For me, it took four years to earn an engineering degree. But that is just step one on a long journey. Most professionals like me spend a lifetime learning engineering concepts and applying them throughout their careers; especially as you start to go beyond the basic and general concepts to the more specialized areas like Structural Simulation and Finite Element Analysis (FEA).
Personally, I dedicated a large part of my engineering career exclusively to thoroughly understanding FEA technology as best I could. I can say from that experience it’s easy to believe that as an engineer we’ve forgotten more than we could ever remember.
In this article, I want to continue to discuss engineering concepts as I reintroduce you to some of the biggest forgotten secrets of simulation. By the end, you will be able to go from theoretical to practical and effectively set up FEA studies using SOLIDWORKS Simulation.
1. Stress
Stress quantifies how a material responds to forces. It measures the intensity of a force on an object. It’s not unlike how we humans experience and respond to stress. External forces or pressures can cause changes to us just like to materials. It’s best to think about this on the microscopic level as the actual atoms move around (react) when acted on by an external force. The simplest definition of stress is shown in the equation below which describes how stress is related to a force acting on it.
Stress is often measured in PSI or Pascals. From an engineering perspective, stress could be used to determine if something will hold up or break. Consider a bar made of steel and chocolate – it’s easy to break the chocolate bar with your hands but nearly impossible (unless you’re Superman) to break a steel bar the same way. This is an example of how different levels of stress cause different things to break — low stress breaks chocolate while steel can hold up to higher stresses.
Components of Stress in 3D Space. (Image: Wikimedia Commons, Sanpaz.)
2. Strain
Strain quantifies how a material’s shape changes when it’s stressed. This is basically doing a comparison of the initial shape (unstressed) to the change in shape when loaded (stressed). It’s a unitless value that can be thought of as a percentage of change in shape. The simple equation for this is shown below.
3. Hooke’s law (Robert Hooke)
Hooke’s law is a core concept for simulation because it introduces us to the concept of “elasticity” which states that the deformation of an elastic material is proportional to the applied force — within the elastic limit for the material (more on this later).
The simple equation for Hooke’s law is shown above, which relates force to material stiffness (k) and its displacement (x). It essentially shows the proportionality of a force to displacement – the greater the force the more the shape will change or deform. In engineering context, Hooke’s law is written as shown below where most importantly the stiffness value (k) is written as E which is the Young’s modulus.
4. Young’s modulus (Thomas Young)
Young’s modulus is another core concept for simulation. It is a material property which describes how stress and strain are related for a particular material. Young’s modulus (E), sometimes known as the modulus of elasticity, is shown below in its simplest form:
This characterizes the “stiffness” of a material where a higher value means a stiffer/stronger material and a lower value means a more flexible material. A few sample values are shown below notice how much stronger steel and aluminum are than something like wood.
| Material | Modulus of elasticity (GPa) |
| Steel, Structural ASTM-A36 | 200 |
| Aluminum | 69 |
| Duglas fir wood | 13 |
5. The stress – strain curve
The stress-strain curve is a plot that defines a material’s journey through loading. Think of it like a road map which defines how a material will perform. It’s built upon the above concepts. This graph is an essential piece to understanding how a material will behave and ultimately how much force (stress) it can withstand before it breaks. As an engineer or designer, you’ll want to stay well below the Yield Strength (except for some exceptions).
An example stress-strain curve. (Image: Stephen Petrock.)
As shown above, there are distinct regions of the curve which are important to understand. Most important for SOLIDWORKS Simulation is the understanding of the linear and nonlinear (plastic) regions of the stress strain curve.
6. Linear versus nonlinear and elastic versus inelastic
This is a good point in the article to begin discussing the capabilities of SOLIDWORKS Simulation and how they relate to the physics within a model. The linear region of the stress strain curve can be thought of as the zone of simple analysis with “small displacements.” It represents stresses below the yield point of a material. This is where any changes in shape are not permanent. The material will change shape (strain), but it will return to its original shape when it’s unloaded. The term for this is elastic deformation. For these models you can use SOLIDWORKS Simulation Standard.
However, anything beyond the yield point can be thought of as nonlinear. This is where the more advanced SOLIDWORKS Simulation Premium must be used. If a material is stressed to this region, it will not return to its original shape when its unloaded. This is known as permanent deformation. Think of when you significantly bend a paper clip it doesn’t return to its original shape. Another term for this is inelastic deformation.
7. Linear v nonlinear in SOLIDWORKS Simulation
Here is a pro tip when using SOLIDWORKS Simulation Standard for linear static analysis. The “large displacement” option can be used to get a pseudo nonlinear answer without the nonlinear price. If you’ve used SOLIDWORKS Simulation, you’ve probably seen this message.
This option uses an iterative solver to gradually apply the load and recalculate the geometric stiffness of the model. This accounts for geometric nonlinearities but not the material nonlinearities if the material goes beyond the Yield Point.
8. Hand calculation examples
So how does this all come together to solve an engineering problem? Let’s answer that with an example that looks at the question: can our part withstand a given loading? Note that for the purposes of this article, we are going to solve this in the same order as SOLIDWORKS Simulation using the four equations shown above which are stiffness, change in shape and then stress. The simplified version of this FEA problem is illustrated below.
Problem Statement: Consider a steel rod 1 foot in length with a diameter of ¼”. Can it hold a load of 2,250 pounds?
Step 0: Convert units & look up material properties.
The very first thing we do is convert to metric because it’s easier in the engineering world. So here are our converted inputs.
- Length L = 1 foot = 0.3048 m
- Diameter D = ¼” = 0.00635 m
- Force = F = 2,250 lb = 10,000 N
- Material Properties of Steel
- Young’s Modulus (E) of 200 GPa (from SOLIDWORKS Material Library)
- Yield Strength of 350 MPa (from SOLIDWORKS Material Library)
Step 1: Determine the stiffness of this scenario.
Starting with Hooke’s Law, we can rearrange to calculate the stiffness (K):
Leverage the equations for stress and strain.
Substitute into Hooke’s Law and leverage the stress strain relationship.
Rearrange the equation to match Hooke’s Law.
Thus,
Step 2: Calculate the change in shape (solve for ∆L).
Step 3: Calculate the stress from the change of shape (strain).
Final step: Ensure the safety factor is greater than 1.
Conclusion: The design will “hold up” (more on this below).
9. Factor of safety
The final step in the above calculation introduced the concept of a factor of safety. With the factor of safety we can determine if the design will “hold up” by comparing the stress to the material limits. This is usually defined as:
By applying this safety factor equation, you’ll ensure that your design stays in the elastic region and therefore no permanent deformations occur.
10. Finite Element Analysis (FEA)
SOLIDWORKS Simulation is a finite element analysis (FEA) tool. FEA is the technique to solve these engineering problems by breaking it down into small pieces, solving each piece, and then putting it all together to give you a complete result. The engineering problem is your model with the loadings. The small pieces are known as elements. A typical problem will have thousands of elements and there could be 30 equations per element. In other words, SOLIDWORKS Simulation does what we just did for the example problem but nearly a million times in a matter of seconds! That’s the power of a tool like SOLIDWORKS Simulation.