Calculation of interlaminar shear stresses in laminated shallow shell panel using refined higher order shear deformation theory

Abstract

In general, calculation of inter-laminar shear stresses in laminated shells using 2D finite element models involves cumbersome post processing techniques. This paper presents a simple and efficient method for accurate evaluation of transverse shear stresses in laminated composite shallow shells by using a displacement based C0 2D FE model derived from refined higher order shear deformation theory (RHSDT) and a least square error (LSE) method. The theory 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. The effect of three curvature terms in the strain components of composite shells is also considered by following the Sander’s approximations. In order to overcome the problem of C1 continuity of transverse displacement encountered at the time of FE implementation of the present shell theory (RHSDT), the first derivatives of transverse displacement have been replaced by a independent C0 variables. The LSE method is applied at the post-processing stage, after in-plane stresses are calculated by using the present FE model based on RHSDT. Thus the proposed method is quite simple and efficient compared to the usual method of integrating the 3D equilibrium equations for calculation of transverse stresses in laminated composite shells. Accuracy of the method is demonstrated in the numerical examples through comparison of the present results with those obtained from different models based on refined higher order shear deformation theory (RHSDT), higher order shear deformation theory (HSDT), exact analytical and 3D elasticity solutions.