Stochastic Strain-Displacement Matrices for Finite Elements with Random Constitutionby Gautam Dasgupta, Columbia Univ, United States,
Shui-cheung Yip, Columbia Univ, United States,
Abstract: A prescribed correlated random field for elastic moduli furnishes an associated population of stochastic shape functions at the element level. The principle of deterministic tractions, which is a consequence of flux invariance from the renormalization scheme for equilibrium, is to be employed. For bars and beams it is shown here that a distinct set of shape functions could be computed from a given spatial realization of the stochastic Young's modulus. The balance of momentum principle is not ignored within a finite element. The novelty of this paper is to present the development of the stochastic finite element stiffness matrices on the basis of the underlying random field that represents the correlation structure in the spatial variation for the constitutive properties. The cardinal aspect of the finite element approximation via the selection of a set of appropriate (local) Ritz functions of stochastic nature is addressed herein.
Subject Headings: Stochastic processes | Finite element method | Elasticity | Matrix (mathematics) | Beams | Constitutive relations | Structural behavior | Strain
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