Publications
Critical time step for a bilinear laminated composite Mindlin shell element
The critical time step needed for explicit time integration of laminated shell finite element models is presented. Each layer is restricted to be orthotropic when viewed from a properly oriented material coordinate system. Mindlin shell theory is used in determining the laminated response that includes the effects of transverse shear. The effects of the membrane-bending coupling matrix from the laminate material model are included. Such a coupling matrix arises even in the case of non-symmetric lay-ups of differing isotropic layers. Single point integration is assumed to be used in determining a uniform strain response from the element. Using a technique based upon one from the literature, reduced eigenvalue problems are established to determine the remaining non-zero frequencies. It is shown that the eigenvalue problem arising from the inplane normal and shear stresses is decoupled from that arising from the transverse shear stresses. A verification example is presented where the exact and approximate results are compared.