Finite Element for the Static and Stability Analysis of Sandwich Plates

A displacement-based finite element for static and stability analyses of sandwich plates is formulated using a three-layer sandwich model. The face sheets are idealized as classical plate elements assuming the Kirchhoff—Love hypothesis. The core displacement field is derived using the solution of the underlying differential equations of the core in the through-thickness direction z and the assumed deflections of the face sheets as boundary conditions. The differential equations are determined based on a three-dimensional material law neglecting the in-plane core stiffnesses. This approach leads to in-plane core deformations uc and vc, which are cubic functions of z, and to an out-of-plane deflection wc, which is a quadratic function of z. Based on the interpolation functions, the linear and geometric stiffness matrix for static and stability problems are derived, whereas the geometric stiffness matrix is set up by considering geometric nonlinearities in the v. Kármán sense in the face sheets.