On Stochastic Finite Element Analysis Of Bar Structures

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.