Accurate calculation of transverse shear stresses for soft-core sandwich laminates

Abstract

Accurate evaluation of transverse stresses in soft-core sandwich laminates using the existing 2D finite element (FE) models involves cumbersome post-processing techniques. In this paper, a simple and robust method is proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in soft-core sandwich laminates by using a displacement-based C0 continuous 2D FE model derived from refined higher-order shear deformation theory (RHSDT) and a least square error (LSE) method. In this refined higher-order shear deformation theory (RHSDT), the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly early varying displacement field. The transverse displacement is assumed to have a quadratic variation within the core, and it remains constant in the faces beyond the core. The proposed C0 FE model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements associated with the RHSDT. The LSE method is applied to the 3D equilibrium equations of the plate problem at the post-processing stage, after in-plane stresses are calculated by using the above FE model based on RHSDT. Thus, the proposed method is quite simple and elegant compared to the usual method of integrating the 3D equilibrium equations at the post-processing stage for the calculation of transverse stresses in a sandwich laminates. The accuracy of the proposed method is demonstrated in the numerical examples through the comparison of the present results with those obtained from different models based on HSDT and 3D elasticity solutions.