Symplectic superposition method-based new analytic bending solutions of cylindrical shell panels

Abstract

Pursuing analytic bending solutions of cylindrical shell panels without two opposite simply supported edges is a classic but very difficult type of problems. The main challenge is on the mathematical complexity of the boundary value problems of the governing high-order partial differential equations. In this paper, the first endeavor is made on extending an up-to-date symplectic superposition method to bending of cylindrical panels, with focus on clamped panels and their variants. By introducing the problems into the Hamiltonian system (in physics) and the symplectic space (in mathematics), they come down to the symplectic eigen problems, which are analytically solved for fundamental analytic solutions of three types of subproblems, followed by superposition for final solutions. The new analytic solutions for the panels with four different combinations of boundary conditions are obtained, with comprehensive results tabulated to serve as benchmarks for future studies, all of which are well validated by the finite element method. The rigorous derivation by the present method without any assumptions/prior knowledge of solution forms may provide an exceptional route to more analytic solutions of some intractable shell problems.