横观各向同性弹性柱体中辛本征解方法

针对横观各向同性弹性柱体问题构造了对偶体系.在辛几何空间中直接描述正则方程和对应的边条件.将问题归结为零本征值及其约当型和非零本征值本征解.采用辛子体系的方法获得了所有本征解的解析表达式,得到了完备的本征解空间.揭示了由圣维南原理所覆盖且体现端部效应的本征解,即本征值对应衰减系数和本征解对应端部非均匀受力下各物理量的变化规律.这种辛方法为解决类似问题提供了一种直接的途径,同时也为工程问题的简化提供了依据.

A method of symplectic eigensolutions in elastic transverse isotropy cylinders

The duality system is introduced for the problem of elastic cylinders with transverse isotropy. The dual equations and conditions of the corresponding boundary are obtained directly in the symplectic space. The problem is reduced to the symplectic eigensolutions, which include the zero eigenvalue solutions and all their Jordan normal forms of the corresponding Hamiltonian matrix operators and the non-zero eigenvalue solutions. With the aid of the sub-symplectic system, analytic expressions of eigensolutions are obtained. Thus a completed space of eigensolutions is established. The local boundary layer effects, which are usually neglected according to the Saint-Venant principle, are described by eigensolutions, or non-zero eigenvalues give the decay rates and the corresponding eigensolutions the characteristics of displacements and stresses to non-uniformity of loads on the ends of the cylinder. The symplectic method gives a direct way for solving the similar problems and provides the basis for simplifying the practicable engineering problem.