Real structures show often randomly distributed properties over space and time domain. These structures are investigated by engineering models, whose variables and parameters possess random behavior. Uncertain parameters may catch irregular excitations, e.g. wind or earthquake excitations, system imperfections or the lack of information about the system as well as material properties and variations of structural or material behavior. Computing engineering problems stochastic models are used to investigate the randomness of parameters and thus responses of engineering structures.
Example: Plate with hole considering scattering material behavior
The material behavior, here presented by a tensile test, is described by means of a mathematical model and attached material-dependent model parameters. The scattering material behavior can be realized by fluctuating sets of model parameters related to certain material classes. The pictures show the different stress-strain-results of a tensile test controlled by a strain rate of 10^-3 [1/sec] for different material classes and the dependence of the stochastic parameters rupture strain and coefficient of variation on the strain rate.
The FE-analysis investigates the plate either deterministically by a Monte-Carlo-method or by stochastic FE-methods. The evaluation considers the probability density function of the results.
For the investigated plate with hole, the probability density function of the material behavior is transferred to the structure by introducing a random field, which is determined by the Karhunen-Loeve-method before.
The influence of scattering material behavior on the results of structural analyses is investigated, as an example, for the stochastic parameter correlation length.