牛顿力学体系中固体力学研究框架的几点注记

本文从四十多年前遇到并解决的三个与固体力学和结构力学相关的机械强度与振动的问题谈起。当时在分析与解决这些问题的方法时,思考并领悟到如何从结构的构形与几何约束、结构承受的外载的性质和结构材料的秉性与行为着眼,实质上就是从以牛顿力学体系的外载(F)、质点质量(m)和物体运动的加速度(a)(即物体的位移、速度、加速度等运动表现的力学运动的几何量)的运动行为作为三个最基本的视点并描述它们之间的联系,在拓广后给出可变形固体力学分析的基本框架。进而刻画出在20世纪70年代、90年代和21世纪初的固体力学的基本框架及其框架内每个不同构元的联系与演进,并以图1,2,3表示。随着现代科技的发展,这一框架下的分析方法近些年已经扩展到更广泛的科技疆域,并在与其他学科的交缘的过程中揭示新的交缘变量的演化方程。人们还期望进入更小和更大尺度时空,研究更广泛的物质包括信息的生成与传递、有生命物质的运动和各种“极端”的力学环境条件下的力学现象,这些新的疆域将是明天的力学工作者耕耘的新天地。

NOTES ON THE RESEARCH FRAMEWORK OF SOLID MECHANICS IN NEWTONIAN MECHANICS 1)

Over 40 years ago, the author once faced with several strength and vibration problems related to the structural mechanics and solid mechanics in the design, manufacturing and operating of machines and tried to solve these failure problems and to improve the working of machines. It was found that three aspects are important, that is, the configuration and constraint, the nature of external loading and the properties of structural materials. They are actually based on three elements in the Newtonian mechanics: the loading $F$, the mass of matter $m$ and the acceleration of motion $a$, and the linking between them. This framework can be extended to describe the analysis of solid mechanics. The research framework is further extended in the 1970s, the 1990s and the early 21st century, as shown in Figures 1,2,3. In recent years, the analytical methodology has already extended to more extensive scientific and technological territory and the coupling between the different disciplines asks people to discover new development directions. Smaller and larger scales in space-time will be considered, as well as the process of information and data production and transformation, and the motion of living matters under conventional or extreme loading environment. These new fields can be expected to open for future solid mechanics.