Mesh quality is a key consideration in finite element analysis, particularly when evaluating localized stresses near geometric discontinuities. To support this evaluation, FEA software commonly provides quantitative mesh quality metrics that help engineers assess element shape, distortion, and whether the selected mesh density and distribution are appropriate for the geometry being analyzed.
Many modern analysis tools include a Mesh Quality Report as part of their tabular output. This type of report presents mesh quality results on a per-region basis and typically focuses on two primary metrics: Aspect Ratio and Jacobian Ratio. In the December release of Paulin Research Group software, this reporting capability is available through the standard tabular output.
The Mesh Quality Report is available through the tabular reports but is not printed by default. To include it, the corresponding checkbox in the ASME/EN Panel within each program must be selected.
The report summarizes mesh quality on a per-region basis, consistent with how shell-element results are organized for stress categorization in accordance with ASME Section VIII, Division 2, Part 5 (Design by Analysis).
The model below shows a NozzlePRO model with the default mesh density for a cylinder-on-cylinder intersection. NozzlePRO is a standalone, template-based pressure vessel and piping analysis tool that uses shell-element finite element analysis to evaluate local stresses at nozzle intersections aligned with applicable design-by-analysis requirements.
In this model, the meshing algorithm places a higher density of elements near the discontinuity i.e. the critical regions, where the highest stresses are expected.
Below is a sample report after analyzing the model.
In shell-element finite element models, results are commonly organized into regions to support stress evaluation and categorization, particularly when assessing localized behavior near geometric discontinuities.
Not all regions are equally important from a meshing standpoint. Regions near discontinuities, where higher stresses and steeper stress gradients are expected, require more careful meshing than regions farther away. The PRG meshing algorithm accounts for this by placing a higher density of elements in critical regions and allowing larger elements in non-critical areas.
The Aspect Ratio is calculated by dividing the largest side length of a quadrilateral element by the smallest side length. The highest aspect ratio within each region is reported.
An aspect ratio of 1.0 represents a perfectly square element. While this is ideal, a commonly accepted guideline is that aspect ratios up to 5.0 are reasonable for shell elements.
PRG software will display a warning when the aspect ratio exceeds 5, but only in critical regions. In regions away from discontinuities, the aspect ratio can exceed 5, as the meshing algorithm focuses on the most important region, where the high stress is located.
The Jacobian Ratio is determined by evaluating the determinant of the Jacobian matrix at all integration points within an element and dividing the minimum value by the maximum value. The smallest Jacobian ratio within each region is reported.
This metric indicates how skewed or distorted an element is. A Jacobian ratio of 1.0 represents a perfect element. A commonly used guideline is that the Jacobian ratio should be greater than 0.5.
If the Jacobian ratio falls below 0.5 in a critical region, PRG software displays a warning. Lower values may occur in non-critical regions where larger elements are used and are not necessarily a concern.
For both aspect ratio and Jacobian ratio, the report identifies the element number associated with the worst value in each region. This allows the user to locate and inspect specific elements if further review is required.
In the example model using the default mesh density for a cylinder-on-cylinder intersection, the results show a smooth transition of stress from element to element. This indicates that the mesh density used is appropriate for the geometry.
Different geometries impose different mesh requirements in different regions. Because PRG software is template-based, it accounts for the expected geometry and automatically places additional elements in regions where higher stresses are anticipated.
Mesh quality metrics such as aspect ratio and Jacobian ratio provide a structured way to evaluate element quality, particularly in critical regions near discontinuities. When reviewed alongside stress results, these metrics help confirm that the selected mesh density is appropriate for the analysis.
For engineers looking to apply FEA to pressure components using geometry-aware, code-aligned workflows, PRG software integrates these mesh quality checks directly into its analysis templates.
Request a personalized demo with our FEA experts to see how PRG solutions can be applied to your specific analysis requirements.