5.4. FURTHER RULES TO LIVE BY IN PRACTICE 79
interpolated between nodes, contoured, and then, generally, artificially smoothed to create
contoured results.
3. When displaying stress contours, it is often good practice to contour element values directly
as well as the nodally averaged values. is is a good practice because:
(a) If the element stresses are observably discontinuous to the eye, then the stress gradients
are larger than the mesh is capable of predicting and one should refine the mesh.
(b) If the element stresses are not overly discontinuous, then the smoothed contours are
sufficient to represent the overall character of the solution.
5.4 FURTHER RULES TO LIVE BY IN PRACTICE
One can establish a set of ground rules that can serve as a starting point for good practical finite
element analysis. Again, this list, while not exhaustive, attempts to address several of the most
common errors made in applying the finite element method.
1. Use the finite element method only when it is necessary, i. e., when the simplest formulae
outlined in Chapter 2 or other analytical methods are not generally applicable.
2. ere are no units involved in formulation of the finite element method. An analyst must
always use dimensionally consistent units and interpret results accordingly.
3. e finite element discretization results in a model that is too stiff, implying:
(a) models upon which only displacement boundary conditions are applied will, in general,
result in stresses that are higher than the actual stresses;
(b) models upon which only force boundary conditions are applied will, in general, result
in displacements that are smaller than the actual displacements; and
(c) no general conclusions can be made once the boundary constraints are mixed, which
is most often the case.
4. One should not generally assume that finite element analysis is conservative.
5. It is not necessarily true that three-dimensional analysis outperforms two-dimensional anal-
ysis or that two-dimensional analysis outperforms one-dimensional analysis.
6. One should consider mesh refinements in regions where there are large gradients in material
stiffness such as dissimilar material interfaces or large discontinuities in load-bearing areas.
7. Consider applying the principle of St. Venant in order to avoid modeling geometric fea-
tures wherein the stress results are not of primary importance, e. g., details at or near load
application points.
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