Extended GDQ and related discrete element analysis methods for transient analyses of continuum mechanics problems

The extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of a continuum mechanics problem. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve a generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the DQEM, FEM, FDM, etc.