A refined asymptotic theory for dynamic analysis of doubly curved laminated shells

The asymptotic theory developed recently for dynamic analysis of doubly curved laminated shells is refined by including the transverse rotations as auxiliary variables. The theory embraces the first-order shear deformation theory (FSDT) and the higher-order shear deformation theory (HSDT) as the first-order approximation. Higher-order corrections to the approximation are determined by solving the FSDT or HSDT equations in a hierarchic way. The secular terms in the asymptotic solution are eliminated systematically by means of multiple scales and solvability conditions for the higher-order equations. The performance of the refined theory is illustrated by applying it to benchmark problems. Numerical comparisons are made to examine the convergence of the solutions. © 1998 Elsevier Science Ltd.