FGM and Laminated Doubly-Curved and Degenerate Shells Resting on Nonlinear Elastic Foundations: A GDQ Solution for Static Analysis with a Posteriori Stress and Strain Recovery

This work focuses on the static analysis of functionally graded (FGM) and laminated doubly-curved shells and panels resting on nonlinear and linear elastic foundations using the Generalized Differential Quadrature (GDQ) method. The First-order Shear Deformation Theory (FSDT) for the aforementioned moderately thick structural elements is considered. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Several types of shell structures such as doubly-curved shells (elliptic and hyperbolic hyperboloids), singly-curved (spherical, cylindrical and conical shells), and degenerate panels (rectangular plates) are considered in this paper. The main contribution of this paper is the application of the differential geometry within GDQ method to solve doubly-curved FGM shells resting on nonlinear elastic foundations. The linear Winkler-Pasternak elastic foundation has been considered as a special case of the nonlinear elastic foundation proposed herein. The discretization of the differential system by means of the GDQ technique leads to a standard nonlinear problem, and the Newton-Raphson scheme is used to obtain the solution. Two different four-parameter power-law distributions are considered for the ceramic volume fraction of each lamina. In order to show the accuracy of this methodology, numerical comparisons between the present formulation and finite element solutions are presented. Very good agreement is observed. Finally, new results are presented to show effects of various parameters of the nonlinear elastic foundation on the behavior of functionally graded and laminated doubly-curved shells and panels