Application of the Monte Carlo λ-Neumann Method to the Euler-Bernoulli Stochastic Beam Flexural Problem
Roberto Mauro Felix Squarcio1; Claudio Roberto Ávila da Silva Junior1
1 Technical Federal University of Paraná
doi:10.20906/CPS/CILAMCE2017-0533
Resumo
The technological evolution witnessed during the recent decades presents amazing results regarding the reliability of structural systems. Structures are complex most of the time and their functionality eventually depends heavily on the ability to predict their performance. Sometimes it happens even in conditions not fully controlled. The problem of quantifying the uncertainty due to from the spatial variability of the mechanical properties of the materials of structural systems has aroused the interest of science in engineering. In this case, the Monte Carlo simulation technique is widely used to evaluate and validate new methods for uncertainty quantification. Recently, the Neumann series has been used, associatively, with the Monte Carlo's simulation method to obtain estimates of the statistical moments and probability distributions of the solution stochastic process, [2] - [4]. Therefore, the Monte Carlo λ-Neumann method was presented to the engineering scientific community [1], for the quantification of the uncertainty of the problem of diffusion-stochastic reaction. This method consists of the imposition of an λ parameter and using the properties of the Neumann series to reduce the computational time, with some intrusiveness. The present work proposes to apply the Monte Carlo λ-Neumann method to quantify the uncertainty in the stochastic bending problem of Euler-Bernoulli beams. In this case the uncertainty is associated with the material and geometric properties of the beam being modeled by parametrized stochastic processes. References [1] Ávila S. Jr., C. R. and Beck, A.T.; "A Fast Convergence Parameter for Monte Carlo - Neumann Solution of Linear Stochastic Systems"; ASCE-ASME.; Journal Risk and Uncert. In Engrg. Sys., Part B: Mech. Engrg, vl., pp. 1-9; 2015 (JUNE). [2] Shinozuka, M.; Deodatis, G.; "Response Variability of Stochastic Finite Element Systems"; Technical Report, Dept. of Civil Engineering, Columbia University, New York; 1986. [3] Yamazaki, F.; "Simulation of Stoch
Palavras-chave: Finite Elements; Galerkin's Method; Monte Carlo Simulation Method; Neumann Series; Uncertainty Quantification; Monte Carlo λ-Neumann