Stability of rectangular Kirchhoff plates using the Stochastic Boundary Element Methods

Abstract

The main objective in this work is to study an application of the Stochastic Boundary Element Methods implemented due to three different probabilistic approaches to analyze stability of the rectangular thin elastic and isotropic plates. This is completed with the use of polynomial approximations applied for the Least Squares Method recovery of critical forces resulting from some material and geometrical random imperfections in the plate, e.g. Young's modulus, Poisson's ratio, thickness. A deterministic core for solving the plate stability problem is the Boundary Element Method in direct approach and modified formulation of the boundary and domain integral equations. Probabilistic approaches employed here include traditional Monte-Carlo simulation, the semi-analytical approach as well as the iterative generalized stochastic perturbation method. Stochastic response in the form of up to the fourth order characteristics are studied numerically in addition to the input uncertainty level.