机器人通过奇点的运动学逆问题的数值解法

机器人在完成其规划动作时,常可能要通过其运动链的奇点,这时求解其运动学逆问题的通用算法遇到本质的困难,本文给出了一种算法,它可以成功地克服这个困难。文中还给出了计算实例。     

Complete solution of the stability problem for elastica of Euler's column

The stability of postcritical equilibrium forms of a simply supported column loaded with an axial force is analyzed. Investigating the sign of the second variation of the column's total energy, we obtain the Sturm-Liouville boundary-value problem, which is solved numerically. The stability conditions are formulated in terms of eigenvalues of the problem. The complete solution to the column plane elastica is given. The ranges of the compressive force corresponding to stable equilibrium configurations of the column are established.     

On the Problem of Dissipative Perturbations of Nonexpansive Mappings

ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ｗｅａｓｓｕｍｅｔｈａｔＨｉｓａｒｅａｌＨｉｌｂｅｒｔｓｐａｃｅ ,〈· ,·〉ｉｓｔｈｅｉｎｎｅｒｐｒｏｄｕｃｔｏｎＨ ,ＰｉｓａｃｏｎｅｉｎＨ .ＢｙｖｉｒｔｕｅｏｆｔｈｅｃｏｍｅＰ ,ａｎｏｒｄｅｒ“≤”ｉｓｉｎｄｕｃｅｄｉｎＨ ,ｉ.ｅ .,ｆｏｒａｎｙｇｉｖｅｎｘ,ｙ∈Ｈ ,ｘ≤ｙｉｆａｎｄｏｎｌｙｉｆｙ -ｘ∈Ｐ .Ａｍｕｌｔｉ＿ｖａｌｕｅｄｍａｐｐｉｎｇＡ :Ｄ(Ａ) Ｈ → 2 Ｈｉｓｓａｉｄｔｏｂｅａｃｃｒｅｔｉｖ…     

A SIMPLIFIED CALCULATING METHOD OF NONLINEAR FREQUENCY OF CABLE NET UNDER MEAN WIND LOAD

The cable net supported glass curtain wallas the most advanced technique in dot point supported glass curtain wall, is widely used in China. Because of its large deflection and high nonlinearity under wind load, the dynamic performance of the cable net is greatly different from that of the conventional linear structures. The continuous membrane theory is used to construct the nonlinear vibration differential equation of the cable net, and the harmonic balance method is used to solve the analytic formula of the nonlinear frequency. In order to verify the accuracy of the above analytic formula, the results of the formula and the nonlinear FEM time-history method are compared and found to be in good agreement. Furthermore, the nonlinear vibration differential equation and the nonlinear frequency obtained in this paper are the basis for the wind-induced response analysis of a cable net under fluctuating wind load.     

Phase volume and size effects on the terminal relaxation of ABS melts

The dynamical viscoelasticity of ABS melts with different particle size was investigated at various levels of rubbery phase contents. The effects of the rubber are more pronounced in the terminal zone: a transition from viscoelastic liquid to viscoelastic solid behavior was observed which can be interpreted as a physical gelation occurring at a critical rubbery phase content. This critical content resulted in being smaller in the case of smaller particles. A quantitative explanation of the experimental findings was proposed in terms of the average interparticle distance and overlapping of the chains grafted onto the neighboring rubber particles. The gel-like transition appeared to correspond to an approximately constant level of grafted chains overlapping.Presented in part at the Symposium Recent Developments in Structured Continua, Montreal (Canada), 26–28 May 1993.     

Stagnation point heat transfer from laminar,high temperature methane flames

Combustion of methane-rich fuels frequently provides forced convective heating in industry, and the ability to predict the rate of heat transfer from such flames to solid surfaces is often desirable. Mathematical modelling of stagnation point heat flux has been achieved by numerical solution of the boundary layer equations, and by an analytical equation modified to include the effects of chemical reaction in the free stream flow and to allow for the enhancement in heat flux caused by the diffusion and exothermic recombination of reactive species in the boundary layer surrounding the heat receiving body. Predictions from these models have been compared with experimental data obtained in high temperature methane flames of various equivalence ratios. Within the equilibrium region of these flames, predictions from the modified analytical equation based on total Lewis numbers equal to and greater than one form a tight envelope around the experimental results, and hence provide a relatively simple method of predicting heat flux. Numerical solutions tend to slightly underestimate predictions from the analytical equation and experimental data, although agreement with the alternative prediction method increases with the surface temperature of the heat receiving body     

点、线接触真实粗糙表面的弹流润滑研究

本文给出了点、线接触的真实粗糙表面的微弹流数值解。在给定随机粗糙表面样本后,求解大小不同的载荷和粗糙的弹流问题。从计算结果可以看出,由于Reynolds方程中速度项的作用,在表面对应粗糙的位置处引起了压力变化,从而因其产生的弹性变形使粗糙变得平滑。对此光滑表面解可以看出,因粗糙引起的压力和膜厚的变化在光滑解附近波动。载荷较大时,压力分节接近固体接触情况。     

复合Logistic映射中的逆分岔与分形

利用分岔图，揭示出复合Logistic映射可按倍周期分岔走向混沌，且混沌区中存在混沌危机及逆分岔现象．同时，分析了复合Logistic映射临界点的轨道，给出了复合Logistic映射Mandelbrot-Julia集(简称M-J集)的定义，推广了Welstead和Cromer所提出的周期点查找技术，并利用该技术，构造出一系列复合Logistic映射的M-J集．在此基础上，研究了M-J集的对称性；探索了M集周期区域分布的拓扑不变性；通过定性地建立M集上J集的整体刻画，发现M集包含了J集构造的大量信息．     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

滑动最小二乘插值函数配点法

给出了利用滑动最小二乘法构造加权残值法中试函数的方法，对试函数中的基函数以及权函数的选取提出了建议；该试函数适用于任何定解问题，采用配点法求出试函数中的系数，进而可得到定解问题的近似解，利用该试函数对简支板的挠曲，悬臂梁的弯曲，以及中心具有小圆孔的大板的均匀拉伸等三个例子进行了数值计算，并与理论结果进行对比，同时还检验了该法的精度对结点数，配点数，以及结点影响半径的依赖情况，结果表明，该试函数适用于多种边值问题，且精度高，该法简化了选择试函数的过程，尤其适用于工程中的各种数值计算。