. Von Mises is the most common, used for most static stress analysis. Tresca is very similar, but can give slightly higher stress values under certain circumstances; it is therefore more conservative, resulting in improved safety.

There is no stress plot listed as Tresca in SOLIDWORKS simulation but the Stress Intensity (P1-P3) gives the same values as Tresca.

For brittle materials, it is best to use the maximum principal stress (P1). However, brittle materials may require more detailed consideration of their fracture mechanics, which describes the way that cracks propagate and result in sudden and catastrophic failures.

Many theoretical failure criteria have been devised for brittle failure. The below plots show that for von Mises, Tresca and maximum principal stress, the results are very similar but slightly different maximum values are calculated.

In this article, I’ve given a quick overview of some of the most important failure criteria for failure under static stress.

It’s important to also check whether your part might fail under buckling or fatigue. In an ideal world, we would have clear rules for which failure criteria to apply for specific materials, loading conditions and functional requirements. Unfortunately, material science isn’t quite there yet. Instead, a number of different theories are in use and each has strengths and weaknesses.

Although a skilled analyst can consider relevant criteria for each case, ultimately no simulation can be considered an infallible way to determine whether a part will fail. Ultimately, testing is still required. Simulation, can however, dramatically reduce the number of design and test iterations.

Simulation is more useful for providing rich qualitative data showing stress fields than it is in predicting exact failure. This can be invaluable in assisting a designer, or optimization algorithm, to design parts which put material where it is needed to carry loads.

To learn more about analysis with SOLIDWORKS Simulation, check out the eBook Understanding Nonlinear Analysis.

SOLIDWORKS Simulation makes it easy to determine whether a structure satisfies its design criteria for a particular set of loading conditions. As many users can attest, having only one loading condition is rarely the case. When offering a product to the general population, the designer must consider different loading scenarios due to differences in environmental loads and in human physiology, as well as user error, to name just a few.

Consider the ladder pictured to the left.

SOLIDWORKS Simulation comes with diverse sets of loading conditions and is able to handle live loads (e.g. a person on the ladder) and dead loads (e.g. the weight of the ladder itself). It would be very time consuming to manually consider not just each case, but every combination of the loading cases. You could try to duplicate studies, but the clutter would soon become unmanageable. You could try to reuse the same study and change the values of the forces, but you would lose the history of what the previous values were, as well as being generally tedious.

Thankfully, SOLIDWORKS Simulation has a way to handle load cases. The Load Case Manager from within SOLIDWORKS is designed to make assigning these different types of loads and, more importantly, combining these loads easy. In this article, we will explore what it takes to assign load cases for the ladder pictured above.

Note: this article will apply to any major version of SOLIDWORKS greater than 2014. SOLIDWORKS 2015 was the first year that Load Cases were implemented.

You can download the simplified ladder model here to follow along if you wish (SOLIDWORKS 2015+). The ladder is simplified because the focus for this article is load cases rather than the intricacies of meshing, different types of bodies etc. that would arise should we use a geometrically accurate ladder.

Step 1: The Plan

The first step is to lay out what the challenge is and what we are looking to analyze. Let’s lay out the situation: This particular ladder is designed to hold two users on it at the same time (not the best idea in real life for safety reasons other than the structural integrity of the ladder, but we are only considering the structural safety of the ladder in this exercise). The users may be carrying tools.

For the ladder resting against a wall at 15 degrees, find the magnitude of the maximum Von Mises stress for the following cases:

• Resting on a wall; no live load
• Live Load 1 only
• Live Load 2 only
• Both Live Load 1 and 2
• [2 × Load 1] + [1 × Load 2]; (heavy user 1, normal user 2)
• [1 × Load 1] + [2 × Load 2]; (heavy user 2, normal user 1)
• [2 × Load 1] + [2 × Load 2]; (both heavy users)

Assume the ladder is made from Aluminum 1060 Alloy.

As you can see, there is much work to do, but thanks to load cases, we only have to define the study once, and the load case manager will take care of the rest.

NOTE: If you have a study already defined and want to get to the load case manager, skip to Step 8.

Step 2: Open the File

Open LADDER.SLDPRT and verify that the Simulation Add-In is turned on.

The simulation add-in can be accessed from either from Tools > Add-ins, or from the SOLIDWORKS Add-Ins tab on the ribbon.

Step 3: Create a New Static Study

There are plenty of ways to do this, but I like accessing it from the Simulation Tab. Make sure that “Use 2D Simplification” is unchecked.

Step 4: Apply the Material as Aluminum 1060 Alloy

If you haven’t already, make sure the material is set. I am using aluminum 1060 alloy here, but you can set it to whatever linear material you desire (practically any metal, for example).

Step 5: Apply Fixtures

In order for the static simulation to run properly, we must ensure that our model is properly fixtured. I used the following:

Specify the two bottom faces as Fixed Geometry. This will represent the feet of the ladder that is firmly planted on the ground.

On the top of the ladder, specify the two vertical faces as Roller/Slider Fixtures. This represents that while the ladder can’t go through our imaginary wall, it can slide along the wall.

Step 6: Apply Loads

This where the bulk of the setup occurs.

There are three main loads to consider: The weight of user 1 (Live Load 1), the weight of user 2 (live load 2) and the weight of the ladder (dead load). It is important that these loads are defined in separate features from each other. This is what is going to allow the Load Case Manager to toggle the consideration of the loads when it runs.

Live Load 1:

Right click the “External Loads” Node in the simulation tree and click “Force.” For its location, pick the second rung from the top. Change the radio button from “Normal” to “Selected Direction” and for the direction, click the Top plane

In this example, the ladder is already oriented 15 degrees with respect to the coordinate system.

Enable the “Normal to Plane” Direction button and hit “Reverse Direction” if necessary, to make sure the force is pointing down. For this, I put 1,000N.

Remember, it may be tempting to include the other rung in the blue selection box as well, but we must keep them separate for the reasons mentioned above. With Face<1> as the only item, click OK. It might be a good idea to rename the item in the tree, too. I named it “LIVE LOAD 1” to make it easier to distinguish when we get into the load case manager. You can do this by clicking on the line item and pressing F2.

Live Load 2:

Make another force with the same parameters as Live Load 1, but with the second rung from the bottom as the selected face. Type, magnitude and direction of the force are identical.

Dead Load:

Right click on the “External Loads” node and select “Gravity.” Usually it will fill out standard parameters by itself, but make sure that the selected reference is the Top Plane, direction reversed with a magnitude of 9.81 m2. I renamed this to “DEAD LOAD.”

Step 7: Mesh the Model

Of course, the penultimate step to running a study is meshing the model. I will use basic mesh settings to make the computation quick for this demonstration. Right click on the Mesh node and select “Create Mesh…”

Here, I specify a draft quality mesh with the standard coarseness settings.

Step 8: Open Up the Load Case Manager

This is where the fun begins! Normally, we would run our study. But instead, we divert to the Load Case Manager!

You can find the load case manager by right clicking the top of the study tree and finding “Load Case Manager” in the drop-down list.

Overview of the Load Case Manager

When you activate the Load Case Manager, a screen similar to this will appear with a table. The columns represent the different elements of your study (forces, fixtures etc.). Some of you may even draw parallels to the Configure Feature functionality found in SOLIDWORKS, which is very similar. It’s practically defining configurations of your study to have SOLIDWORKS run all at once!

Step 1: Add the Primary Load Cases

Looking at the rows, and you will see there are a couple sections: Primary Load Cases, Load Case Combinations and Track Results.

Let’s look at the first one, Primary Load Cases. The idea is to have each one of our three loads to have its own line, so that SOLIDWORKS can combine them. This is why it was important to separate the live loads earlier.

Click where it says, “Click here to add Primary Load Cases.” Then click inside one of the cells of a force to un-suppress it. Repeat for each of the load conditions. If you are following along, the table should look like this:

You’ll notice that this is the setup for three of the seven load cases.

Step 2: Define the Secondary Load Case Combinations

To get the other four cases, click where it says, “Add a load case combination.”

The idea here is that we can now use the load cases like variables and make equations for whatever we want. Click in the white space to pick the cases or see mathematical functions to put in the equation.

You can see that the window above has the two normal users condition that we described in step 1.

Hit OK and add the other equations! The table should now look like this:

Step 3: Add a Sensor for Tracking Results

With all the cases added, we can hit run if we wish. But before that, I will add a sensor to make it simple to see what the maximum Von Mises stress is for every case. Click “Add a sensor to track a result” then click “add sensor.”

The following image describes how I set the sensor up:

The only thing I changed from the standard settings was the units (I prefer my stress units to be in MPa).

Step 4: Run the Study

Finally, hit run and reap the benefits of your set up! It may take some time to complete based on model complexity, meshing, solver in use and the number of load cases.

Step 5: Consider the Results

After some time, SOLIDWORKS will bring you one tab over into the Results View. Here you can see a tabularized view of all the results:

As you can see in the first column (Stress1) it lists all of the maximum Von Mises values for all of the Load Cases we were interested in. Hopefully, this tutorial helps you save some time when running an analysis with multiple load cases.

Hopefully, this tutorial helps you save some time when running an analysis with multiple load cases.

Learn more about SOLIDWORKS in the whitepaper Designers Greatly Benefit from Simulation-Driven Product Development.

Here are a few types of buckling.

• Column buckling (Will be discussed further below)
• Snap through buckling (Will also be discussed further below)
• Flexural-torsional buckling
• Lateral-torsional buckling

While there are several different types of failure with buckling at its core, overall buckling is a failure characterized by sudden movement of the geometry of the structure in response to a compressive load. If a column is loaded axially downward, then the column’s rapid deformation to the left or right is due to buckling.

The mechanism of column buckling is caused by the fact that loading something perfectly in line with its geometric center is an impossibility. Nothing is ever perfectly straight, nothing is ever perfectly loaded and no atomic structure is ever arranged without flaws. Our world just doesn’t work that perfectly—but that is all fine provided this behavior is understood and checked for safety.

Here are some rules to determine whether buckling needs to be considered:

1. Are compressive forces present? If not, forget about it—tensile forces don’t lead to buckling.
2. Is the component long, or does it contain slender features? A column that has a small cross-section is an example of this.

For number 1, compressive forces can lead to failure through crushing as well. That isn’t the same as a buckling failure. In buckling, failure typically happens before reaching the yield stress, which makes it the governing failure mode in those cases.

The Mathematics of Buckling

In the image below is the mathematical derivation, that will hopefully provide some insight into the mechanics of buckling. The mathematics start with this assumption that no matter how well-crafted, a structural member can never be manufactured completely straight.

As a result, a compressive load is never perfectly aligned with a straight axis, meaning that any axial load creates a moment in the structural member that causes it to start bending, which increases the misalignment of the load and the center of the beam leading to an increase in the moment of the beam. It’s basically a feedback loop.

When the mathematics of buckling were first being explored by Leonhard Euler, he didn’t understand how to calculate the stiffness of the beam, but he understood it was a constant, and so he used the variable C, in order to represent the stiffness of the beam’s cross-section. The image below shows the equation he came up with as well as the column to the right that he assumed represented any column.

Euler assumed that the beam had an infinitesimally small deformation at the middle, and that its deformation was the shape of a sine curve to make the math simpler. Below is an image of the breakdown of these mathematics.

Going through the equations above, equation 1 is from general beam theory. It says the moment at any point is related to the 2^nd derivative of the displacement function multiplied by the stiffness of the beam, C in this case, and acts in the opposite direction of the displacement.

Equation 2, w(x), represents the displacement function. Euler assumed the shape of a half sine curve with a maximum amplitude of an infinitely small misalignment, ẟ. From there, he calculated the first derivative and the second derivative of the displacement function, equations 3 and 4 above.

The image on the right is the free-body diagram Euler used to plug in values into equation 1, along with the equation 4. By calculating a value for M and plugging in the second derivative of the displacement function, Euler was left with equation 5. The sine functions on both sides of the equation cancel out, as do the ẟ’s, leaving Euler with equation 6, also known as the critical buckling load calculation.

This is the pure compressive load that a member can hold before it buckles. It should be noted that n was an integer which was removed because checking values with higher order sine functions would result in a displacement shape with more “waves.” It is clear that n=1 creates the lowest critical buckling load and as a result would be the worst-case scenario, so n can be removed from the equation entirely.

It should also be noted that decades after Euler’s work was done, it was discovered that the constant C was calculated as E*I, where E is the modulus of elasticity of a material, while I is the moment of inertia of the cross-section. Euler didn’t discover this portion because his forte was mathematics, while those who experimented to learn this were scientists.

Determining If Buckling is a Governing Failure Mode

With the mathematics of buckling explained, it’s important to understand when it governs as a failure mode. As mentioned, buckling only happens under compressive loads because tensile loads would “flatten” out the sine curve. Compressive loads instead exacerbate the issue. If high compressive forces exist a system can either fail via buckling, or it can fail due to crushing—so determining which failure mode governs is critical for engineers.

If P/A > σ then crushing will happen before buckling. In this case:

• P = Compressive Load Applied (the critical buckling load can be substituted here if the actual applied loads are unknown. This would tell you which would govern, if the critical buckling load/cross sectional area is above the yield stress, material failure is going to govern the design.)
• A = Cross-sectional area of the column
• σ = Ultimate compressive stress of the material or yield stress depending on whether it is a brittle material or ductile.

In general, buckling can be prevented by using a larger cross-section or stiffer material. Whatever can be done to increase the stiffness of the cross-section, E*I will help. Additionally, it can be seen in the critical load calculation that the buckling load is inversely proportional to the length of the structural member squared, so if required, reducing the length of the structural member or bracing the member can be used to increase the critical buckling load.

Tools for Determining Buckling Loads

There are many tools available for calculating the critical buckling load, including spreadsheets, tables and FEA software. Each has its own merits and benefits:

Spreadsheets are easy; just plug in data and go. They can be cumbersome to build, or can be purchased for a nominal cost. However, they usually aren’t customizable, so if your project is slightly different, you’re out of luck.

Tables are cheap and easy to use. The most common ones provide for determining different effective lengths that modify the calculation of the critical load. One such source is the Manual of Steel Construction that many civil engineers use, as well as mechanical engineers that work on parts of larger scale. Discussion of effective lengths will be provided later in this article.

Finally, software such as SOLIDWORKS Simulation professional can be used to run a buckling study to calculate the critical load. This can be particularly beneficial when the geometry involved is that of a system acting more as a larger system in a composite action, or if it has irregular cut outs that make the stiffness change along the length of the beam. That is something that Euler’s calculation didn’t account for specifically, as it assumes the moment of inertia is constant along the length of the beam, without the cross-section changing. If the cross-section does change, it requires a numerical approach to solve efficiently and accurately.

Spreadsheets can be created by a user. Tables can be found from sources like the Manual of Steel Construction, and as mentioned Finite Element Analysis software like SOLIDWORKS Simulation Professional can be used.

Learning How to Use Simulation for Buckling Analysis

For SOLIDWORKS Simulation Professional users, there is a tutorial built right-in. Open SOLIDWORKS, make sure the simulation tool add-in is turned on, then go to Help > Tutorials > Simulation Tutorials > Simulation Professionals then look for the buckling tutorial under the Frequency and Buckling tutorials section.

This tutorial will walk you through the basics of any buckling analysis:

1. Parts definition – Materials and mesh type. The goal of this step is to tell the software the properties and how to derive the stiffness.

2. Loads. This determines what the structure is attempting to withstand.

3. Fixtures. This tells the software how the structural system is restrained from moving.

4. Meshing. This describes the shape and stiffness of the structure. This step relates to the accuracy of the analysis. If the mesh is too coarse at this step, the model results will over-predict the size of the critical buckling load—a negative trait in this case.

5. Run. Takes all the inputs and solves them.

6. Processing results, also known as post-processing. Every software is a little bit different, but in SOLIDWORKS Simulation, for example, the result provided is called a buckling load factor. It essentially tells you how much you would have to scale the loads by in order to cause buckling.

When looking at the results, buckling load factors are the factor of safety on the critical load. A buckling load factor of 3 means the applied load would have to be increased by a factor of 3 for buckling to happen. It is also possible to have negative buckling factors of safety. These mean that the system is in tension, so the load direction would have to be reversed and multiplied by that amount in order to see buckling occur.

When the buckling load factor is anywhere between 0 and 1, the design doesn’t work. In those cases, that means the software is predicting a buckling load failure.

Effective Lengths and Boundary Conditions

Like any analysis, results are dependent on your boundary conditions. The table below shows how important the boundary conditions of your simulation are. The values from these tables don’t need to be input into your simulation; the behavior is already included in the analysis.

The reason I’m including the table here is to illustrate that if you mismanage your boundary conditions, setting up your analysis with a fully fixed condition when in fact the true behavior is rotationally fixed-pinned, it’s possible to be off by a factor of 4! That’s not safe, so be certain your boundary conditions are correct in the simulation, or else use the worst-case scenario shown below.

The table below comes from the Manual of Steel Construction and is used to modify the hand calculations for different end mounting conditions, modifying the length in the critical buckling load calculation. The reasoning is that when Euler was doing his work, he was assuming both ends are pinned, so his deformation function representing half of a sine wave was correct.

However, other end conditions change this behavior. Both ends fixed “shortens” the sine function as seen in (a) in the table below, so the effective length of the column becomes half its normal length in the critical buckling load equation.

For other end conditions like (e) and (f) below, they only represent a quarter of a sine curve, as such they double the effective length in the critical buckling load calculation. The table shows you the numbers for other conditions as well.

Snap-Through Buckling

At this point, we’ve talked about column buckling and linear simulation methods that can be used to determine that behavior. However, there is also a more complex form of buckling called snap-through buckling. The most common example of this would be a Snapple cap. Taking that cap and pressing the “button” on it, it goes from bulging outward towards you to bulging away from you. That system has a “switch” and once it’s pushed to a neutral or flat position, just another small increase in force, and it “snaps through” and becomes resistant to the applied load in tension.

This is a non-linear phenomenon because it involves a significant change in the geometry as it happens. Linear analysis tools can’t predict this behavior; it must be solved iteratively, which is the realm of non-linear solvers.

Luckily, SOLIDWORKS also has a tutorial built into it for this purpose; the catch is that you need SOLIDWORKS Simulation Premium to have access to the non-linear analysis tools needed to analyze this. You can find this tutorial in SOLIDWORKS at Help > Tutorials > Simulation Tutorials Tab > Simulation Premium > “Snap through/Snap back Analysis of a cylindrical sheet”.

This is the model used in the tutorial. It is a thin sheet with a slight curvature to it. The tutorial utilizes symmetry to run a ¼ model, saving computational time. It will also walk you through the setup and running of this type of analysis.

Snap-through behaviors come from geometries that are thin sheets with curvature to begin with. Depending on the material used and the geometry, snap-through behavior may not damage a structure, as can be illustrated with the Snapple cap. It can be pressed repeatedly, however, if its purpose is to support a load and it snaps through, then this could be considered a failure.

I know far fewer rules of thumb for this sort of analysis, so it is generally only calculated using tables or FEA tools such as SOLIDWORKS Simulation Premium.

A couple questions to ask after running this sort of analysis:

1. Is there a material failure prior to this behavior? That can depend on your definition of failure. However, it could be that the yield is reached, or that ultimate failure is reached. If the yield stress is reached, the analysis needs to be re-run using a more complex material curve, like a bilinear model or a stress strain curve if linear behavior was assumed. If those were used and failure stress was reached prior to the snap-through behavior, then snap-through isn’t a governing failure mode.
2. What is the deformation that happens after the snap-through and is it acceptable to operation? If a component is attached to this, or if this behavior is represented as something like a mechanical switch, will it contact the piece it’s supposed to?

Buckling is one possible failure mode in a system that has compressive loading present. It needs to be understood and checked to make sure that designs are safe. By following the guidelines outlined above you can better analyze your designs and be more confident that they will operate as they are supposed to. While this article can’t possibly hope to cover every possible consideration for buckling, it has introduced some of the basic concepts and hopefully given you an understanding as a foundation.

Disclaimer: When designing any structural component, make sure that you are qualified to do so and have proper credentials and do proper safety checks. There are numerous factors that this article cannot possibly account for.

Learn more with the whitepaper Design Through Analysis: Simulation-Driven Design Speeds System Level Design and Transition to Manufacturing.

About the Author

Brandon Donnelly is a Technical Account Specialist with GSC. He produces a podcast for engineers called, “Stories for Engineers” that can be found on Spotify, Apple Podcasts, Stitcher and iHeartRadio. He is always available for questions or conversations about SOLIDWORKS, Simulation, 3D Printing and general engineering talk.

Engineers need to remember to perform thermal analysis on industrial equipment like the shredder pictured above. Otherwise, the equipment can overheat during use, damaging the equipment. (Image courtesy of Dassault Systèmes.)

Take an industrial shredder. At first glance, a thermal analysis might not seem necessary when designing the equipment, but any mechanical engineer worth their salt will know that when metal shreds, heat will be generated, resulting in thermal stresses on the equipment. If this heat isn’t accounted for in the design phases, then production processes can suffer from a lot of downtime while waiting for material cool-downs.

As for consumer products, they are becoming more complex, smarter and smaller. “This is a very common challenge in electronic devices,” said Lotfi Derbal, senior product portfolio manager at SOLIDWORKS. “Electronic devices have less and less space to provide airflow as they get smaller and smaller, so it is an ongoing issue that needs to be examined to keep the equipment in good health. Finding effective solutions to heat transfer problems has become an increasingly important part of new product development.”

By simulating the heat transfer of a product, engineers will be better informed through the development of the product. Prototypes are costly to work with and it is quite difficult to map out heat flux when dealing with prototypes. As a result, simulation is a much faster and affordable option when looking to optimize a product’s thermal flow.

“While designing your product, you can compare temperature distribution, heat flux and air circulation,” noted Derbal. “With this type of insight and knowledge, you will be able to analyze innovative new concepts more cost-effectively. It doesn’t matter if you’re designing high-tech electronic gadgets, consumer products, medical devices, HVAC systems or industrial heaters/coolers.”

Simulation in CAD Brings Thermal Analysis Early into the Development Cycle

A great way to bring thermal assessments into the early design cycle is to use simulation-in-CAD tools. This particular breed of computer-aided engineering (CAE) software integrates the simulation tools into the CAD environment.

Simulation in CAD democratizes the workflow by packaging it into a familiar user interface (UI). This will reduce the amount of training engineers will need as they will be using a tool that is already familiar to them. SOLIDWORKS offers a series of simulation-in-CAD tools that incorporate thermal analysis.

“With SOLIDWORKS Simulation and/or Flow Simulation, you can simulate structural thermal and fluid flow as well as coupling it with heat transfer, such as convection, conduction or radiation,” said Derbal. “Designers can apply heat sources, thermal properties on components, and define fan position. [Users also] get the resultant temperature distribution for both the fluid and the product itself.”

SOLIDWORKS Simulation and Flow Simulation have the capability to assess numerous heat transfer problems. And as it is incorporated into the CAD environment, an engineering team can save time—and often money—using the simulation-in-CAD option.

How Thermal Simulations Differ from Structural Simulations

Engineers familiar with simulation in CAD have likely spent much of their time with the structural finite element analysis (FEA) capabilities. Though much of the workflow will transfer over, thermal assessments are not as easy as modeling a structural simulation.

Natural and forced convection problems, like the ones pictured above, have heat transfer coefficients that are hard to pinpoint without computational fluid dynamic studies. (Image courtesy of Dassault Systèmes.)

Derbal explained that, “thermal analysis is not as intuitive as structural analysis because of the complexity of combining heat transfer laws like conduction, radiation and convection.”

Much of this difficulty comes from determining the convective heat transfer coefficients needed to create an accurate assessment. Engineers can make an educated guess or model the fluid flow within Flow Simulation to determine a more accurate coefficient value.

“Conduction is easy; it’s based on material properties,” explained Derbal. “But for forced or natural convection, you have to deal with known or estimated heat transfer coefficients for wall conditions as well as for emissivity and thermal resistance.”

“Using SOLIDWORKS Flow Simulation,” he added, “you may take into account the real environment. Engineers can couple the fluid flow, both internal and/or external, and heat transfer analysis. Then most of the coefficients will be calculated by the software.”

Engineers who are having difficulty setting up their thermal simulations can gain access to online learning material, such as tutorials and manuals, on MySolidWorks.

Versatility of SOLIDWORKS’ Thermal Simulation Offerings

The thermal simulation tools available in the SOLIDWORKS Simulation portfolio offer design engineers a lot of the versatility that they will need for their early development cycle assessments. However, like many other simulation-in-CAD options, an analyst might find the UI too restrictive for their advanced CAE needs.

Simulation is targeting engineering designers who are trying to give themselves direction when producing their designs early in the development cycle. It isn’t meant to be used for the advanced product verification stages.

In this respect, the simulation-in-CAD tool should be considered for its numerous thermal assessments and multiphysics simulation options such as:

• Coupling thermal and static loadings to assess thermal stresses
• Thermal contractions and expansions
• Fully coupled computational fluid dynamics (CFD) and thermal conjugate heat transfer when using Flow Simulation

“Most of thermal analysis can be simulated as steady state at least for predesign,” recommended Derbal. “However, transient thermal analysis can be necessary for strongly nonlinear and time-dependent problems, which need computer resources and large solver times.”

Performing a transient simulation will, of course, require more computational power than the steady-state analysis. This might be a lot of work for a computer optimized to work with CAD but not CAE.

To combat this, Simulation allows for a few tricks to keep the computation analysis down when working with transient simulations. Derbal suggested the following processes:

• Increase the time step if there is little risk of missing transient detail
• Use a function to govern the time step based on manual and automatic intervals
• Assess the flow field using time-averaged results

As for engineers working with heating, ventilation and air conditioning (HVAC) or electronics cooling, Derbal suggested that there are SOLIDWORKS modules with thermal analysis tools specifically tailored to these disciplines. For instance, HVAC engineers can access tools like human comfort factors, while electronics design engineers can perform Joule heating calculations that assess the heat released from a direct electrical current.

To find out more about the capabilities of SOLIDWORKS Simulation, read: SOLIDWORKS 2016 Adds Tools to Help Simulations and Validation.

About the Author

Shawn Wasserman (@ShawnWasserman) is the Internet of Things (IoT) and Simulation Editor at ENGINEERING.com. He is passionate about ensuring engineers make the right decisions when using computer-aided engineering (CAE) software and IoT development tools. Shawn has a Masters in Bio-Engineering from the University of Guelph and a BASc in Chemical Engineering from the University of Waterloo.

Today, humans live on all seven of the world’s continents and make passages across those same blue oceans, both vast and bounded. But beneath the surface of the sea lies an uncanny world yet to be explored. To be sure, in the centuries that humans have been sailing the seas we’ve discovered schools of flora and fauna that have amazed and terrified us, but the simple fact remains that much of the ocean is unexplored. In fact, the depth of human ignorance about the ocean is so great that according to the National Oceanic and Atmospheric Administration of the United States, “to date, we have explored less than five percent of the ocean.”

The Bathyscaphe Trieste, one of four crafts to reach the Mariana Trench. (Image courtesy of Wikipedia.)

But the ocean’s mysteries are slowly beginning to reveal themselves. Progress in exploring the aqueous depths is proceeding slowly, but because of modern communication and good design, the ocean is revealing itself to us evermore thanks in part to the ubiquity of cameras on our beaches and under our ocean’s waves.

Bringing Eyes to the Deep

Steve Ogles has been fascinated by making underwater exploration and documentation easier for years. In 1995, Ogles bound this fascination to a small group of engineers and started a company whose goal was to build the highest quality underwater enclosures for professional photographers and cinematographers. Named Watershot, the company began its life as what Ogles would describe as a job shop.

A Watershot underwater video camera rig. (Image courtesy of Watershot.)

“Initially, we were more of a job shop—designing, machining, and assembling waterproof enclosures for professional filmmakers,” Ogles explained. But while the short-run specialized market for underwater housings was lucrative, Steve and his team started to notice a trend.

The world of photography was changing.

People around the planet, not just professional photographers, were starting to carry around 12-megapixel cameras everywhere they went. With cameras embedded into every smartphone, photography was becoming more accessible and popular than ever. Watershot recognized that people would soon want to bring their cameras into the water to capture and share their own underwater explorations.

To start their new venture into the world of mass-market products, Watershot’s engineers turned to a design tool that they were familiar with: SOLIDWORKS. With its easy-to-use modeling tools, Watershot’s engineers were able to rapidly design new underwater housings that would fit their ideal modern camera, the iPhone. In addition, by using SOLIDWORKS’ simulation tools, Watershot’s engineers have been able to iterate through designs quickly and catch potentially costly design flaws before the expense of tooling begins to eat into the bottom line.

Take, for example, Watershot’s iPhone 4 enclosure.

The Watershot iPhone 4 underwater housing. (Image courtesy of Watershot.)

During the enclosures development, engineers using SOLIDWORKS design analysis tools began inspecting the case’s tooling. As the team began to push the case through simulated atmospheres of water, a major error was discovered. In that design, as the pressure on the case continued to mount, a warping in the enclosure forced the case to come into contact with the iPhone’s screen. Because of this unintentional “touch,” all of the phone’s functions, including taking photos or videos, were rendered useless. Because Watershot’s team was able to observe this deflection problem before tooling began, the project was able to stay on budget.

“We are a small, growing company with limited resources,” said project engineer Stephanie Griffin Peña. “SOLIDWORKS Simulation allows us to understand the influence of underwater pressure and forces during design, which saves time and money.”

Today, Watershot’s engineers have developed a wide array of underwater housing for the iPhone with the aim of bringing more and more cameras into the water so that people can document their own journeys in the ocean. Watershot is also looking to push the boundaries of high-end camera enclosures, working with the likes of camera giant ARRI to build sophisticated carbon fiber underwater rigs for large cinematic productions.

Humans aren’t built to explore alien realms. We were constructed for life here on the surface of Earth. But our curiosity has always gotten the better of us—and we’ve engineered solutions that can deliver us to our fantasies, sate our curiosity and provide for our need to capture and share what we discover.

About the Author

Kyle Maxey is a mechanical designer and writer from Austin, TX. He earned a degree in Film at Bard College and has since studied Mechanical and Architectural drafting at Austin Community College. As a designer Kyle has had vast experience with CAD software and rapid prototyping. One day he dreams of becoming a toy designer.