Stochastic Finite Element Methods in Dynamics

by M. Shinozuka, Columbia Univ, New York, NY, USA,
G. Dasgupta, Columbia Univ, New York, NY, USA,



Document Type: Proceeding Paper

Part of: Dynamic Response of Structures

Abstract:

This paper develops a stochastic finite element solution method utilizing a Neumann expansion of the operator matrix involved and at the same time, devises an efficient Monte Carlo method consistent with the solution method. These analytical and Monte Carlo methods both utilize the successive nature of approximation. The methods demand inversion of the 'average' operator matrix only once, achieve successive improvements of the solution by means of a stationary operator, and require no evaluation of the partial derivatives of the operator matrix. The generic system deviator formulation, which is analogous to that of a static case, is illustrated in order to avoid lengthy algebraic expressions. The computational steps for natural extension to steady-state and transient response analyses are then indicated.

Subject Headings: Finite element method | Stochastic processes | Approximation methods | Monte Carlo method | Matrix (mathematics) | Mathematics | Transient response

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