A new method for the solution of problems involving material variability is proposed. The material property is modeled as a stochastic process. The method makes use of a convergent orthogonal expansion of the process. The solution process is viewed as an element in the Hilbert space of random functions, in which a sequence of projection operators is identified as the polynomial chaos of consecutive orders. Thus, the solution process is represented by its projections onto the spaces spanned by these polynomials. The proposed method involves a mathematical formulation which is a natural extension of the deterministic finite element concept to the space of random functions. A beam problem and a plate problem are investigated using the new method. The corresponding results are found in good agreement with those obtained through a Monte-Carlo simulation solution of the problems.
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March 1990
Research Papers
Polynomial Chaos in Stochastic Finite Elements
Roger Ghanem,
Roger Ghanem
Department of Civil Engineering, Rice University, Houston, TX 77251-1892
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P. D. Spanos
P. D. Spanos
Rice University, Houston, TX 77251-1892
Search for other works by this author on:
Roger Ghanem
Department of Civil Engineering, Rice University, Houston, TX 77251-1892
P. D. Spanos
Rice University, Houston, TX 77251-1892
J. Appl. Mech. Mar 1990, 57(1): 197-202 (6 pages)
Published Online: March 1, 1990
Article history
Received:
October 10, 1988
Revised:
May 2, 1989
Online:
March 31, 2008
Citation
Ghanem, R., and Spanos, P. D. (March 1, 1990). "Polynomial Chaos in Stochastic Finite Elements." ASME. J. Appl. Mech. March 1990; 57(1): 197–202. https://doi.org/10.1115/1.2888303
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