沿直边简支环扇形薄板弯曲问题的辛几何法

摘要

Based on the analogy between plane elasticity and plate bending problems with radial coordinate treated as "time", the paper is discussed bending problems of thin elastic annular sector plate simply supported along two radial edges and yielded to present an analytical method by the application of the pro-Hellinger-Reissner variational principle . The conclusions of this paper provide a theoretical basis for application research of the symplectic eigensolutions and analytic solutions of related problems.%由平面弹性与薄板弯曲问题的相似性，本文在辛体系中以径向模拟为时间，研究了两直边简支时的环扇形板弯曲问题。利用分离变量和本征函数展开等方法，给出其一个分析求解法，本文所得的结论为辛本征解的应用研究以及相关问题的解析求解提供了理论基础。