Mesh Convergence and Result Verification in Frame FEA

The problem

Most student FEA reports show a single stress plot with no evidence that the mesh is fine enough or that the setup is right. Stress singularities at sharp corners and point restraints are often reported as real failures. A careful convergence and verification study is a skill every design engineer needs.

Objectives

• Model a simple EV frame member or sub-frame with beam, shell and solid representations.
• Run mesh refinement studies and plot convergence of stress and displacement.
• Use h-adaptive and p-adaptive meshing and compare with manual refinement.
• Identify singularities and verify results with hand calculations.

What you need

Key concepts

Mesh convergence

Refining the mesh until the result of interest stops changing significantly. Displacement converges faster than stress.

Stress singularity

A point where theory predicts infinite stress, such as a sharp re-entrant corner or a point restraint. Its value keeps rising with refinement and is not a real result.

h- and p-adaptivity

h-adaptive refines element size where errors are high; p-adaptive raises the polynomial order of elements. Both aim at a target accuracy automatically.

Verification and validation

Verification checks the model solves the equations correctly, for example against hand calculations; validation checks it represents reality, usually by testing.

Step-by-step guide

1. 1

   Choose the test case

   Pick a simple but realistic part: for example an L-shaped battery bracket sub-frame made from rectangular tube, fixed at two frame mounts and carrying an example 15 kg battery with a stated vertical factor. Choose result quantities: tip displacement, bending stress at mid-span, stress at the corner joint and stress near a bolt hole. Write down a target, such as less than 5 per cent change between meshes.

   Checkpoint: A one-page test case definition with geometry, loads, fixtures and the results to track.

2. 2

   Hand-calculate the benchmark

   Treat the bracket as a cantilever or frame of beams and calculate reaction forces, bending moment, stress at mid-span and tip deflection with standard beam formulas. For the bolt hole, use a published stress concentration factor for a hole in a plate or tube. These values are the benchmark for each model, with the joint stress not available by hand.

   Checkpoint: Hand-calculated stress and deflection values, with formulas and assumptions recorded.

3. 3

   Run the beam model

   Model the bracket with Weldments and run a static study with a beam mesh. Apply fixtures at the mount joints and the battery load at its centre of mass as a force on a joint or a remote load. Compare tip deflection and mid-span stress with the hand calculation. Note that beam models cannot show stress at the joint corner or the hole.

   Checkpoint: Beam results agree with hand calculations within a few per cent for deflection and mid-span stress.

4. 4

   Run the shell model

   Create a mid-surface or surface model of the tube walls and mesh with shell elements of the correct thickness. Apply the same fixtures and loads, using split lines for load patches. Refine the shell mesh in three or four steps and track all result quantities. Compare with the beam model and hand calculations and note where shells show local effects the beam missed.

   Checkpoint: Shell convergence table for all quantities, with mid-span stress agreeing with the beam and hand values.

5. 5

   Run the solid model with manual refinement

   Mesh the solid bracket with a standard or curvature-based mesh and run at four or five global sizes, with mesh controls at the corner joint and bolt hole. Track each result quantity using Probe at fixed locations. Plot result against element size or number of nodes. Check mesh quality for elements with high aspect ratio or poor Jacobian. Use the same probe locations in every run so results are comparable.

   Checkpoint: Convergence plots for each quantity from the solid model, and mesh quality checks without badly shaped elements in key regions.

6. 6

   Find and handle singularities

   Look at the corner joint modelled with a sharp internal corner and at any point restraint. If stress keeps rising with each refinement, it is a singularity. Add a realistic fillet radius at the corner and replace point restraints with face restraints, then repeat. Show that the stress now converges. Explain how to read stresses at a distance from singular points when geometry cannot be changed.

   Checkpoint: A plot showing a diverging stress at the sharp corner and a converging stress after adding a fillet.

7. 7

   Use adaptive methods

   Enable h-adaptive meshing in the study properties with a target accuracy and a maximum number of loops, run it and record the convergence graph SOLIDWORKS produces. Repeat with p-adaptive. Compare final results and compute time with your manual refinement. Remember adaptive options work on solid meshes only. Note how many loops each method needed and whether it refined where you expected, near the corner and the hole. Adaptive meshing helps most when you do not know where the hot spots are.

   Checkpoint: h- and p-adaptive results that agree with the converged manual result within your target, with compute times recorded.

8. 8

   Check the bolt-hole stress

   Compare the converged stress at the bolt hole with the hand value from the stress concentration factor. Explain any difference, such as the tube's curvature or the load path. Check that the restraint and load are applied far enough from the hole to avoid influencing the result, following Saint-Venant's principle. Move the load patch and fixtures further from the hole in one test run and confirm the hole stress does not change. This shows the result is not affected by the boundary conditions.

   Checkpoint: Converged hole stress compared with the stress-concentration hand value, with the difference explained.

9. 9

   Write a verification report

   Summarise each model's results against the hand values in one table, with convergence plots and the compute time for each method. Write a short guide for your classmates: which model to use for what, how to check convergence, how to spot singularities and when adaptive meshing helps. State that validation still needs a physical test, such as a strain gauge on a real bracket.

   Checkpoint: A report with a summary table, convergence plots and a practical guide others can follow.

Testing & validation

• Beam and shell results agree with hand calculations.
• Convergence shown for every tracked quantity.
• Singularities identified and handled.
• Adaptive results agree with manual refinement.

Expected results

A documented verification study showing how beam, shell and solid models compare, how to achieve mesh convergence, how to recognise singularities and when adaptive meshing helps, with a short practical guide.

Take it further

• Validate the converged result with a strain gauge test on a real bracket.
• Repeat the study for a frequency analysis.
• Compare linear and quadratic (draft and high-quality) elements.

Viva and review questions

Learn it at DIYguru

These DIYguru courses and programmes teach what this project needs.