Sandwich shell finite element for dynamic explicit analysis

The contribution of this paper consists of new development of transverse shear stresses through the thickness and nding an expression for the critical time step for explicit time integration of layered shells. This work presents the nite 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 di erential equilibrium equations and the interlayer requirements, special treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. 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 non-linear explicit dynamic FE code DYNA3D. Several problems are solved and results are presented and compared to other theoretical and numerical results