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

Based on the polynomial series expansion of kinematic 0elds throughout the thickness of a plate, hierarchical models are constructed by selected truncations. The models are formulated with the threedimensional second Piola–Kirchho? stress and Green–Lagrange strain at large deformation. The adaptivity of the models in the framework of 0nite element method is devised for not only the compatible combination of the elements of di?erent 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 0eld by 0xing a set of common active hierarchical expansion degrees of freedom for each node, which may be shared by the elements of di?erent 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 e?ects 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 illustratetheadvantageof this new strategy