On a formulation of a nonlinear theory of plates and shells with applications

Abstract

A nonlinear theory of plates and shells based on only one consistent kinematical approximation is employed to investigate finite strain and large deformation structural problems. The kinematics, expanded with respect to the thickness parameter, include consistently and adequately higher-order terms to allow fibers initially straight to deform nonlinearly in the large deformation range. A full Lagrangean formulation is considered. Starting from a three-dimensional principle of virtual work, the equilibrium equations and the resultant stresses of the shell together with their incremental form are derived employing an incremental constitutive relation valid for a wide class of rate-independent material. And, to assess the accuracy of the theory adopted, some boundary value problems are solved using a proposed hyperelastic material to model the constitutive behavior of a semi-infinite plate. The analytical and numerical (finite element method) results show good agreements between the exact and the approximate theories.