通过引入弯矩函数和恰当的变换，环扇形薄板弯曲问题可导入到二类变量的辛空间，应用分离变量以及辛本征函数展开的数学物理方法进行解析求解。首先，从环扇形薄板弯曲问题的通解出发，讨论了两直边固支，以及一直边自由、另一直边固支边界条件的板，给出了这两种边界条件下相关问题的辛本征解。其次，对相应边界条件下V形切口尖端应力奇异性进行了讨论。环扇形薄板弯曲问题的成功求解再次验证了辛对偶体系方法的有效性。%By introducing bending moment functions and appropriate transformations ,the bending problem of a circular sector thin plate can be led into the symplectic space with two kinds of variables and solved using the methods of mathematical physics of a scheme of separation of variables and symplectic eigenexpansion . Firstly , based on the general solution for the bending problem of the circular sector thin plate ,plates with both straight sides clamped ,and with one straight side free and the other straight side clamped are discussed , and their symplectic eigensolutions are obtained . Secondly ,the stress singularities around the V-shaped notch in a thin plate are analyzed .The validity of methodology of symplectic duality system is verified by the successful solution of bending problem of a circular sector thin plate .
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