Engineering | Finite Element Analysis | Stress
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The best way of ensuring that your mesh is sufficiently refined is to plot the results with node & element averaging switched off. A problem will materialise in the form of a discontinuity (or step) of the solution parameter between elements (the contours will be stepped across the element boundary rather than smooth as they should be).
The analyst should be aware of derivative type solutions. In a displacement analysis, the stress is obtained by differentiating the displacement results. Therefore, if the element is parabolic, then a linear variation of stress will be obtained. It is important that this is kept in mind when defining the mesh density & grade. Remember that derivatives always require more elements to converge. Heat flux in thermal analyses are also derivative based results. The image shows how displacement & stress results converge to the correct solution.
Formulation Error.
Formulation error results from the use of elements that don't precisely describe
the behaviour of the physical problem. Elements which are used to model physical
problems that they are not suited, are sometimes referred to as ill-conditioned or
mathematically unsuitable elements for the problem in hand.
For example a particular
finite element might be formulated on the assumption that displacements vary in a
linear manner over the domain. Such an element will produce no formulation error
when it is used to model linearly varying physical problem (linear varying displacement
field in this example), but would create a significant formulation error if it used
to represent a parabolicly or cubically or logarithmically varying displacement field.
Formulation error can be reduced by selecting the proper element type and mesh.
Numerical Errors.
Numerical error occurs as a result of calculation procedures and round off errors. Therefore, this problem mainly concerns the FE developer.
Errors in FEA - formulation
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