Hierarchical model adaptivity in finite element analysis for non-linear plate problems

Based on the polynomial series expansion of kinematic fields throughout the thickness of a plate, hierarchical models are constructed by selected truncations. The models are formulated with the three-dimensional second Piola-Kirchhoff stress and Green-Lagrange strain at large deformation. The adaptivity of the models in the framework of finite element method is devised for not only the compatible combination of the elements of different models but also the evolution of the models in an element when the function of its interested property changes during analysis procedures. The key idea in the method is to meet the continuity requirement of the primary displacement field by fixing a set of common active hierarchical expansion degrees of freedom for each node, which may be shared by the elements of different models. The von Mises criterion is used here to describe material plasticity. Unilateral contact phenomena are examined on the upper and/or lower surfaces of the plates by using a penalty method. Friction effects are taken into account with a regularized Coulomb law. Examples on the numerical simulation of sheet metal forming and the analysis of a cracked plate are included to illustrate the advantage of this new strategy. Copyright (C) 2001 John Wiley Sons, Ltd.