Sandwich Shell Finite Element for Dynamic Explicit Analysis

Abstract

This work presents the finite element (FE) formulation and implementation of a higher order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement based third order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, a treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom (DOF) per node. Only C0 continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most common 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation. To assess the performance of the present shell element it is implemented in the general nonlinear explicit dynamic FE code DYNA3D. Several problems are solved and results are compared to other theoretical and numerical results. The developed sandwich shell element is much more computationally efficient for modeling sandwich shells than solid elements.