Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis

Abstract

AbstractA new computational tool, referred to as the polynomial correlated function expansion (PCFE), has been developed for predicting response statistics of nonlinear stochastic dynamic problems. This method facilitates a systematic mapping between the input and output by expressing the output as a ranked order of component functions, with higher-order component functions representing higher-order cooperative effects. The component functions are expressed in terms of extended bases, and the unknown coefficients associated with the basis are determined by using a homotopy algorithm. This algorithm considers the hierarchical orthogonality of the component functions as a constraint and determines the coefficients associated with the basis. Implementation of the proposed approach for nonlinear stochastic dynamic problems has been demonstrated with three numerical problems. Results obtained certify the accuracy of the proposed method. Furthermore, the proposed approach significantly reduces the number of cal...