Three-Dimensional Analysis of Doubly Curved Laminated Shells

Abstract

Analysis of the bending and stretching problem of doubly curved laminated shells is formulated on the basis of three-dimensional elasticity. The basic idea underlying the approach is to make the formulation amenable to asymptotic analysis, which otherwise would be too complicated to deal with. In the formulation, the basic field equations are first rearranged into equations in terms of displacements and transverse stresses, and then they are made dimensionless by proper scaling of the field variables. By means of asymptotic expansion the recast equations can be decomposed into recurrent sets of differential equations at various levels. It turns out that the asymptotic equations can be integrated in succession, leading to the two-dimensional equations in the classical laminated shell theory (CST) at each level. Higher-order corrections as well as the first-order solution can be determined by treating the CST equations at multiple levels in a systematic and consistent way. The essential feature of the present analysis is that accurate three-dimensional elasticity solution can be determined by solving the CST equations in an adaptive and hierarchic manner without treating the layers individually. Several illustrative examples are given to demonstrate the performance of the theory.