Refined Global Approximation Theory of Multilayered Plates and Shells

A refined global approximation theory of thin multilayered anisotropic shells is developed. The effects of the laminated material response, transverse shear, and transverse normal strains are included. The material of each layer of the shell is assumed to be linearly elastic, anisotropic, homogeneous, or fiber reinforced. As unknown functions the tangential displacements of the face surfaces and transverse displacements of the face or middle surfaces of the shell are chosen. It is an important feature of the proposed theory. This fact simplifies, for example, an analysis of the contact problems and allows to elaborate universal numerical algorithms. An exact solution for the problem of the bending of homogeneous isotropic rectangular plates subjected to a sinusoidal load has been found. Numerical solutions for the problem of the bending of multilayered composite plates and cylindrical shells have been also obtained. The influence of anisotropy, and transverse shear and transverse normal deformation response of the stress state of the shell is examined.