Contribution to Nonlinear Finite Element Analysis of Structures with Emphasis on Buckling and Post-Buckling Problems

Summary

The present paper is devoted to finite element analysis of structures based on the equations of nonlinear elasticity theory. In this framework the emphasis in the following article will be on the analysis of the stability and post-buckling behaviour of trusses, beams, and shells. Our starting point was a variant of the NONSAP-code (see Bathe,Ramm and Wilson [1]) which we have modified and extended in order to make it capable of calculating stability problems and tracing highly nonlinear load-deflection curves also in the deep post-buckling region. This is achieved by introducing a displacement control method which we have developed following partly the works of Ramm [2], Waszczyszyn [3], and Stricklin a.o. [4]. Automatic change from load control to displacement control method and vice versa allows limit points to be passed. This control method is realized in the framework of standard or modified Newton-Raphson method. We shall present here results for some typical highly nonlinear truss, beam and shell problems and compare them with those given in literature e.g. by Papadrakakis [5], Paradiso, Reale and Tempesta [6], and Sabir and Lock [7]. One of our main interests in carrying out the present research work was to develop a method which is able to yield reference solutions for checking the validity of several novel finite rotation beam and shell theories (see [8] for a review) without using explicitly beam and shell theory as such. For lack of space the numerical examples concerning the latter aspect of the present work, which have been obtained with the approach described below, will be given in [9]. Further numerical studies related to those given here will be presented in [10].