Hand Calculations and FEA for Component Validation

1. The 'Why': Verification Before Validation

In your engineering studies and work, you've likely heard the phrase "Garbage in, Garbage out" applied to simulations. Finite Element Analysis (FEA) is an incredibly powerful tool, but it's only as reliable as the inputs and assumptions you provide. A real-world engineer never blindly trusts a colorful stress plot. They first verify their simulation against known principles.

This process is formally known as Verification and Validation (V&V).

• Verification: "Am I solving the equations right?" This involves checking that your computational model (the FEA setup) accurately reflects your mathematical model (the hand calculations).
• Validation: "Am I solving the right equations?" This involves comparing the simulation results to real-world experimental data.

For this lesson, we will focus on verification—using hand calculations to ensure our FEA setup is giving us a sensible answer.

The following article from XCEED Engineering provides an excellent overview of this professional practice.

As the article demonstrates with the beam bending example, the goal is to create a simplified mathematical model that approximates the behavior of your component. You can then compare its results to the more detailed FEA. If the results are in the same ballpark, you can have much higher confidence in your simulation.

2. Identifying Critical Components and Performing Hand Calculations

Your first task is to examine the 3D assembly you created and identify a critical component. This is a part that is essential for the mechanism's function and is likely to experience significant stress or deflection. It might be a long bracket, a lever arm, or a pin carrying a heavy load.

Once you've chosen a component, the next step is to simplify its geometry and loading conditions to make a hand calculation feasible. For example, a complex mounting bracket might be simplified to a cantilever beam.

Given your mechanical engineering background, you are already familiar with the fundamental stress equation: $\sigma =F/A$. However, real parts have holes, fillets, and changes in cross-section that create stress concentrations. These are localized areas where stress is significantly higher than the nominal calculation would suggest.

A more refined hand calculation accounts for these using a stress concentration factor, K. The video below demonstrates this process, comparing the simple F/A approach to a K-factor calculation and an FEA result.

Your Task: Part 1 - Hand Calculation (10 minutes)

1. Identify: Look at your project assembly and choose one critical component to analyze.
2. Simplify: Sketch a free-body diagram (FBD) of the component. Simplify its geometry (e.g., as a beam, plate, etc.) and define the loads and boundary conditions you expect it to see.
3. Calculate: Perform a hand calculation for the maximum stress.
   • Start with a simple formula (e.g., bending stress $\sigma =My/I$ or axial stress $\sigma =F/A$).
   • If there are significant geometric discontinuities (holes, sharp corners), try to estimate a stress concentration factor (K) from a standard engineering textbook or online resource and calculate the peak stress ${\sigma }_{max}=K\cdot {\sigma }_{nominal}$.

3. Performing FEA in Onshape

Now that you have a theoretical estimate, you can use Onshape's built-in simulation tools to analyze the component's true, complex geometry. Onshape Simulation is designed to be an intuitive part of the design workflow. It leverages the mates in your assembly to automatically understand how parts are connected.

The official Onshape documentation provides a step-by-step guide to setting up a basic study.

Your Task: Part 2 - Onshape FEA (15 minutes)

Return to your Onshape assembly and follow these steps to set up your analysis on the component you chose.

1. Isolate the Analysis: While you can run simulations on full assemblies, it's often easier to start with a single part or small sub-assembly. Ensure your critical part is in an assembly tab.
2. Fix a Reference: Use a Fastened mate to fix a part of your assembly to the origin, or right-click a part and select Fix. This provides the "ground" that your loads will react against.
3. Assign Materials: Open the Bill of Materials (BOM) table or right-click the part in the Part Studio and assign a realistic material (e.g., "Steel 1020," "Aluminum 6061"). The material's yield strength is crucial for calculating the safety factor.
4. Apply Loads: From the assembly toolbar, select a load type (e.g., Force). Apply the load to your critical part with the same magnitude and direction you used in your hand calculation.
5. Run and Interpret: Open the Simulation panel on the right. Check that your connections are correct and click Show results.
   • Start by viewing the Displacement plot and animating it. Does the part deform in the way you expect? This is a fundamental sanity check.
   • Switch to the von Mises stress plot. Where is the area of maximum stress? Does it align with where you predicted?
   • Note the maximum stress value from the color bar legend.

4. Comparing Results: The Moment of Truth

You now have two numbers for the maximum stress: one from your hand calculation and one from the FEA. The final step is to compare them. Don't expect them to be identical! The hand calculation is an approximation, while the FEA accounts for the full geometry. However, they should be in the same order of magnitude.

• Qualitative Check: Does the location of max stress in the FEA match your intuition and FBD?
• Quantitative Check: Calculate the percent difference: (|FEA_Stress - Hand_Calc_Stress| / Hand_Calc_Stress) * 100%. A difference of 5-20% is often considered good for initial verification, but this can vary.
• Explain Discrepancies: If there's a large difference, why? Did your hand calculation neglect a significant stress riser that the FEA captured? Is the mesh in that area too coarse in the FEA? (As seen in the SolidWorks video, a finer mesh can be needed for sharp corners). This critical thinking is what separates a technician from an engineer.

Conclusion

Congratulations on completing a full verification loop! This is a process you will repeat countless times in your career. By grounding your advanced simulation work in fundamental engineering principles, you build robust, reliable products and demonstrate a high level of professional diligence.

Key Takeaways:

• Verification is essential: Always perform a "sanity check" on FEA results using hand calculations to avoid the "Garbage in, Garbage out" pitfall.
• Simplify for hand calculations: Abstracting complex geometry into simpler models (like beams) is a key skill for performing quick, effective analysis.
• Onshape's FEA workflow is integrated: Use the tools to apply loads, fix components, and visualize results like displacement, von Mises stress, and factor of safety.
• Compare and interpret: The goal is not to get identical numbers, but to confirm that both methods tell a similar story and to be able to explain any differences.

Preview of the Next Lesson:
We have now analyzed the strength of a critical component. Next, we will analyze its fit. We will shift our focus from stress to geometry and learn how to conduct a tolerance stack-up analysis for a critical assembly interface, ensuring that your design can be manufactured and assembled reliably.