A curved axisymmetric shell element for nonlinear dynamic elastoplastic problems—I. Formulation

Abstract

A numerical procedure based on a curved C 1 shell element is developed for the solution of nonlinear dynamic problems of elastoplastic axisymmetric shells of revolution and of cylindrical bending of plates or beams. The element development is based on approximations to the strain rate and angular velocity distributions in the element. Some additional features of the procedure include: Time-dependent thickness changes, linearly varying normal stress distribution in the thickness direction, inclusion of transverse shear and normal stresses in the yield envelope and the adaptation of Krieg's radial return method to the resulting mixed constitutive equations. The procedure is useful especially for solving problems associated with short-duration large-deformation elastic and inelastic responses to intense impulsive loads. In this paper, the theoretical background, element development and constitutive relations are presented and discussed. Problems associated with implementation, as well as some nontrivial examples are presented in Part II of the paper.