Linear finite elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling

Abstract

The dynamic explicit finite element method is commonly used in earthquake ground motion modeling. In this method, the element mass matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal mass matrix and can be applied to dynamic explicit finite element analysis. In this paper, we propose finite elements based on orthogonal discontinuous basis functions, the element mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4-node tetrahedral and 8-node hexahedral elements. The relationship between the proposed finite elements and conventional finite elements is investigated, and the solutions obtained from the conventional explicit finite element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three-dimensional crust structure. Copyright © 2010 John Wiley & Sons, Ltd.