Dynamic response of cross-ply laminated shallow shells according to a refined shear deformation theory

The dynamic response of cross-ply laminated shallow shells is investigated using the third-order shear deformation shell theory of Reddy [J. Appl. Mech. 4 1, 47 (1984)]. The theory accounts for cubic variation of the in-plane displacements through the thickness and does not require shear correction coefficients. The state-space approach is used to develop the analytical solutions of simply supported, cross-ply shells using the classical, first-order, and higher-order theories. The use of the separation of variables technique for the higher-order theory is also presented. Numerical results of the higher-order theory for center deflection and normal stresses of spherical shells under various loadings are compared with those obtained using the classical and first-order [or Sanders, Q. Appl. Math. 2 1, 21-36 (1963)] shell theories. Copyright 1989 Acoustical Society of America