Standard shape function method for finite element formulation

Abstract

A simple method to generate element matrices for various sets of shape functions is presented. A standard set of shape functions is first chosen to establish standard element matrices and the actual shape functions are related to the standard ones through function evaluations. Then, the actual element matrices are obtained by transforming the standard element matrices. The computation requires simple matrix multiplications and shape function evaluation only. The method is very suitable for microcomputers that it drastically reduces the core requirement and very large element library can be included without difficulty. The element matrices are also formulated readily in a way to explore the advantage of parallel computation.