Geometrically non-linear dynamic analysis of laminated shells using Bézier functions

Abstract

In this paper a geometrically non-linear theory for the analysis of open deep laminated shell panels is presented. Parabolic variation of the transverse shear stresses through the thickness of the shell and the effects of rotary inertia are included in the formulation. Linear and non-linear stiffness matrices are derived using orthogonal curvilinear coordinate system for a general doubly curved deep laminated shell. The solution of the equation of motion is based on the Ritz method. Therefore, the Bézier surface patches are used as the admissible displacement fields to represent the shell's middle surface displacement and rotation components and the resulting equation of motion is solved to obtain the transient response, using Beta- m time integration and Newton-Raphson iterations. A very good convergence of the responses is observed by using only the fifth order Bézier surface patches. The dynamic responses of cross-ply laminated circular and non-circular cylindrical panels pinned at the straight edges under a central point load are studied. Effect of the eccentricity on the dynamic response of non-circular cylindrical panels having the same plan form as the circular cylindrical panel is also examined.