Solutions of Materially Nonlinear Analysis Obtained by Strain Combinations Control

摘要

This paper discusses the determination of the equilibrium paths in the nonlinear finite element structural analysis. A brief study about the incremental-iterative procedures, that use load and displacement combinations as the analysis controlling parameters, is presented. The limitations of the classical methods in materially nonlinear problems are discussed. A method, that includes the mechanics of the material deterioration process, using strain combinations in subdomains of the problem, is proposed. The combinations are strain measures such as mean, invariants, eigenvalues, among others. The subdomains are characterised as groups of integration points, once in the Finite Element Method, normally, the strains are obtained in these points. Such groups can be chosen as the whole finite element mesh, one or more finite elements or just one integration point. The proposed method permits the change of the control subdomain (one integration point or one finite element) during the analysis process. This change is based on the search for region that sampled the biggest increase on the standing control combination in the last incremental step.The computational implementation details of the proposed model into a object oriented finite element program is discussed.Some numerical simulations of materially nonlinear problems are presented. The analysis of the obtained results permits to discuss the adequacy of the classical and proposed methods in the solution of the problems.