Euler-Bernoulli梁的非同位控制

对一端固定,一端加剪切力反馈的Euler-Bernoulli梁,运用Legendre谱方法对一个非同位控制系统进行研究,得到了最优反馈增益系数和系统衰减率.结果表明这样的非同位控制系统可以有效的增大系统衰减率,使系统具有更好的稳定性.同时指出所研究的系统是极小相位的.     

梁振动边界反馈的最优反馈增益的数值解

本用Legendre谱方法估计一端固定,一端加弯矩耗散线性反馈的梁振动的闭环系统使能量最快衰减的最优反馈增益,我们给出了数值产生的图形结果,通过比较发现另一种非耗散的线性反馈在最优反馈增益下比相应的耗散线性反馈有更好的衰减率。     

Timoshenko梁点反馈的稳定性

研究T im oshenko梁点反馈的稳定性.用线性算子半群方法证明了闭环系统的适定性,并应用算子谱特征得到了闭环系统的强渐近稳定性的充分必要条件.同时,给出了保守系统的几个能观性不等式.     

两端固定n根系列连接的Timoshenko梁在连接点加控制的镇定问题

文章研究两端固定n根系列连接的Timoshen]K0梁系统的镇定问题,假设该系统在连接点处剪切力和弯曲力矩是连续的,而横向位移和旋转角度是不连续的.在连接点处设置控制器,观测节点处的力,通过补偿器补偿后反馈回系统,构成闭环系统.通过对系统的矩阵化处理,对算子谱采用渐近分析的技巧,证明得到该闭环系统是渐近稳定的.并利用算子谱的分布等性质,在一定条件下得到了闭环系统的Riesz基性质,从而系统满足谱确定增长条件.     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．     

一类柔性梁系统的谱分析和半群生成

讨论了一类双臂三关节柔性梁系统的分析问题．首先,建立了一个与柔性梁的偏微分方程组及初值边值条件相应的希尔伯特空间中的一阶发展系统．接着讨论系统算子的谱性质和半群性质．最后借助系统算子的谱性质和半群性质提出并证明了柔性梁系统的指数稳定性．     

一个复合系统边界反馈的Riesz基性质

该文考虑一端固定 ,一端具负荷的梁的振动问题 .证明了线性反馈的闭环系统是一个 Riesz谱系统 ,即系统存在一列广义本征函数列构成状态空间的 Riesz基 .从而系统的谱确定增长条件成立 .在此过程中 ,简单的导出了系统本征值的渐近展开式 .并因此推论出系统的指数稳定性的条件     

复合弹性系统边界反馈镇定的Riesz基方法

考虑一个航天器控制实验室实验模型的振动镇定问题。证明了高阶微分线性反馈的闭环系统是一个Riesz系统,即系统存在一列广义本征函数列构成状态空间的Riesz基。从而系统的谱确定增长条件成立。在此过程中,简单的导出了系统本征值的渐近展开式。并因些推论出系统的指数稳定性的条件。     

浅论数学课堂教学信息反馈与调控

浅论数学课堂教学信息反馈与调控魏诗明（福建柘荣一中３５５３００）系统论的反馈原理指出：任何系统，只有通过反馈信息，才能实现控制，没有反馈信息的系统，要实现控制是不可能的．课堂教学过程是教与学之间的信息传递和反馈的控制过程，即教师围绕着某一教学目标和要...     

具有临界和非临界操作错误的人机系统的渐近稳定性

讨论具有临界和非临界操作错误的可修复人机系统．利用系统算子生成的Banach 空间中的正压缩C0半群的性质,证明了此系统的唯一非负时间依赖解恰是系统算子0本征值对应的规范化后的本征向量;同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的一个直接结果,得出了该可修人机系统的渐近稳定性．     

Analytical inverse solution for coupled thermoelastic problem for the evaluation of contact stress during steel strip rolling

Knowledge of the contact stress between roll and strip is a critical factor in modern, high-speed rolling mills. Previously two inverse analytical methods have been developed to determine the elastic contact stress on the one hand and the heat flux or the temperature in the whole roll (and especially at the surface) on the other hand, by measuring the stress tensor inside the roll body with fibre optics and by measuring the temperature with a thermocouple fully embedded at only one point inside the roll. However measurements done by fibre optics take into account the elastic stress and the thermal stress. However the contact stress was determined under isothermal assumption, which is strongly incorrect for hot rolling conditions. In this paper, the coupled thermoelastic problem is solved analytically using the theorem of superposition and the expression of the temperature field exhibited previously. A significant improvement of the accuracy of the inverse method for reconstructing the contact stress is observed by taking into account thermal stress. Hot rolling simulation is given to demonstrate this result. The computation time is studied to rapidly optimise the industrial parameters during the rolling process, and considering that both inverse methods have been run, the computation of thermal stress does not cost significant additional CPU times.     

Some results on the analysis of asymmetric stress

The structure of the principal directions of stress is characterized for the general case of asymmetric stress. It is shown that, for asymmetric stress, the principal directions can comprise either only one direction, or only two directions, or only three directions, or a plane of directions, or a plane of directions together with a direction external to this plane. The asymmetric stress obtained by combining a one-dimensional stress field with a skew-symmetric stress field is analyzed in detail.     

采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题

采用新的方法研究非局部理论中Ⅰ_型裂纹的断裂问题,进而确定裂纹尖端的应力状态,这种方法就是Schmidt方法·　所得结果比艾林根研究同样问题的结果准确和更加合理,克服了艾林根研究同样问题时遇到的数学困难·　与经典弹性解相比,裂纹尖端不再出现物理意义上不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题·     

螺位错场的非线性力学解

本文以非线性连续体几何场论为理论基础,分析了无限大体中一个螺位错引起的应力场。结果揭示了非线性高阶效应的影响。当不考虑高阶效应时,所求得的应力场可退化为经典线弹性理论的结果。本文还对螺位错引起的体力矩场进行了求解。获得了无限大体中单个螺位错引起的体力矩的解析表达式。作为理论结果的应用,本文研究了界面附近螺位错的应力场和体力矩场。揭示了它们对界面力学性能的影响。     

论拖带坐标系中应力的客观速率

应力客观速率是有限变形力学中一个十分重要的问题,本文利用非线性几何场论方法,推导出拖带坐标系中应力客观速率公式,并应用新公式计算了拉伸、拉伸与转动复合、简单剪切大变形问题.通过将计算结果与用Jaumann等其它应力速率计算的结果进行比较,说明了本文所得结果是合理的.     

Analytic solutions for twin tunneling at great depth considering liner installation and mutual interaction between geomaterial and liners

Analytic solutions for stress and displacement of twin tunneling at great depth considering liner installation and mutual interaction between geomaterial and liners are the key context in this paper. Twin tunneling is a continuous procedure, in which after one tunnel is excavated and lined, the other one is hysteretically excavated and lined. The presented solutions mainly focus on stress and displacement in geomaterial and liners for the hysteretical phases through an iterative combination of the complex variable method and the Fourier transform via the Schwarz alternating method. The presented solutions are verified by comparing to a corresponding numerical solution of a general case, in which a good agreement is observed after three iterations. Subsequently, a dimensionless parametric investigation is performed to investigate the influence of tunnel geometry (including twin tunnel spacing, relative angle of twin tunnels and relative size of twin tunnels), liner properties (including liner thickness and liner installation), and lateral stress coefficient on stress and displacement in both liners and geomaterial.     

Computation of mixed mode stress intensity factors in a four-point bend specimen

Four-point bend specimen is one of the most important specimens of the fracture mechanics because it can produce mixed modes I and II. Therefore, computation of stress intensity factors in this specimen is of practical interest. Several relations have been suggested that no one of them has completely considered the effects of the loading point and crack geometry. In this paper, mixed mode stress intensity factors of the bend specimen are computed by finite element method (FEM) and after validating by comparing with the available results in the literature, the results will be assessed to determine the effects of different crack location and loading distances from the middle of the specimen. Finally, two new coefficients comprising these effects are introduced.     

拟牛顿流的一种三变量域模型的有限元方法的数值分析

0．引言目前，涉及高温条件下材料蠕变性质的粘弹性流动问题已引起人们广泛的研究兴趣，不少文章讨论了如何对其进行数值求解（见［1］－－［41），首先，人们研究了较简单的仅以速度，压力两个变量来表述此现象的模型问题（如［1，2］）等．鉴于应力变量在材料性质方面的特殊重要性，最近J．Baxanzer等人在［3］中首次对应力满足幂函数规律的蠕变流研究了包含应力、速度和压力三种变量的模型问题的有限元逼近，当粘性的牛顿部分为零时（详见下述）在假定速度与应力、速度与压力有限元空间之间同时满足两种＊＊B条件以后，证明了有限元解…     

弹性平面孔洞形状优化复变函数方法

本文提出了弹性平面孔洞形状优化的复变函数方法,充分利用了复变函数方法分析孔洞应力的有效性,进行应力分析.对孔洞形状的优化,是将保角变换函数中的一些系数做为设计变量,采用敏度分析和梯度法降低绝对值最大的周向应力,同时使绝对值次大的周向应力不超过绝对值最大的周向应力(这两个周向应力实际是周向应力的两个极值点处的周向应力值)逐次迭代修正保角变换函数中的系数值,直至绝对值最大的周向应力降低至绝对值次大的周向应力相等为止.这个方法保证了应力解在边界上的连续性、可微性和高精度性,比差分法和有限元法有着明显的优越性.     

Assessment of transmission of the shear stress in potted anchors for composite rods 1. Sleeve of constant thickness

The key problem facing the application of fiber-reinforced polymer (FRP) stay cables and tendons is the anchorage. Potted (bond-type) anchors have been used more extensively than anchors of any other type. The main aim in the design of anchors is to minimize the peak shear stress at the FRP rod-pottant interface. To this end, parametric analyses of the stress state in the anchors are carried out. Since parametric studies can not be easily performed by the finite-element method, an analytical model of the anchor is proposed. The model involves significant simplifying assumptions and allows one to obtain a relatively simple analytical solution for shear-stress distributions at the FRP rod-pottant interface. The use of this solution at various boundary conditions and various geometrical and mechanical parameters of anchor components enables one to search for and evaluate, at least qualitatively, different methods for decreasing the peak interfacial shear stress in the anchor. In this part of the investigation, an anchor consisting of a sleeve of constant thickness is considered. Russian tanslation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 321-346, May-June, 2009.