Static analysis of sandwich panels with non-homogeneous soft-cores by novel weak form quadrature element method

The extended high order sandwich panel theory (EHSAPT) is employed to analyze the static behavior of sandwich beams with non-homogeneous soft-cores. The material properties of the orthotropic core vary along the thickness direction according to a power-law form starting from its middle plane to the upper or bottom faces. Due to complexity of the theory, the solutions are obtained numerically by using the weak form quadrature element method. Based on the expanded EHSAPT and differential quadrature rule, a novel N-node weak form quadrature sandwich beam element with Gauss Lobatto Legendre (GLL) nodes is established. The element stiffness matrix and work equivalent load are obtained by using GLL quadrature. Detailed formulations are worked out. Different materials for the face sheets and core of the sandwich beam structure are considered. Numerical results are presented to investigate effects of the power-law exponents, boundary conditions, different types of material system and loading on the displacements and stresses of the sandwich panel with non-homogeneous soft core.