# 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 .

 Cable-like structures 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.

 Beam-column connections

## 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.

 Pounding of structures