An asymptotic theory for dynamic response of doubly curved laminated shells

An asymptotic theory for dynamic analysis of doubly curved laminated shells is formulated within the framework of three-dimensional elasticity. Multiple time scales are introduced in the formulation so that the secular terms can be eliminated in obtaining a uniform expansion leading to valid asymptotic solutions. By means of reformulation and asymptotic expansions the basic three-dimensional equations are decomposed into recursive sets of equations that can be integrated in succession. The classical laminated shell theory (CST) is derived as a leading-order approximation to the three-dimensional theory. Modifications to the leading-order approximation are obtained systematically by considering the solvability conditions of the higher-order equations. The essential feature of the theory is that an accurate elasticity solution can be determined hierarchically by solving the CST equations in a consistent way without treating the layers individually. Illustrative examples are given to demonstrate the performance of the theory.