General Higher-Order Equivalent Single Layer and Layer Wise Theories for Laminated Composite Shells and Panels Using GDQ Method

This paper focuses on the study of laminated composite completely doubly curved shells and panels using the Generalized Differential Quadrature (GDQ) method [1]. The mechanical model is based on the so called Carrera’s Unified Formulation (CUF) [2]. The curvature effect is also included. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell [3,4,5]. The fundamental operators, concerning a laminated composite doubly-curved shell in orthogonal curvilinear coordinate system, are obtained for the first time by the authors. The formulation takes the meridian and the circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Complete revolution shells are obtained as special cases of shell panels by satisfying the kinematical and physical compatibility at the common meridian. Numerical solutions of the fundamental system of equations in terms of displacements are evaluated by applying the GDQ method. The determination of accurate values for interlaminar normal and shear stresses is of crucial importance, since they are responsible for the activation and the development of delamination mechanisms [5,6]. In this work, the transverse shear and normal stress profiles through the laminated thickness are reconstructed a posteriori by simply applying the local three-dimensional equilibrium equations. The reconstruction procedure only needs to be corrected to properly account for the boundary equilibrium conditions, when the GDQ procedure through the thickness is used. In order to verify the accuracy of the present method, the new results are compared with the ones obtained using analytical and 3D FEM solutions for laminated composite doubly curved and degenerate shells. Very good agreement is observed.