各向异性弹性力学场论的Hamilton体系

来源期刊：中南大学学报(自然科学版)2003年第2期

论文作者：郭少华 谢伟

文章页码：211 - 213

关键词：弹性力学; Hamilton体系;对偶变量;正则方程;本征解

Key words：elastic mechanics; Hamilton′s system; dual variable; normal equation; eigen solution

摘    要：在弹性力学本征化理论的基础上,通过定义正则共轭动量密度,得到了不同变形条件下弹性力学场的Hamil-ton密度函数,并由此给出了相应的Hamilton正则方程.采用分离变量方法,将弹性动力学解转变为Hamilton空间算子矩阵的本征值问题,对偶变量(模态应变和模态应变率)的全解通过本征解来展开而获得.此外,讨论了不同变形条件下弹性力学场论Hamilton体系的具体应用,得到了弹性小变形、弹性大变形和率相关变形条件下的静力学基本求解方程.

Abstract: Based on the eigen theory of elastic mechanics , theHamilton density functions for various deformation process are obtained by defining the normal conjugate momentum density , and the Hamilton normal equations for elastic body are also given . Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton’s space differential operator matrix , and the total solution of dual variables (modal strain and modal strain rate ) can be obtained by expanding the eigen solutions . Finally ,some specific applications of the elasticHamilton principle for various deformation process are discussed , and the fundamental equations of elastic statics for several process, such as the little deformation process , the large deformation process and the deformation related to strain rate are given in details.