Journal of Mechanical Science and Technology

, Volume 31, Issue 4, pp 1813–1824

# Stochastic analysis of thin plates on elastic foundation by combining the generalized polynomial chaos and element free Galerkin method

Article

## Abstract

Uncertainties associated with a physical system are of great importance as they cause the system response to behave randomly. Plated structures exhibit considerable variation in mechanical properties, material density and dimensions due to inadequate control in the manufacturing processes. In this paper, the element free Galerkin method is combined with the generalized polynomial chaos to quantify the uncertainties in the bending analysis of thin plates on a Pasternak elastic foundation with random system properties. The uncertainties in plate and foundation stiffnesses are represented using a truncated Karhunen-Loeve expansion. The applicability of the presented method is demonstrated by solving numerical examples for various combinations of boundary conditions, different types of lateral loading, various values of aspect ratio and different values of coefficient of variation and foundation parameters. Further, by comparing the results of the present method with the results of the Monte Carlo simulations, a very good agreement is obtained.

### Keywords

Generalized polynomial chaos Karhunen-Loeveexpansion Pasternak elastic foundation Stochastic bending analysis Thin plates

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© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2017

## Authors and Affiliations

1. 1.Department of Maritime EngineeringAmirkabir University of TechnologyTehranIran