Rational transverse shear deformation higher-order theory of anisotropic laminated plates and shells

A rational transverse shear deformation higher-order theory of multilayered anisotropic plates and shallow shells is developed for the solution of statical problems for two possible cases: cross-ply and angle-ply laminates. The theory developed differs from existing ones by three features. Firstly, it is based on the hypotheses which are fully tied to the physical and mechanical characteristics of the anisotropic layers. Secondly, the theory is built on a rational level of difficulty, i.e. it does not add complexity in comparison with other known theories developed for more simple laminated structure. Thirdly, the hypotheses take directly into account the influence of external subject to both normal and tangential loads. Relying on the specific approach for the derivation of hypotheses all the relations of the stress–strain state of anisotropic laminated shells are obtained. Using the variational approach the system of governing differential equations and corresponding boundary conditions are derived. The analytical solution for this system is given, and both special cases are stated, namely, cross-ply and angle-ply laminates, for which such solution exists. The results of the calculations are given and compared with exact three-dimensional and some approximate solutions available in the literature. The influence of the laminated structure upon the exactness of results and the characteristics of stress–strain state is studied and discussed.