Hybridized dual-mixed hp-finite element model for shells of revolution

Abstract

A locking-free hp-version finite element is presented for linear elasticity problems of thin shells of revolution. The constructed hp-finite element is based on a hybridized dual-mixed variational formulation. The related theoretical model does not rely on the standard hypotheses used in the Naghdi- and Koiter shell theories, thus the unmodified three-dimensional constitutive equation can be applied. Nevertheless, since employing its inverse form, the hp-shell finite element is incompressibility locking-free. Besides, neither the thickness variation nor the membrane stress normal to the shell mid-surface is not eliminated from the shell formulation, thus it can be extended to much complicated (contact) problems of more complex (composite), extremely thin and moderately thick shell structures. The new hp-shell finite element is tested through some representative mixed and pure boundary value problems, namely bending- and membrane dominated situations, for singly and doubly curved shells of negative and positive Gaussian curvature. From the convergence behavior of the relative errors it follows that the developed hp-version shell finite element is insensitive to the decrease of the thickness value, i.e., membrane and shear locking-free, providing excellent numerical results not only for the displacement- but also for the stresses computations.