78 5. WISDOM IS DOING IT
1. Point loads are idealized load applications and will generally result in unreasonably large
internal stresses in the vicinity of the application point. One should consider applying lo-
calized pressures when possible.
2. Usually, when concentrated loads are applied the stresses resulting from statically equivalent
loads will be independent of the method of application a distance away from the load that
is of the order of the transverse dimensions of the structure locally. is is the principle of
St. Venant. It should be employed liberally in application of the finite element method and
in interpreting its results.
3. In an analogous manner as with prescribing boundary constraints, when one models do-
mains in two or three dimensions, element formulations may not have rotational degrees
of freedom. For such cases, application of a concentrated moment or couple is no longer
unique and not as straightforward as it is when using one-dimensional elements. In such
cases, one should consider experimenting with different possible prescriptions of the cou-
ple using local point loads and compare stresses a St. Venant’s decay distance away from the
concentrated moment.
4. Generally, the order of complexity of the solution to boundary value problems will increase
with the order of the loading. Given a specific finite element formulation, the more complex
the loading, the more approximate the solution. is was illustrated in the beam example
of Fig. 5.1. Such one-dimensional beam elements capture bending stress and shear forces
exactly when only point loads and couples are applied. ese same bending stresses and
shear forces are only approximately predicted when distributed or more complex loading is
applied.
5.3 POST-PROCESSING
Computer graphics has achieved such a level of polish
and versatility as to inspire great trust in the underlying
analysis, a trust that may be unwarranted. (One can now
make mistakes with more confidence than ever before.)
R.D. Cook, D.S. Malkus, and M.E. Plesha
Concepts and Applications of Finite Element Analysis,
3rd Edition
ere are several rules of thumb to consider when post-processing results.
1. Plotting deformed shapes of structures is a good way to spot particular errors in application
of boundary constraints.
2. Element stresses are most accurate at internal integration points where they are calculated.
ese stresses are averaged at nodes shared by elements. e nodal-averaged stresses are
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