An analytical approach for structural synthesis of substructures

Abstract

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types : fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.