# Abstract

Nonlinear static response of laminated composite Elliptic Panels of Revolution Structure(s) (EPRS) having variable thickness resting on Winkler-Pasternak (W-P) Elastic Foundation is investigated in this article. Generalized Differential Quadrature (GDQ) method is utilized to obtain the numerical solution of EPRS. The first-order shear deformation theory (FSDT) is employed to consider the transverse shear effects in static analyses. To determine the variable thickness, three types of thickness profiles namely cosine, sine and linear functions are used. Equilibrium equations are derived via virtual work principle using Green-Lagrange nonlinear strain-displacement relationships. The deepness terms are considered in Green-Lagrange strain-displacement relationships. The differential quadrature rule is employed to calculate the partial derivatives in equilibrium equations. Nonlinear static equilibrium equations are solved using Newton-Raphson method. Computer programs for EPRS are developed to implement the GDQ method in the solution of equilibrium equations. Accuracy of the proposed method is verified by comparing the results with Finite Element Method (FEM) solutions. After validation, several cases are carried out to examine the effect of elastic foundation parameters, thickness variation factor, thickness functions, boundary conditions and geometric characteristic parameter of EPRS on the geometrically nonlinear behavior of laminated composite EPRS.

**Keywords:**

Variable thickness; Elliptic shells of revolution; Generalized differential quadrature; Winkler-Pasternak elastic foundation; Geometric nonlinearity