doi:10.3850/978-981-08-7619-7_P026

ABSTRACT

In this paper a collocation approach is used for determining the statistics of the response of structures operating under deterministic excitation and having random material properties. In this context, a mesh free approach is adopted utilizing the multi-quadrics collocation method. In this method, nodes are distributed inside the domain at the points of interest and the multi-quadrics radial basis functions are used to approximate the displacements of the domain at the nodes. Values from the field are treated at each point as correlated random variables, and thus the random field is sampled at the collocation points. This approach yields a set of linear equations involving a random matrix. Unlike the Galerkin and FE methods, the random matrix representing the stiffness can be represented as the product of a stochastic diagonal matrix with a full deterministic matrix. If the random variables on the diagonal are correlated, a polynomial chaos expansion is used for the random field, and the Neumann expansion is used for the approximation of the stochastic matrix inverse. Obviously, all the matrices involved in the standard Neumann series expansion are diagonal; thus the computational cost of the procedure is reduced significantly. Specific numerical examples are given and they are supplemented by pertinent Monte Carlo simulation data.

Keywords: Element free multi quadrics, Stochastic meshless, Radial basis functions (RBF), Elastostatics, Polynomial chaos expansion.

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