粘弹性厚壁筒问题的辛本征解方法  

A method of symplectic eigensolutions for viscoelastic hollow circular cylinders

作　　者：徐新生[1] 张维祥[1] 李雪[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《计算力学学报》2007年第2期153-158,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10272924)资助项目

摘　　要：将哈密顿体系引进到粘弹性力学厚壁筒问题中,在辛体系下重新描述了基本问题,即建立了正则方程组。借助于积分变换,得到了拉伸、扭转和弯曲等问题的解以及有边界局部效应的解。将原问题归结为辛几何空间中的零本征值本征解和非零本征值本征解问题,从而建立了一种有效的分析问题方法和数值方法。为解决同类问题提供了一条可行的路径。This paper introduces Hamiltonian system to the viscoelastic hollow circular cylinders and redescribes fundamental problem in symplectic system or symplectic equations. With the aid of the integral transformation, solutions extension, torsion and bend not only are obtained but also local solutions of boundary effects. The original problem is reduced to finding zero eigenvalue solutions and non-zero eigenvalue solutions. A symplectic method and numerical method are shown. The method also provides some foundation for other researching.

关 键 词：哈密顿体系 辛几何 粘弹性 厚壁筒 

分 类 号：O345[理学—固体力学]