TABLE OF CONTENTS Computational stochastic mechanics involves the numerical solution of stochastic mechanics problems, typically by the finite element method. Since early 1980's, this field has received increasing attention and presently is an active area of research A. Der Kiureghian (1994).
Many different interpretations are possible for the terminology: stochastic finite element analysis E. Vanmarcke, M. Shinozuka, S. Nakagiri, G. I. Schu ller, and M. Grigoriu (1986).
If no parameters in the world were very large or very small, science would reduce to an exhaustive list of everything L. N. Trefethen (1998).
the older and broad subject of asymptotics seems to be losing its popularity it once enjoyed and the impact it had. This is partly because many believe that asymptotics deals with exceptional cases which are usually outside the practical domain H. K. Kuiken (2000).
In this chapter we first give a brief review of the FEM for stochastic structures. As was noted by Ghanem, the Stochastic Finite Element Method has seen a number of incarnations over the past few years . Our brief review covers several of these incarnations . We describe the asymptotic analysis, the series expansion based method, and finally its formulation via the concept of homogeneous chaos. Then, we present a new incarnation , namely the improved version of the perturbative FEM. Finally, the chapter elucidates the lessons learned from the simplest example in stochastic strength of materials in order to contrast perturbation-based FEM, improved perturbation, polynomial chaos, and the response surface methodology.
The perturbation...
