Self-adaptive predictor-corrector algorithms for static nonlinear structural analysis

Abstract

This paper develops a multi phase self-adaptive predictor corrector type algorithm to enable the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as potential pre/postbuckling behavior. The hierarchy of the strategy is such that three main phases are involved. The first features the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive INR type iterations. The second corrector phase uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior. The third involves the use of quality of convergence checks which enable various self-adaptive modifications of the algorithmic structure when necessary. Such restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels so as to improve the convergence process. Included in the paper are several numerical experiments which illustrate the capabilities of the procedure to handle varying types of nonlinear structural behavior.