中文摘要：

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。

英文摘要：

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.