Stress and Strain Recovery of Laminated Composite Doubly-Curved Shells and Panels Using Higher-Order Formulations

One of the major problems in composite engineering design is the evaluation of stresses and strains at the interfaces of plies within a stacking sequence. In the present study, a recovery procedure is shown for the calculation of the through-the-thickness stresses and strains of laminated composite doubly-curved shells. The displacement field of the present two-dimensional formulation is based on the Carrera Unified Formulation (CUF) which allows to study several Higher-order Shear Deformation Theories (HSDTs) [1,2], some of which are presented in the following (1). The two models EDZ4, ED4 are fourth order Equivalent Single Layer (ESL) models in terms of displacements with and without the zig-zag effect (Z), respectively. The last one of (1) is the well-known First-order Shear Deformation Theory (FSDT). The curvature effect is only embedded in the formulation at the constitutive equation level. It is pointed out that the fundamental system of equations in orthogonal curvilinear coordinates was obtained for the first time by the authors in [3]. The static equilibrium equations are solved by using Differential Quadrature (DQ) method [4-7], that leads to an algebraic system of equations that can be solved numerically by Gaussian elimination technique. The present recovery procedure starts from the computed displacement field and three-dimensional equilibrium equations of shells are used for the evaluation of the through-the-thickness shear and normal stresses. Moreover, the shear and normal strains are computed using the constitutive equations of the three-dimensional solid. In order to verify all the numerical results, a comparison between analytical and numerical solutions is carried out. For instance, all the components of the stress tensor for a clamped laminated spherical panel subjected to a normal load at the top surface ( ) have been studied along the thickness of the structure shown in Fig. 1. The panel at hand has a radius , the meridian angles and the width of the circumferential angle is . The lamination scheme is a (Zirconia/Aluminum/Zirconia) with the top and bottom sheets of thickness and the core for a total shell thickness .