Solving the Convergence Gap: Optimizing Mesh Density in Ansys Mechanical

The Problem: When Your Results Keep Moving

In structural Finite Element Analysis (FEA), a common frustration is the "shifting result." You run a simulation, get a maximum stress value, refine the mesh to be more accurate, and suddenly the stress jumps by 15%. This indicates that your initial mesh was too coarse to capture the physics of the part, and your results were not yet converged.

The takeaway is simple: a single simulation result is an estimate, not a fact. To trust a value in Ansys Mechanical, you must demonstrate mesh convergence—the point where further refining the mesh no longer significantly changes the output.

Targeted Refinement vs. Global Sizing

The instinct for many engineers is to lower the global element size. While this ensures accuracy, it creates a computational bottleneck. Doubling the resolution in three dimensions increases the element count by a factor of eight, which can lead to excessive RAM usage or solver crashes without providing meaningful gains in most of the model.

A more efficient strategy is Local Refinement. By using the 'Sizing' tool in Ansys Mechanical, you can apply a dense mesh only where high stress gradients occur—such as fillets, holes, or contact interfaces—while keeping the rest of the geometry coarse. This minimizes the total degrees of freedom (DOF) while maintaining accuracy where it matters most.

Linear vs. Quadratic Elements

The choice of element order drastically affects how quickly a model converges. Linear elements (first-order) have nodes only at the corners. In bending applications, these elements suffer from shear locking, where they appear artificially stiff, leading to underestimated displacements.

Quadratic elements (second-order) include mid-side nodes, allowing the element edges to curve. These are far superior for capturing stress gradients and typically reach convergence with a much coarser mesh than linear elements. For most structural components in Ansys, quadratic elements are the default and recommended choice.

Worked Example: Convergence Study for a Cantilever Beam

To verify convergence, follow this systematic approach using a simple cantilever beam with a known analytical solution.

Setup and Execution

1. Baseline (Coarse): Set a global element size that provides roughly 2 elements across the thickness of the beam. Run the solver and record the maximum Von Mises stress.
2. Iterative Refinement (Medium): Apply a Local Sizing control to the fixed support area and the loading point, reducing the element size by 50%. Run the solver and record the new stress.
3. Final Pass (Fine): Further reduce the local sizing by another 50%. Record the result.

Diagnostic Decision Table

In this example, the change between Medium and Fine is only 1.2%. Since this falls below a typical engineering threshold (usually < 5%), the result is considered converged.

The Trap of the Stress Singularity

It is critical to distinguish between a lack of convergence and a stress singularity. A singularity occurs at sharp internal corners with a zero radius. Because the theoretical stress at a perfectly sharp corner is infinite, Ansys will continue to show increasing stress values every time you refine the mesh. The result will never asymptote.

If you observe stress increasing linearly with mesh density without ever leveling off, check your geometry for sharp corners. The solution is to either add a realistic fillet radius or ignore the stress at that specific node and look at the stress in the surrounding bulk material.

Verification and Limits

To verify your results, plot the target value (e.g., Max Stress) on the Y-axis and the number of elements on the X-axis. You are looking for an asymptotic curve that flattens out. If the curve is still climbing steeply, your results are unreliable.

Rollback: If a refined mesh causes the solver to crash due to memory limits, delete the local sizing controls or increase the element size of the non-critical regions to free up RAM.