Numerical Examples

Abstract

The methods introduced in sections (3.3.5) and (3.3.6) are exemplified in this chapter by considering three problems reflecting some interesting applications from engineering mechanics. These problems involve a beam with random rigidity, a plate with random rigidity, and a beam resting on a random elastic foundation and subjected to a random dynamic excitation. In addressing these problems, it is reminded that the ultimate goal of a stochastic finite element analysis is the calculation of certain statistics of the response process. These statistics can be in the form of either statistical moments, or probability distribution function, or some other measure of the reliability of the system. As a first step in the solution procedure, the variational formulation of the finite element method is used to obtain a spatially discrete form of the problem. Following that, the Neumann expansion for the inverse, as given by equation (3.46), and the Polynomial Chaos expansion, as given by equation (3.81), are used to derive a representation of the response process. Statistical moments and probability distribution functions are then obtained as discussed in Chapter IV.