Computational semi-analytical method for the 3D elasticity bending solution of laminated composite and sandwich doubly-curved shells

In this paper, a three-dimensional numerical solution for the bending study of laminated composite doubly-curved shells is presented. The partial differential equations are solved analytically by the Navier summation for the midsurface variables; this method is only valid for shells with constant curvature where boundary conditions are considered simply supported. The partial differential equations present different coefficients, which depend on the thickness coordinates. A semi-analytical solution and the so-called Differential Quadrature Method are used to calculate an approximated derivative of a certain function by a weighted summation of the function evaluated in a certain grin domain. Each layer is discretized by a grid point distribution such as: Chebyshev-Gauss-Lobatto, Legendre, Ding and Uniform. As part of the formulation, the inter-laminar continuity conditions of displacements and transverse shear stresses between the interfaces of two layers are imposed. The proper traction conditions at the top and bottom of the shell due to applied transverse loadings are also considered. The present results are compared with other 3D solutions available in the literature, classical 2D models, Layer-wise models, etc. Comparison of the results show that the present formulation correctly predicts through-the-thickness distributions for stresses and displacements while maintaining a low computational cost.