Errors in FEA - simplification

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Engineering | Finite Element Analysis | Stress

Value Design

Consulting

For the same mesh density (same number of elements), parabolic elements provide better results because they represent the a model’s curved boundaries more accurately, as well as producing better mathematical formulations (see formulation error above). However, parabolic elements require much greater computational resources than linear elements (usually takes about double the time to solve a parabolic element mesh than it does to solve a linear element mesh of the same problem, with the same mesh density being employed).

Solution accuracy depends primarily on how well the assumed variation of stress within an element fits the actual variation of stress within an element fits the actual variation in a structure. Linear pyramid (tetrahedral) elements often provide inaccurate results, especially for bending type problems. However, accuracy can be improved dramatically by choosing parabolic elements instead.

Well shaped linear brick (hexahedral) elements can provide accurate results. The elements perform at their best as regular prisms (cubes). Automatic hex (brick) meshers meshing complicated geometry, however will introduce distorted or transitional elements in unexpected zones, thus considerably affecting the accuracy of the results. Parabolic pyramid elements provide results at least as accurate as linear brick elements and are less sensitive to distortion to poor orientation in the model.

Both 20 noded brick and 10 noded pyramid elements provide good stress results for reasonable meshes with a comparable number of nodes, while 8 noded bricks and 4 noded pyramids require many more elements for solids with curved boundaries to achieve the same geometrical and stress accuracy.

Over Simplification.

Often the suppression of small details is a good way of reducing the time to solution. However, there are times when small details should not be removed. If a small detail is located directly on the load path within a structure, then it may have a considerable effect on the stress results. Details should be included in cases where their removal would cause a considerable reduction in the neutral axis of bending. The shorter the neutral axis, the stiffer the structure.