Asymptotic theory of laminated circular conical shells

Abstract

An asymptotic theory is presented for the analysis of laminated circular conical shells. The formulation begins with the basic equations of three-dimensional elasticity. By means of proper nondimensionalization and asymptotic expansion, the equations of three-dimensional elasticity can be decomposed into recursive sets of differential equations at various levels. After integrating these equations through the thickness direction in succession, we obtain the recursive sets of governing equations for the bending of a laminated circular conical shell. Note that the stiffness coefficients in the formulation are functions of the longitudinal coordinate. This involves the mathematical complexities in the formulation and the use of the existing analytical approach is restricted. The method of differential quadrature (DQ) is adopted for solving the problems of various orders. The formulation reveals that the differential operators corresponding to the governing equations of various orders remain the same. The nonhomogeneous terms of the higher-order problems are related to the lower-order solutions. Solution procedure of the DQ method for the leading order can be repeatedly applied for the solution to the higher-order level. In view of the efficiency and accuracy of the DQ method, the asymptotic solution of the present study is obtained readily and asymptotically approaches the three-dimensional solution. The illustrative examples are given to demonstrate the performance of the theory.