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Mesh refinement: what are the considerations?

Consideration should always be given to the mesh refinement to avoid the following pitfalls:

a)  Mesh too coarse.  Using a small number of elements may produce stress results which are significantly different from the stresses in the "real" structure.  Moreover, a coarse mesh may produce results which are unconservative for design purposes.

b) Mesh too fine. Beyond a certain level of refinement, the accuracy of the results does not improve significantly.  Using a more refined mesh will increase the time taken to carry out the solution and the engineer's subsequent post processing time. It may increase the PC burden to such a degree that hardware resource problems are encountered when attempting to solve the model or display results graphically.

To take a simple example, the bending moment along a beam under a trapezoidal load varies as a particular curve.  To use a finite element that assumes a linear variation of bending moment would mean that a large  number of such elements would be required to mimic that curve with sufficient accuracy for the results to be acceptable for use in a design calculation. Using an element that assumes a quadratic variation will produce acceptable results with less elements.  

This example demonstrates the importance of mesh refinement (irrespective of the element type being used) and of interpolation order.  

Checking the mesh refinement in a model is an essential part of any FE analysis.  By nature, all FE analysis is an approximation, a "model" of a real (or potentially real) object.  The results will only be accurate if the mesh is defined in such a way as to simulate the change in load effects across the structure effectively.

How to check mesh refinement in a model

How to control mesh refinement

Element aspect ratio considerations

Converging to an "exact" solution

Finite element equilibrium

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