改革教学,创新教学———"材料力学"课程教学改革实践与体会

正清华大学的材料力学(含工程力学)课程教学改革,从20世纪80年代开始,当时从因才施教的角度提出"分层次"教学,同时开展启发式教学。改革的措施以及成果,均已见之于当时的相关报刊,在校内外都有一定的影响。自1996年开始,我们三校作为教育部"面向21世纪力学课程教学内容与体系改革"项目的牵头单位和参与单位,都做了大量卓有成效的工作,取得了包括教材建设在内的一系列成果,大大推动了我国     

Shape gradient and classical gradient of curvatures: driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a general theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived: (a) Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. (b) On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. (c) Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradients form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. (d) The direction of the driving force induced by the hard curved surface is independent of the hydrophilicity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.     

曲面物理和力学

回顾了平坦空间中的经典物理和力学, 综述了卷曲空间中物理和力学的三个典型案例, 即生物膜力学、扁壳力学和曲面扩散动力学, 揭示了平坦空间与卷曲空间物理和力学的根本差异. 论文阐明了, 平坦空间的物理和力学只有一个基本微分算子------经典梯度, 而曲面物理和力学必然存在两个基本微分算子------经典梯度和形状梯度.     

Nonlinear Deformation Processes and Damage Modes of Super Carbon Nanotubes with Armchair-Armchair Topology

The tensile deformations and fractures of super carbon nanotubes （SCNTs） with armchair-armchair topology are investigated by using the atomic-scale finite element method. SCNTs generated from carbon nanotubes （CNTs） with different characteristic aspect ratios are found to have different nonlinear behaviours under uniaxial tensions. Specifically, an SCNT wi~h higher aspect ratio has three distinct stages： rotation, stretch and rupture, while an SCNT with lower aspect ratio has only two stages. This information may compensate for previous work and enrich our knowledge about Y-branched CNTs and SCNTs.     

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed     

曲率的形状梯度和经典梯度:微纳米曲面上的驱动力

近期的实验和分子动力学模拟均表明:圆锥面上粘附液滴能自发地定向运动,且自发定向运动的方向与粘附面的亲水、疏水性质无关．针对这一重要现象,拟从曲面微纳米力学几何化的角度,提供一般性的理论解释．借助于粒子对势,研究了孤立粒子与微纳米硬曲面之间的相互作用,分析了粒子/硬曲面相互作用的几何学基础．可以证实:（a） 粒子/硬曲面的作用势均具有统一的曲率化形式,均可以统一地表达成曲面平均曲率和Gauss曲率的函数;（b） 基于曲率化的作用势,能够实现曲面微纳米力学的几何化;（c） 曲率与曲率的内蕴梯度构成卷曲空间上的驱动力;（d） 驱动力方向与曲面的亲水、疏水性质无关,解释了自发定向运动实验．     

微纳米空间弯曲诱导的反常驱动力 —— 从泡利的魔鬼谈起

介绍了高度卷曲的微纳米物质空间诱发的反常驱动力,指出构成反常驱动力的基本要素有两个：一个是空间的弯曲程度,即曲率, 另一个是空间弯曲的不均匀程度,即曲率的梯度.     

Nonlinear effects of line tension in adhesion of small droplets

Three-phase line tensions may become crucial in the adhesion of miero-nano or small droplets on solid planes. In this paper we study for the first time the nonlinear effects in adhesion spanning the full range of physically possible parameters of surface tension, line tension, and droplet size. It is shown that the nonlinear adhesion solution spaces can be characterized into four regions. Within each region the adhesion behaves essentially the same. Especially, inside the characteristic regions with violent nonlinearities, the co-existence of multiple adhesion states for given materials is disclosed. Besides, two common fixed points in the solution space are revealed. These new results are consistent with numerical analysis and experimental observations reported in the literatures.     

坐标变换系数张量观与杂交张量概念分析

本文致力于澄清一个十分基本的问题:坐标变换系数是否为张量?传统观念认为,坐标变换系数不是张量。为了揭示坐标变换系数的本质,本文采用"从一般到特殊"的研究策略,重塑了张量的内涵和外延,引入了杂交张量概念,进而颠覆了坐标变换系数不是张量的传统观念,确切地讲,它就是度量张量的杂交分量。这一结果扩张了张量概念的集合,提升了张量分析学内在的统一性、对称性和不变性,减少了连续介质力学的运算量。