Hamiltonian Structure and Wedge Body in Elasticity
Xu Xinsheng  Zheng Xinguang  Zhang Hongwu  W.X.Zhong
£¨State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology£¬ 116023£©

Abstract: In this paper, the Hamiltonian structure is introduced into the wedge body in elasticity in polar coordinate formulation. Based on the properties of adjoint symplectic orthonormalization relationship of symplectic mathematics, the direct solution is first to find the eigenvalues and their respective eigenfunction vectors of the Hamiltonian operator matrix. The completed solution space is obtained,and the tranditional considerations of semiª²inverse method, the method of stress function, in the elasticity with Lagrange structure is updated. The classical solutions with the homogeneous boundary condition, the solutions with the
non-homogeneous boundary condition and the solutions with the mixed boundary conditions are obtained. Meanwhile, it gives a new direct method.
Keywords: elasticity, Hamiltonian structure, wedge body,eigenvalue problem.

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