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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

Academic Department of Mechanics, Federal Technological University of Paraná / PPGEM-UTFPR / PPGMNE-UFPR, Curitiba, PR, Brazil.
Federal Technological University of Parana, Curitiba, Brazil.
Department of Structural Engineering, University of Sao Paulo, Sao Carlos, SP, Brazil.

Computer Modeling in Engineering & Sciences 2010, 67(2), 119-150.


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.


Cite This Article

APA Style
Silva, C.R.A., Deus, H.P.A.D., Mantovani, G., Beck, A. (2010). Galerkin solution of stochastic beam bending on winkler foundations. Computer Modeling in Engineering & Sciences, 67(2), 119-150.
Vancouver Style
Silva CRA, Deus HPAD, Mantovani G, Beck A. Galerkin solution of stochastic beam bending on winkler foundations. Comput Model Eng Sci. 2010;67(2):119-150
IEEE Style
C.R.A. Silva, H.P.A.D. Deus, G. Mantovani, and A. Beck "Galerkin Solution of Stochastic Beam Bending on Winkler Foundations," Comput. Model. Eng. Sci., vol. 67, no. 2, pp. 119-150. 2010.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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