On analytical solutions to boundary-value problems of doubly-curved moderately-thick orthotropic shells

Abstract

Hitherto unknown analytical solutions to the boundary-value problems of shear-flexible doubly-curved orthotropic shells of rectangular planform are presented. Sanders' kinematic relations, extended to the first-order shear deformation theory, yield five coupled linear second-order partial differential equations with constant co-efficients. These are solved in conjunction with five admissible boundary conditions at each edge by utilizing a recently developed novel double Fourier series approach, which takes into account the ordinary discontinuities, if any, of the assumed solutions and/or their first derivatives. The numerical results presented herein, for the C4 and SS4 boundary conditions prescribed at all edges, contribute to our fundamental understanding of the complex deformation behavior of finite doubly-curved shear flexible orthotropic shells. These results should serve as bench-mark solutions for future comparison.