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Modern finite element analysis achieves accurate results with little effort

Dr Jody Muelaner

Simulating stress in thin-walled structures (Credit: Shutterstock)
Simulating stress in thin-walled structures (Credit: Shutterstock)

Getting reliable results from a finite element analysis (FEA) can be very time consuming. Structural analysis often involves thin-walled structures which may be simulated using shell elements.

This usually means creating surfaces from the solid bodies of the CAD part files. If there are thicker regions, thin plates meeting to form Ts or radii at the joints, a mixed mesh may be required. Creating a mixed mesh means cutting out the sections to be meshed as shells, creating the surfaces and then managing contact sets when the solid and shell elements are connected. This is all time consuming.

For someone without a stress analysis background it can be tempting to simply use the automatic solid mesh. This requires little pre-processing, perhaps just removing some small features. With modern meshing algorithms and FEA solvers the increased computing time won’t be an issue for many parts. Saving two minutes of solver time can hardly justify spending hours or days creating a robust mixed mesh. 

Unreliable results

However, the results from a solid mesh of a thin-walled part may not be reliable. Conventional wisdom says that several solid elements are required through the thickness of bodies to give reliable results. If the mesh is fine enough to achieve this for a thin-walled part it may result in a very long solution time.

The requirement for multiple solid elements through the thickness of a body really only applies to first-order elements. These are elements that only have nodes at their vertices and which interpolate stress and strain linearly between them. 

Modern FEA software doesn’t generally use first-order elements. Second-order elements are now the standard. These have mid-side nodes and interpolate stress and strain using a first-order polynomial. Using second-order elements very good results can be obtained using a single element through the thickness of thin-walled structures. Aspect ratios of two or three are also often acceptable, meaning that for a 1mm wall thickness a mesh size of 2-3 mm is often acceptable.

The accuracy of higher-order elements for thin shells can be demonstrated by modelling a simple plate, with elastic supports at each end and a uniform load inducing bending. 

When first-order solid elements are used there are significant errors. However, when a single layer of second-order solid elements is used the results are almost identical to when there are four elements through the thickness or shell elements are used. Good results are still seen for second-order solid elements as the aspect ratio starts to increase so that there was a single element through the thickness but its in plane dimensions were two to three times larger than the plate thickness. Shell elements only show significantly improved accuracy for coarse meshes with elements much larger than the plate thickness. 

By comparison, first-order solid elements are far less accurate, even when there are four elements through the plate thickness.

Complex geometry

Similar results can be obtained for more complex shell geometry. The size of elements in relation to the radius of tightly curved features is of far more importance, highlighting the value of curvature-based meshing algorithms which automatically reduce element size in these areas. 

Using second-order solid elements, one can ignore the conventional advice that shell elements should be used unless a solid mesh is able to achieve several elements through the wall thickness. This means that the time-consuming task of preparing geometry for shell meshing can now normally be avoided. The combination of higher-order solid elements together with automated curvature-based meshing allows modern FEA software to often achieve accurate results with little effort. 

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Content published by Professional Engineering does not necessarily represent the views of the Institution of Mechanical Engineers.


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