- A dynamic, shear deformation theory of a doubly curved shell is used to develop a finite element for geometrically non-linear (in the von Karman sense) transient analysis of laminated composite shells. The element is employed to determine the transient response of spherical and cylindrical shells with various boundary conditions and loading. The effect of shear deformation and geometric non-linearity on the transient response is investigated. The numerical results presented here for transient analysis of laminated composite shells should serve as references for future investigations. 1985.