Structural Nonlinearities
Major sources of structural nonlinearities encountered in practical
applications are as follows:
Geometric Nonlinearities
In nonlinear finite element analysis, a major source of nonlinearities
is due to the effect of large displacements on the overall geometric configuration
of structures. Structures undergoing large displacements can have significant
changes in their geometry due to load-induced deformations which can cause
the structure to respond nonlinearily in a stiffening and/or a softening
manner.
For example, cable-like structures
generally display a stiffening behavior on increasing the applied loads
while arches may first experience softening followed by stiffening, a
behavior widely-known as the snap-through
buckling.
Material Nonlinearities
Another important source of nonlinearities stems from the nonlinear
relationship between the stress and strain which has been recognized in
several structural behaviors. Several factors can cause the material behavior
to be nonlinear. The dependency of the material stress-strain relation
on the load history (as in plasticity problems), load duration (as in
creep analysis), and temperature (as in thermo-plasticity) are some of
these factors.
This class of nonlinearities, known as material nonlinearities, can
be idealized to simulate such effects which are pertinent to different
applications through the use of constitutive relations.
Yielding of beam-column connections
during earthquakes is one of the applications in which material nonlinearities
are plausible.
Contact Nonlinearities
A special class of nonlinear problems is concerned with the changing
nature of the boundary conditions of the structures involved in the analysis
during motion. This situation is encountered in the analysis of contact
problems.
Pounding of structures,
gear-tooth contacts, fitting problems, threaded connections, and impact
bodies are several examples requiring the evaluation of the contact boundaries.
The evaluation of contact boundaries (nodes, lines, or surfaces) can be
achieved by using gap (contact) elements between nodes on the adjacent
boundaries.