Transverse shear and normal deformation higher-order theory for the solution of dynamic problems of laminated plates and shells

An improved transverse shear and normal deformation higher-order theory is developed for the solution of dynamic problems involving multilayered plates and shells with an arbitrary number and sequence of transversely isotropic layers. The layers may differ significantly in their physical and mechanical properties. The theory developed is based on the kinematic hypotheses which are derived using iterative technique. Dynamic effects, such as forces of inertia, and the direct influence of external loading on the components of stress and strain are included in the initial stage of derivation where kinematic hypotheses are formulated. New variables which have clear physical meanings are introduced. The system of governing differential equations and the complete set of boundary conditions are derived. The closed form solutions are given for problems involving forced and natural vibrations. The numerical results are compared both with three-dimensional solutions, which are available in the literature, and with experimental data. The significant features of the present theory and the implications of the numerical results are discussed.