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    Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

    C. R. A. Silva1, H. P. Azikri de Deus1, G.E. Mantovani2, A.T. Beck3

    CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.2, pp. 119-150, 2010, DOI:10.3970/cmes.2010.067.119

    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… More >

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