ABSTRACT

Formulation of the Variable-Element Topology Finite Element Method for prob­ lems in solid mechanics is described. The method differs from conventional finite element methods in that the shape functions are generated without recourse to an isoparametric (or similar) mapping. Instead, optimized polynomial shape func­ tions are defined on arbitrary polygonal elements. Restrictions relating to element geometry and number and arrangement of nodes are thereby circumvented. The task of automatic mesh generation is a significantly less complex one for the new method than it is for the conventional F E M . Aspects of convergence are discussed for the new method, which is nonconforming in general. Computational results are presented that illustrate the performance of the method in the setting of planar elas­ ticity.