Pinched cylinder benchmarks for shear deformable laminated shells

Abstract

The concept of the pinched cylinder benchmark has been extended to cover shear deformable laminated shells. The unified shear deformable shell theory of Soldatos and Timarci is used to obtain a twelfth order partial differential equation, which is solved using the method of Yuan by representing the concentrated load via a Fourier series containing a Fourier integral, evaluating the latter using the theory of residues. The solution is used to obtain a number of benchmark results relating to homogeneous and laminated orthotropic cylindrical shells with simply supported ends. Numerical problems in the form of repeated roots within the solution limit the method's usefulness in obtaining such a solution for an isotropic cylinder, although interpolation around regions of numerical difficulties allows a useful approximate solution to be obtained.