哈密顿体系与弹性楔体问题  

Hamiltonian Structure and Wedge Body in Elasticity

作　　者：徐新生[1] 郑新广[1] 张洪武[1] 钟万勰[1] 

机构地区：[1]大连理工大学

出　　处：《应用力学学报》1999年第2期140-144,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学重点基金

摘　　要：将哈密顿体系引入到极坐标下的弹性力学楔体问题。利用该体系辛空间的性质，将问题化为本征值和本征向量求解上，得到了完备的解空间，从而改变了弹性力学传统的拉格朗日体系以应力函数为特征的半逆法讨论去解决该类问题的思路。给出了一条求解该类问题的直接法。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 semi inverse 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.

关 键 词：弹性 哈密顿体系 楔体 本征值 

分 类 号：O343[理学—固体力学]