3-DIMENSIONAL ANALYSIS OF DOUBLY-CURVED LAMINATED SHELLS

Analysis of the bending and stretching problem of doubly curved lamina ted shells is formulated on the basis of three-dimensional elasticity. The basic idea underlying the approach is to make the formulation ame nable 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 st resses, 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 va rious levels. It turns out that the asymptotic equations can be integr ated in succession, leading to the two-dimensional equations in the cl assical laminated shell theory (CST) at each level. Higher-order corre ctions as well as the first-order solution can be determined by treati ng the CST equations at multiple levels in a systematic and consistent way. The essential feature of the present analysis is that accurate t hree-dimensional elasticity solution can be determined by solving the CST equations in an adaptive and hierarchic manner without treating th e layers individually. Several illustrative examples are given to demo nstrate the performance of the theory.