Method of initial functions for the analysis of laminated circular cylindrical shells under axisymmetric loading

The method of initial functions has been used for the static analysis of an infinite and simply supported, orthotropic, and laminated, circular cylindrical shell of revolution subjected to axisymmetric load. In this method the three-dimensional state equations for an individual ply of a laminated shell are established without making any a priori assumptions regarding the distribution of stresses and displacements across the thickness of the shell By using the continuity conditions of displacements and stresses on each interface between adjacent layers, the state equation for the laminate is obtained. Using the Cayley-Hamilton theorem, the transfer matrix that maps the initial state vector into the field is evaluated explicitly, leading to an exact solution of the problem (MIF-exact). Alternatively, depending on the number of terms retained in the series expansion of the transfer matrix, different-order theories of MIF are derived The results of different-order MIF theories, classical theories, and shear deformation shell theories are compared with the results of MIF-exact to assess their accuracy and limitations.