超静定梁变形计算的有限差分法

推导了超静定梁变形计算的有限差分方程，研究了边界条件，编制了计算程序，计算 了超静定梁的变形. 文中工作扩大了有限差分法的应用范围.     

有限变形弹塑性理论及一致性算法

通过对对数应变的引用，成功地将小变形弹塑性理论移植到有限变形之中，形成了一套完整的有限变形弹塑性理论，进一步发展了具有一阶精度的一致性弹塑性算法。最后，给出几个算例以证明此理论的正确性及算法的有效性。     

用记忆材料模拟流变大变形问题

本文采用具有记忆特性的有机玻璃材料结合网格法测量技术，以软岩巷道围岩流变形为例展开了有限变形模拟试验的研究工作，并以有限变形理论为基础结合现代计算机技术进行了实验数据处理。实例分析表明，所用方法和技术具有广泛的灵活性、可靠性的实用性。     

有限变形论的若干运动学关系

有限变形论的若干运动学关系陈良森（上海工业大学，上海市应用数学和力学研究所，上海２０００７２）郭仲衡（北京大学数学系，北京１００８７１）在这篇记注里，我们给出有限变形理论的若干简单运动学关系。本文中拉丁下标或求和指标总是从１到３取值。设Ｆ（ｔ）是变形...     

三维有限变形线性光弹性材料研究

制成了１５％应变量的三维有限变形线性光弹性材料，可供对橡胶类零件的应力分析之用；在该材料中，以尼龙６作内含体，可以制作初应力很小的三维有限变形复合光弹性模型。     

有限空心截圆锥扭转变形问题解析解

对有限空心截圆锥扭转变形问题进行了力学分析，确定其外锥面的内柱面上的载荷分布规律，应用三维弹性理论求解了有限空心截圆锥扭转变形问题，得到了应力解析式。文中给出了实际算例。     

梁板壳的几何大变形--从近似的非线性理论到有限变形理论

对梁板壳的线性理论、近似几何非线性理论与有限变形理论作了比较,介绍了有限转动理论,指出了应用有限变形理论求解梁板壳的大变形问题的高效率、高精度的巨大优越性。     

有限变形弹性动力学的非传统Gurtin型变分原理

根据古典阴阳互补和现代对偶互补的基本思想，通过作者早已提出的一条简单而统一的途径，系统地建立了有限变形弹性动力学的各类非传统Gurtin型变分原理，给出一个以卷积表示的重要关系式，可以认为，该式是有限变形动力学的广义虚功原理的表式。从该式出发，不仅能得到有限变形动力学的虚功原理，而且通过给出的一系列广义Legendre变换，还能系统地成对导出5类变量，3类变量，2类变量和1类变量非传统Gurtin型变分原理的互补泛函。通过这条途径还能清楚地阐明这些原理之间的内在联系。     

热—塑变形局部化的有限元分析及其对激光破坏效应的应用

本文给出了热力耦合的热弹粘塑性材料的有限分析方法，并讨论与之相关的时间积分算法。为改善线性插值函数所引起的不协调性及提高运算速度，应力协调迭代理论被引入相应的算法及程序中，最后对非绝热过程中热－塑变形局部化及激光诱导的剪切变形集中进行了数值模拟，其结果与理论分析有限好的吻合。     

有限变形下应力集中的三维效应

用三维有了奶变形光弹性方法研究了在有限变形下含半圆槽试件和含圆孔试件的应力集中的三维效应，考察了三维效应的基本规律，所得结果与Ｎｅｕｂｅｒ和Ｈｅｙｗｏｏｄ所提供的在小变形下的相应数据作了比较。     

On the Dynamic Interaction and Cross-Interaction of 2D Rigid Structures with Orthotropic Elastic Media Possessing General Principal Axes Orientation

A direct boundary element method (BEM) implementation for the dynamic interaction analysis in the frequency domain of 2D rigid structures with elastic orthotropic media is presented. The BEM implementation is based on non-singular full-space influence functions. The rigid structure response is obtained by applying equilibrium and kinetic compatibility conditions. The method is applied to the analysis of the dynamic response of a rigid tunnel in a half-space with various elasticity principal axes inclinations and to the analysis of two rigid rectangular galleries in a half space with various distances between them.     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

Open-plus-closed-loop control for chaotic motion of 3D rigid pendulum

An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.     

压电螺型位错和共线界面刚性线夹杂的干涉效应

研究了压电材料中压电螺型位错和共线界面导电刚性线夹杂的电弹干涉效应．运用复变函数解析延拓技术与奇性主部分析方法,获得了该问题的一般解答．作为算例,求出了界面含一条刚性线夹杂时两种压电介质区域广义应力函数的封闭形式解．导出了作用在位错上的像力和刚性线夹杂表面剪应力和电位移的解析表达式．讨论了界面刚性线长度,两种材料的剪切模量比和压电系数比对位错力和刚性线表面剪应力的影响规律．为进一步研究该类问题提供了一个基本解。     

周期裂纹和刚性线尖端场干涉效应研究

研究双周期裂纹和刚性线夹杂非均匀材料的反平面剪切问题。基于保角变换技术和椭圆函数理论,获得了问题应力场的全场精确解,给出了裂纹和刚性线尖端应力强度因子的封闭形式解答,讨论了裂纹和刚性线尖端场的干涉效应。数值结果表明：改变水平和垂直分布周期对裂纹和刚性线尖端场影响明显不同;裂纹长度2a逐渐增大时(0≤a/ω1≤0.5),裂纹尖端应力强度因子从1逐渐增大到无限大,而刚性线的尖端场变化不大;刚性线长度2d逐渐增大时(0≤d/ω2≤1),刚性线尖端应力强度因子逐渐减小,而裂纹的尖端场仅略微增大。     

Application of the integral manifold method to the analysis of the spatial motion of a rigid body fixed to a cable

We analyze the spatial motion of a rigid body fixed to a cable about its center of mass when the orbital cable system is unrolling. The analysis is based on the integral manifold method, which permits separating the rigid body motion into the slow and fast components. The motion of the rigid body is studied in the case of slow variations in the cable tension force and under the action of various disturbances.We estimate the influence of the static and dynamic asymmetry of the rigid body on its spatial motion about the cable fixation point. An example of the analysis of the rigid body motion when the orbital cable system is unrolling is given for a special program of variations in the cable tension force. The conditions of applicability of the integral manifold method are analyzed.     

和界面接触的刚性线夹杂对SH波的散射

利用积分变换方法，得出了两相材料中单位简谐力的格林函数。根据简谐集中力的格林函数得出了和界面接触的刚性线的散射场。利用无穷积分的性质，把和界面接触刚性线的散射场分解为奇异部分和有界部分。通过分解后的散射场建立了和界面接触剐性线在SH波作用下的Cauchy型奇异积分方程。根据所得奇异积分方程和刚性线的散射场得到了刚性线端点的奇异性阶数及奇性应力。应用刚性线端点的奇性应力定义了刚性线端点的应力奇异因子。对所得Cauchy型奇异积分方程的数值求解，可得刚性线端点的应力奇异因子。     

Analog-discrete approach for the solution of a class of rigid-contact problems

This investigation consists in finding stresses and displacements produced by a rigid footing (or punch) at the plane boundary of a semi-infinite elastic solid. The proposed method is a combined application of electrical analog and finite-difference technique and can be applied to any arbitrary shape of rigid footing (or punch). The experimental setup is very simple and the numerical-analysis part is easily amenable to computer programming. The method has been exemplified by 3 cases: (1) rigid strip footing (or punch); (2) rigid circular footing (or punch); and (3) rigid square footing (or punch) on a three-dimensional semi-infinite solid. The results, wherever possible, have been compared with exact solutions and have been found to be in close agreement.     

Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.     

Global Weak Solutions¶for the Two-Dimensional Motion¶of Several Rigid Bodies¶in an Incompressible Viscous Fluid

We consider the two-dimensional motion of several non-homogeneous rigid bodies immersed in an incompressible non-homogeneous viscous fluid. The fluid, and the rigid bodies are contained in a fixed open bounded set of ?². The motion of the fluid is governed by the Navier-Stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies. The time variation of the fluid domain (due to the motion of the rigid bodies) is not known a priori, so we deal with a free boundary value problem. The main novelty here is thedemonstration of the global existence of weak solutions for this problem. More precisely, the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary. We give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero.