求解弹性地基上自由矩形中厚板弯曲问题的辛-叠加方法

Abstract

Based on the symplectic superposition method proposed in recent years, the bending problems of free-edge rectangular thick plates resting on elastic foundations were analytically solved. The original problem was split into 3 subproblems corresponding to the bending problems of rectangular thick plates with 2 opposite edges slidingly clamped and resting on elastic foundations, which were solved with the symplectic geometry method. The analytic solution of the original problem was then obtained through superposition. Compared to the conventional analytic approaches such as the semi-inverse method, the symplectic superposition method has the advantages of both rationality of the symplectic method and regularity of the superposition method. The solution procedure starts from the basic equations of elasticity, and a rigorous derivation yields the analytic solutions, thus extending the scope of problems to be solved. The present method can serve as an effective analytic approach to complex boundary value problems of high-order partial differential equations in elasticity, as represented by the rectangular plate problems.