Finite Element Method for Stochastic Beams Based on Variational Principles

[+] Author and Article Information
Y.-J. Ren, I. Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Glades Road 777 Boca Raton, FL 33431-0991

M. Shinozuka

Department of Civil Engineering, University of Southern California, University Park, Los Angeles, CA 90089-0242

J. Appl. Mech 64(3), 664-669 (Sep 01, 1997) (6 pages) doi:10.1115/1.2788944 History: Received May 25, 1995; Revised September 30, 1996; Online October 25, 2007


This paper proposes a new version (fundamentally different from the existing ones) of finite element method for the mean and covariance functions of the displacement for bending beams with spatially random stiffness. Apart from the conventional finite element method for stochastic problems, which utilizes either perturbation or series expansion technique or the Monte Carlo simulation, the present method is based on the newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covariance function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution function of the random stiffness to obtain the covariance function of the displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in contrast to conventional technique. Several examples are given to illustrate the advantage of the proposed method, compared with the conventional ones.

Copyright © 1997 by The American Society of Mechanical Engineers
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