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On Stochastic Finite Element Analysis of Bar structures

Abstract

The Finite Element Analysis of structures is one of the most powerful and well known methods to determine the displacements, member forces and member stresses or strains. The external loads and properties of members are generally assumed deterministic, meaning that the variation of loads are not random in time or the member properties are of constant values over time. In this paper, the analysis will be discussed on bars structures with stochastic loads and/or with random member properties. The random member properties are input with its mean values and its standard deviation (or variances) values. A simple perturbation technique is applied to develop the stochastic finite element analysis of bars and beams with applied external random loads and member properties. The resulting random displacement solution of the analysis is written also in terms of the displacement mean and variance values. Hence, member forces, stresses and strains can be computed from the computed random displacements. One bar example is used to apply the discussed stochastic analysis with a given random load or a given member random property.

Introduction

In dealing with real world problems, uncertainties are unavoidable1. It is well known that most engineering material properties, external applied loads on structures, and hence, the material point displacements, material element stresses or strains are not deterministic at all. In reality, these quantities are all random in nature, and some of them are more random than others. But it is easy to assume these quantities as deterministic to make our analyses simple and determination of these material property values as the mean statistical mean of the physical tests. The central variation of these quantities is ignored in the mechanical analysis of structures while computing material point displacements or material element stresses or strain. One usually wonders whether such a deterministic analysis is satisfactory in terms of reliable and safe. The engineers doing such deterministic analysis rely on the standards for safety in terms of the allowable stresses.

The sources of uncertainty may be classified into two broad types1: (1) Those that are associated with natural randomness, also known as ‘aleatory’ type of randomness, and (2) those that are associated with inaccuracies in prediction and

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Narayanan, G. (2010, June), On Stochastic Finite Element Analysis Of Bar Structures Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--16992