基于郭仲衡先生现代张量分析及有限变形理论知识体系的相关研究  

Some Related Studies Based on Guo Zhong-heng's Knowledge Systems of Modern Tensor Analysis and Finite Deformation Theory

作　　者：谢锡麟[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《力学季刊》2013年第2期337-351,共15页Chinese Quarterly of Mechanics

基　　金：上海市教委2011年上海高校本科重点教学改革项目"‘现代连续介质力学理论及实践’课程体系";上海市教委2011年重点课程立项项目"<数学分析>(一年制;面对力学等技术科学专业)";国家自然科学基金面上项目(11172069;10872051)

摘　　要：作为我国理性力学先驱之一的郭仲衡先生在其所著《张量(理论和应用)》以及《非线性弹性理论》中记述了现代张量分析以及有限变形理论知识体系。本文按有限维Euclid空间上微积分以及一般赋范线性空间上微分学认识相关知识体系的理论框架,相关思想及方法,阐述了有关思想及方法的发展及其应用。本文未涉及现代几何学在连续介质力学中的应用。It is well known that Prof. Guo Zhong-heng is one of the national pioneers of the foundations and developments of rational mechanics. His two monographs one is ＂Tensor （theories and applications）＂ and the other ＂Nonlinear Elastic Mechanics＂ include systemetic knowledge of modern tensor analysis and finite deformation theory. The theoretical frameworks of related knowledge systems with some ideas and methodologies have been expatiated in the point of view of calculus in finite Euclidian spaces and differen- tial calculus in general normed linear spaces, including some developments of related ideas and methodolo- gies with applications. The applications of modern geometry in continuum mechanics have not been in- volved in the present paper.

关 键 词：郭仲衡 现代张量分析 有限变形理论 有限维Euclid空间上微积分 一般赋范线性空间上微分学 

分 类 号：O331[理学—一般力学与力学基础]