A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

• FE physical and geometrical nonlinear analysis of plates and shells by a solid-shell-like formulation.
• Strain enhancement for continuous transverse stress distribution for laminated plates and shells.
• Generalized vectors for shell and plates large rotation description.
• Alternative failure surface and plastic flow determination for orthotropic plasticity.
• Orthotropic hardening depending on orthotropic directions.

In this work, we propose a new enhancement strategy that can be applied to the calculated strain field in the analyses of shells by the unconstrained-vector finite element approach, a Solid-Shell-like formulation. This new enhancement is proposed to satisfy the continuity of the shear and normal stresses fields in the transverse direction. The kinematic enhancement is based on the in-plane longitudinal stress equilibrium that is associated with maintaining the elastic strain energy potential in the transverse direction of the shell or plate. No additional degrees of freedom are introduced, and a coherent continuous stress distribution is achieved from the enhanced strain field. Moreover, in contrast to typical elastoplastic procedures, we propose an alternative plastic flow rule, which includes a new concept of the hardening parameter that depends on the orthotropic directions of the material and a general failure surface that degenerates into the von-Mises or Drucker−Prager criteria for isotropic materials. The resulting alternative position-based finite element and the enhanced field strategies are tested for elastic and elastoplastic situations by comparing the results with other solutions and known benchmarks.