Static reanalysis of discrete elastic structures with reflexive inverse

Abstract

This paper presents a direct method for the static reanalysis of structures. We use the concept of the reflexive inverse in the sense of Moore–Penrose generalized inverse to express a general solution of discrete systems without any boundary condition. We use a simple decomposition of the stiffness matrix to avoid its inversion. We give a comparison of the processing time of this method with the duration of a complete analysis with finite elements. The reanalysis of the stiffness is based on the mixed conditions linking displacements and related efforts. In the second part we concentrate on this reanalysis and we give as an application the reanalysis of the geometry and the reanalysis for mesh refining. This method is general, enabling the reanalysis of structures with variation of the boundary conditions in loading and displacement. It also enables reanalysis of the structural stiffness and makes it possible to add or remove structural elements. It can easily be applied to the study of nonlinear behavior (case of damaging, plasticity, nonlinear elasticity…).