Efficient finite element analysis using graph-theoretical force method with brick elements

In this paper an efficient method is presented for the analysis of finite element models (FEMs) composed of brick elements. In the present method, special graphs are associated with the considered FEM and minimal subgraphs are selected using these graph models. Localized self-equilibrating systems are constructed on these subgraphs, forming a suitable statical basis of the FEM. This basis corresponds to highly sparse and banded flexibility matrix. Finally the applicability and the efficiency of the present method are illustrated through some examples.

► A new brick element is developed for the analysis of finite element models by the force method.
► Utilizing special graphs, minimal subgraphs are selected to form suitable statical bases.
► Localized self-equilibrating systems are constructed to form highly sparse and banded flexibility matrices.