Isogeometric Collocation Method for Random Field Discretization Based on Adaptive Moment Abscissae

Abstract

The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters. The essential step of discretization is solving the Fredholm integral equation to obtain the eigenvalues and eigenfunctions of the covariance functions of the random fields. The collocation method, which has fewer integral operations, is more efficient in accomplishing the task than the time-consuming Galerkin method, and it is more suitable for engineering applications with complex geometries and a large number of elements. With the help of isogeometric analysis that preserves accurate geometry in analysis, the isogeometric collocation method can efficiently achieve the results with sufficient accuracy. An adaptive moment abscissa is proposed to calculate the coordinates of the collocation points to further improve the accuracy of the collocation method. The adaptive moment abscissae led to more accurate results than the classical Greville abscissae when using the moment parameter optimized with intelligent algorithms. Numerical and engineering examples illustrate the advantages of the proposed isogeometric collocation method based on the adaptive moment abscissae over existing methods in terms of accuracy and efficiency.