Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

Author(s)

Silva, C. R. A. ^[1] ; Azikri de Heusi, H. P. ^[1] ; Mantovani, G. E. ; Beck, A. T. ^[2]

Affiliation

^[1] Fed Technol Univ Parana, Acad Dept Mech, PPGEM UTFPR PPGMNE UFPR, Curitiba, Parana - Brazil

^[2] Univ Sao Paulo, Dept Struct Engn, Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES; v. 67, n. 2, p. 119-149, OCT 2010.
• Web of Science Citations: 7

Abstract

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering. (AU)

• FAPESP's process: 08/10366-4 - Claudio Roberto Ávila da Silva Junior | Universidade Tecnológica Federal do Paraná - campus Curitiba - Brazil
• Grantee: André Teófilo Beck
• Support type: Research Grants - Visiting Researcher Grant - Brazil