Winkler-Pasternak Foundation Effect on the Static and Dynamic Analyses of Laminated Doubly-Curved and Degenerate Shells and Panels

This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on the Winkler–Pasternak elastic foundation using the generalized differential quadrature (GDQ) method. The analyses are worked out considering the first-order shear deformation theory (FSDT) for the aforementioned moderately thick structural elements. 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 and revolution shells, singly-curved and degenerate shells are considered in this paper. The main novelty of this paper is the application of the differential geometry within GDQ method to solve doubly-curved shells resting on the Winkler–Pasternak elastic foundation. The discretization of the differential system by means of the GDQ technique leads to a standard linear problem for the static analysis and to a standard linear eigenvalue problem for the dynamic analysis. 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 the Winkler modulus, the Pasternak modulus, and the inertia of the elastic foundation on the behavior of laminated doubly-curved shells.