Large displacements of shells including material nonlinearities

Abstract

The paper presents a finite element formulation of shells with large deflections including elastoplastic material behaviour. The elements utilized are the so-called degenerated shell elements, with special emphasis on the simple 4 node quadrilateral. Both the total Lagrangian and the updated Lagrangian formulation are considered. For the treatment of plastic behaviour the concept of a layered element model is proposed and investigated for both the tangential modulus method and the initial load method. In the final section sample problems are presented and compared with reference solutions. It is shown that the 4 node element is very well-suited to the class of problems under consideration. It is characterized by an easy applicability, high accuracy and low rates of computer time. In Appendix A an analytical solution of a cantilever beam, subjected to an end load, including geometrical and material nonlinearities is presented.