An efficient FE model and Least Square Error method for accurate calculation of transverse shear stresses in composites and sandwich laminates

Accurate evaluation of transverse stresses in laminated composites and sandwich plates using 2D FE models involves cumbersome post-processing techniques. In this paper a simple and efficient method has been proposed for accurate evaluation of through-the-thickness distribution of transverse stresses in composites and sandwich laminates by using a displacement based C⁰ FE model (2D) derived from Refined Higher Order Shear Deformation Theory (RHSDT) and a Least Square Error (LSE) method. The C⁰ FE model satisfies the inter-laminar shear stress continuity conditions at the layer interfaces and zero transverse shear stress conditions at the top and bottom of the plate. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of C¹ continuity associated with the above plate theory (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 calculation of transverse stresses in a composite laminate. In the proposed method, the first two equations of equilibrium are utilized to compute the transverse shear stress variation through the thickness of a laminated plate whereas the third equation of equilibrium gives the normal stress variation. Accuracy of the proposed method is demonstrated in the numerical examples through comparison of the present results with those obtained from different models based on higher order shear deformation theory (HSDT) and 3D elasticity solutions.