A refined asymptotic theory of laminated circular conical shells

A refined asymptotic theory for the static analysis of laminated circular conical shells is presented. The formulation begins with the basic equations of three-dimensional (3D) elasticity in curvilinear circular conical coordinates. By means of proper nondimensionalization and asymptotic expansion, the 3D equations can be decomposed into recursive sets of differential equations at various levels. After bringing the effect of transverse shear deformations to the picture earlier and then applying successive integration, we obtain the recursive sets of governing equations leading to the ones of first-order shear deformation theory (FSDT). The FSDT becomes a first-order approximation to the 3D theory. The method of differential quadrature (DQ) is used for determining the present asymptotic solutions for various orders. The illustrative examples are given to demonstrate the performance of the present asymptotic theory.