Hierarchic plate and shell models based on p-extension

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.