Stochastic Finite Elements
The finite element method (FEM) has become the dominant computational method in structural engineering. In general, the input parameters in the standard FEM assume deterministic values. In earthquake engineering, at least the excitation is often random. However, considerable uncertainties might be involved not only in the excitation of a structure but also in its material and geometric properties. A rational treatment of these uncertainties needs a mathematical concept similar to that underlying the standard FEM. Thus, FEM as a numerical method for solving boundary value problems has to be extended to stochastic boundary value problems. The extension of the FEM to stochastic boundary value problems is called stochastic finite element method (SFEM).
The first developments of the SFEM can be traced back at least to Cornell (1970), who studied soil settlement problems, and to Shinozuka (Astill et al. 1972), who combined FEM with Monte Carlo simulation for reliability...
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