New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs' approach

Author Type

Faculty

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Computer Methods in Applied Mechanics and Engineering

Publication Status

Version of Record

Abstract

This paper proposes an alternative way of constructing the global stiffness matrix of the finite element method for bending beams, it also applies the new formulation to first and second moment analysis of stochastic beams, which involve spatially uncertain bending stiffness. Originating from Fuchs' idea of decoupling the shear and bending components in the bending beam, the element level stiffness matrix is diagonalized. The generalized stress-strain, strain-displacement and equilibrium relationships are assembled, respectively, and then are combined to form the global stiffness matrix. The advantage of the new formulation is that the bending stiffness explicitly appears in the global stiffness matrix. The mean vector and covariance matrix of the displacement of the beam are then obtained in terms of probabilistic characteristics of the uncertain bending stiffness. This is in contrast to the conventional finite element method in stochastic setting, which is based on the perturbation technique. The example is given to illustrate the efficacy of the new formulation and its application to bending of stochastic beams.

First Page

235

Last Page

243

DOI

10.1016/S0045-7825(96)01173-5

Publication Date

1-1-1997

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