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Simulation of the Deflection of Thin Plates Under the Action of Random Loads

Authors:
Vitaly Lukinov

Keywords: plate bending; Monte Carlo methods; biharmonic equation, walks by spheres

Abstract:
In this work new results are obtained using constructed probability representation of the first boundary value problem for polyharmonic equation.It is shown that corresponding solution is presented by the parametric derivative of a solution to the specially constructed Dirichlet problem for Helmholtz equation. On this base new algorithms of 'random walk by spheres' for solving biharmonic equation are derived. Also, a new ``walk-on spheres'' estimates and probabilistic representation for solutions of the Helmholtz equation are constructed by analytical continuation of the resolvent in case of divergence of classical methods. The novelty of the work consists in the application the G.A. Mikhailov approach of parametric differentiation to build a scalar ``walk on spheres'' estimates. It is shown that the necessary estimates of iterations of the resolvent can be obtained by parametric differentiation of the special boundary value problem. On this approach the analytic extension of estimates for solutions and the covariance function of biharmonic equations with random right-hand side and interior Dirichlet boundary condition are constructed. The optimal parameters (number of trajectories, value determining the boundary error, the number of iterations) were obtained. The numerical results confirming the theoretical assertions are presented.

Pages: 103 to 106

Copyright: Copyright (c) IARIA, 2012

Publication date: November 18, 2012

Published in: conference

ISSN: 2308-4537

ISBN: 978-1-61208-234-9

Location: Lisbon, Portugal

Dates: from November 18, 2012 to November 23, 2012