Geometrically Nonlinear Dynamic Analysis of an Imperfect, Stiffened, Functionally Graded, Doubly Curved Shell - Boutros Azizi; Habib Eslami; Kais Jribi (Dynamics)
An analytical study of the nonlinear response of imperfect stiffened doubly curved shells made of functionally graded material (FGM) is presented. The formulation of the problem is based on the first-order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain–displacement relationships. The nonlinear equations of the motion of stiffened double-curved shells based on the extended Sanders’s theory were derived using Galerkin’s method. The material properties vary in the direction of thickness according to the linear rule of mixture. The effect of both longitudinal and transverse stiffeners was considered using Lekhnitsky’s technique. The fundamental frequencies of the stiffened shell are compared with the FE solutions obtained by using the ABAQUS 6.14 software. A stepwise approximation technique is applied to model the functionally graded shell. The resulting nonlinear ordinary differential equations were solved numerically by using the fourth-order Runge–Kutta method. Closed-form solutions for nonlinear frequency–amplitude responses were obtained using He’s energy method. The effect of power index, functionally graded stiffeners, geometrical parameters, and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed.