Achieving Mesh Independence in Ansys Mechanical: A Convergence Guide

The Problem: Numerical Uncertainty in FEA

In Finite Element Analysis (FEA), the accuracy of your results depends on the density of the mesh. If your mesh is too coarse, the software cannot capture steep gradients in stress or strain, leading to underestimated peak values. However, simply making the mesh as fine as possible is inefficient and can lead to hardware crashes. The goal is mesh independence: the point where further refining the mesh produces negligible changes in the result.

The takeaway is to identify a specific target value (such as maximum von Mises stress) and refine the mesh iteratively until the relative change between iterations falls below a threshold—typically 1% to 5%.

The Mechanism of a Convergence Study

A convergence study involves creating a series of models with progressively smaller element sizes and plotting the resulting value against the total number of elements. When the plot levels off (asymptotic behavior), the solution is considered converged.

Worked Configuration: Localized Refinement

Refining the entire model is computationally expensive. A more efficient approach uses Sizing controls to refine only the areas of interest, such as fillets or contact zones, while keeping the rest of the geometry coarse.

Setup Example:

1. Baseline Mesh: Set a Global Element Size of 10mm. Solve and record the maximum von Mises stress at the critical region.
2. Local Sizing: Right-click Mesh → Insert → Sizing. Select the face or edge of the critical region. Set the element size to 5mm. Solve and record the result.
3. Refined Sizing: Change the Local Sizing to 2.5mm. Solve and record the result.

To verify convergence, use the following calculation for the relative change between the last two iterations:

Relative Change (%) = |(Result_n - Result_n-1) / Result_n| * 100

If the result changes from 250 MPa to 254 MPa, the change is approximately 1.5%, indicating the model has likely reached mesh independence.

Critical Limitations and Common Pitfalls

The Singularity Trap

A common mistake is attempting to converge a stress singularity. This occurs at sharp internal corners or point loads where the theoretical stress is infinite. In these areas, the stress value will continue to increase linearly as the mesh is refined, and the convergence plot will never level off. To fix this, add a realistic fillet (radius) to the geometry or ignore the peak stress at that specific point in favor of an average stress over a small area.

Topology Inconsistency

You must maintain the same element type throughout the study. If you start with Tetrahedrons (four-node pyramids) and switch to Hexahedrons (six-sided bricks) to improve accuracy, the previous data points on your convergence plot become invalid. The mathematical error associated with different element shapes varies, meaning you are no longer measuring the effect of size, but the effect of element formulation.

Computational Exhaustion

Over-refining a large assembly can lead to memory exhaustion (RAM). If the solver fails due to memory, use Inflation layers on boundaries to capture gradients without filling the entire volume with tiny elements.

Verification and Result Check

To verify that your final mesh is truly independent, perform a final "sanity check" by reducing the element size in the critical region by another 50%. If the result changes by less than 1%, the mesh is verified.

Checklist for Final Validation:

• Confirm that the element shape quality (Aspect Ratio) remains acceptable in refined zones.
• Ensure that the convergence is based on a physical value (e.g., Displacement or Stress) rather than a global average.
• Verify that the mesh density is sufficient to capture the curvature of the geometry (at least 3 elements across a fillet).