A New Analytic Symplecticity Approach for Static and Dynamic Analyses of Plates and Shells

Description

Plates and shells are primary and important components for complicated structural systems in modern engineering. Understanding of dynamic behaviour of these structural components is of great significance for their optimized design and safety evaluation during service. Hence, it is very crucial to model these problems as accurately as possible. However, exact analytical solutions to the dynamics of these structures are very limited and have long been bottlenecks in the history of elasticity.In this project, a new symplectic elasticity approach will be developed to analyze the dynamics of plates and shells with arbitrary boundary conditions. It is based on the Hamiltonian variational principle with the Legendre transformation. The variable separation method with expansion of eigenfunctions will be employed to construct the exact solutions. Some preliminary breakthroughs to the long-standing bottleneck problems have been reported and more established and comprehensive solutions are expected. Outcomes of the project will play substantial roles in the completeness of the group of exact solutions, and will provide concrete references for future theoretical analyses and engineering applications.