ANALYTICAL SOLUTIONS FOR THICK, DOUBLY CURVED, LAMINATED SHELLS

The state equations for orthotropic, doubly curved shells are established in an orthogonal curvilinear coordinate system. Simplifying hypotheses about displacement models or stress distribution that were assumed in early work are not introduced in this paper. The continuity conditions of stresses and displacements at the interfaces between the contacting layers are satisfied, and analytical solutions for statics and dynamics of the simply supported, doubly curved shells with orthotropic layers are presented by means of the Cayley-Hamilton theorem. For any number of layers considered, the problem reduces to solving a set of linear algebraic equations with three unknowns. A unified analytical solution is given for thin, moderately thick, and thick laminated shells. The solution satisfied all the equations of elasticity, and each of nine elastic constants is considered. Arbitrary precision of the desired order can be obtained. Numerical results are given to compare with solutions available in the literature.