An efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach

Abstract

For geometrically and physically nonlinear analyses of shell structures a computational model employing a Reissner-Mindlin type kinematic assumption, a layered finite element approach and a closest-point projection return mapping algorithm, completely formulated in tensor notation is presented. As a result of a consistent linearization, a tangent modulus is derived, expressed also in tensor components. The applied constitutive model includes a von Mises yield criterion and linear isotropic as well as kinematic hardening. All stress deviator components are employed in the formulation. The material model is implemented into a four-noded isoparametric assumed strain finite element, which permits the simulation of geometric nonlinear responses considering finite rotations. The proposed numerical concept is unconditionally stable and allows large time steps, as the numerical examples illustrate. Further, the numerical simulations demonstrate the expected quadratic convergence in a global iterative technique.