Post-collapse analysis of plates and shells based on a rigid–plastic version of the TRIC element

Abstract

The knowledge of the post-collapse response of structures is required in several situations. Typical examples are shells used as energy absorbers or bumpers, which must be able to undergo large plastic deformations by dissipating a sufficient amount of energy. The procedure known as sequential limit analysis can be employed to this purpose. The evolution of the structure after collapse is tracked by a sequence of rigid–plastic limit analyses, with the structural geometry progressively updated on the basis of the collapse mechanism computed in the previous step. A number of methods have been developed, mostly in recent years, for the finite element solution of the limit analysis problem. In this paper, a procedure proposed by one of the authors is employed, which a rather extensive computational experience proved reliable, stable and accurate. The procedure demands that the finite element be formulated on the basis of the natural approach, which suggests the use of a simple but well performing triangular shell element, named TRIC, recently developed within this framework by Argyris and co-workers. The formulation has to be modified to some extent to adapt to the rigid–plastic context, but the quality of the element performances is maintained. Some computations, referring to plates and shells, are presented, which assess that the “marriage” between the TRIC element and sequential limit analysis is successful.