Layer-Wise and Equivalent-Single-Layer Theories for Laminated Composite Doubly-Curved Shells and Panels Using Differential Geometry and GDQ Method

There are three different ways to study anisotropic shell structures: the 3D Elasticity, Equivalent-Single-Layer (ESL) and Layer-wise (LW) theories. The mechanical model used for the two ESL and LW approaches is based on the Carrera’s Unified Formulation (CUF) with curvature effect included. The main aim of this work is to determine the explicit fundamental operators for the fundamental nuclei that can be used not only for the ESL approach, but also for the LW approach. 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 description of the shell geometry is made by using the Differential Geometry. The Differential Quadrature (DQ) rule allows one to numerically evaluate all the derivatives needed for completely describing the doubly-curved shell. Then, the governing equations are expressed as functions of various kinematic parameters, when the constitutive and the kinematic relationships are used. The system of second-order linear partial differential equations is solved using the Generalized Differential Quadrature (GDQ) method. After the solution of the fundamental system of equations in terms of displacements, the generalized strains and stress resultants can be evaluated by applying the DQ rule to the displacements themselves. Finally, the transverse shear and normal stress profiles through the shell thickness are reconstructed a posteriori by solving the local 3D equilibrium equations in each point of the reference surface. In order to verify the procedure accuracy, GDQ results are compared with the ones obtained using analytical and numerical solutions. Very good agreement is observed.