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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
Recommended
text books
