多体动力学程序切断铰的处理方法

多体系统动力学从非树系统派生出树系统的计算需要进行切断铰的处理。切断铰约束方程的形成是进行多体系统程序编写时的重要部分,其处理过程复杂,需要一定的技巧。本文引入了约束正交补轴的概念,详细介绍了几种典型(旋转铰、万向节、棱柱铰、旋转棱柱组合铰)切断铰位移约束方程、速度约束方程、加速度约束方程的形成方法,并给出了详细的程序化过程,该方法适用于任何类型的切断铰。最后给出相应算例,结果表明本文的方法能快速、正确地形成切断铰约束方程。     

三维复合型断裂的试验方法探讨

探讨了一种能够揭示三维复合型断裂现象并能记录这些现象的三维复合型断裂研究的实验方法，用此方法完成了LC4－CS航空结构铝合金不同厚度紧凑拉伸试样的I＋Ⅱ复合型断裂试验。结果表明：此方法能够简便地确定出复合型裂纹的起裂载荷、破坏载荷、裂尖张开位移、滑移位移和起裂角，基本解决三维复合型断裂研究所需实验数据问题。同时发现此种材料试样的承载能力和超裂方向的确具有明显的厚度效应。     

具有非线性homologous变形约束的桁架结构形态分析

研究了具有非线性homologous变形约束条件的桁架结构形态分析问题。在已有的线性homologous变形约束桁架形态分析的基础上,将结构的节点分成三类:homologous变形约束节点,形状可变节点和边界点。运用Moore-Penrose广义逆矩阵性质,将基础方程组解的存在条件表示为包含形状可变节点未知坐标的非线性方程组,为采用Newton-Raphson方法求解非线性方程组,对AA (A为任意矩阵,A 为A的Moore-Penrose广义逆矩阵)求偏导数,找到了满足保型要求的形态,给出的桁架算例说明了本文方法的有效性。     

Multiple Non-Smooth Events in Multi-Degree-of-Freedom Vibro-Impact Systems

The behaviour of a multi-degree-of-freedom vibro-impact system is studied using a 2 degree-of-freedom impact oscillator as a motivating example. A multi-modal model is used to simulate the behaviour of the system, and examine the complex dynamics which occurs when both degrees of freedom are subjected to a motion limiting constraint. In particular, the chattering and sticking behaviour which occurs for low forcing frequencies is discussed. In this region, a variety of non-smooth events can occur, including newly studied phenomena such as sliding bifurcations. In this paper, the multiple non-smooth events which can occur in the 2 degree-of-freedom system are categorised, and demonstrated using numerical simulations.     

Finite element modeling of contact conditions in multibody system dynamics

In this paper a new method is developed for the dynamic analysis of contact conditions in flexible multibody systems undergoing a rolling type of motion. The relative motion between the two contacting bodies is treated as a constraint condition describing their kinematic and geometric relations. Equations of motion of the system are presented in a matrix form making use of Kane's equations and finite element method. The method developed has been implemented in a general purpose program called DARS and applied to the simulation and analysis of a rotating wheel on a track. Both the bodies are assumed flexible and discretized using a three dimensional 8-noded isoparametric elements. The time variant constraint conditions are imposed on the nodal points located at the peripheral surfaces of the bodies under consideration. The simulation is carried out under two different boundary conditions describing the support of the track. The subsequent constraint forces associated with the generalized coordinates of the system are computed and plotted. The effects of friction are also discussed.     

路径约束条件下车辆行为的时空演化模型

复杂地理环境下车辆运行线路具有空间三维特征, 它对车辆行为的约束是显然的, 非一维空间和二维空间所能描述. 将复杂地理环境下车辆运行线路抽象为空间曲线, 引入微分几何理论, 利用弧长、曲率和挠率等几何不变量参数建立沿空间曲线运动的Serret-Frenet活动标架; 然后, 对空间曲线上任意一点处Serret-Frenet标架具有时变属性的动态行为进行数学描述, 进而建立路径约束条件下车辆行为的时空演化模型, 并在数学上严格证明了所建时空演化模型适用于车辆(Serret-Frenet标架)直线运行和做匀速圆周运动的特殊情形. 为后续复杂地理环境中交通线路上的车辆跟驰、变道等微观行为和交通流宏观行为研究, 奠定了理论基础.     

一类弹性和阻尼双分段非线性约束系统周期响应特性研究

考虑动态条件下的两种典型分段非线性约束, 根据广义耗散Lagrange原理建立一类具有弹性和阻尼双分段非线性约束系统动力学模型. 采用平均法求解得到系统在周期激励下的幅频响应关系. 分别比较系统在不同分段非线性约束条件下的时域响应、分岔响应和幅频响应, 得到受分段非线性约束的系统响应特性以及约束条件变化时系统响应的变化规律. 对比两种约束条件下的幅频响应, 研究得到系统稳定性受不同分段非线性因素影响及两种分段非线性约束之间的相互影响规律.     

Bilinear approach for a symmetry constraint of the modified KdV equation

The paper investigates the mKdV equation with the potential under symmetry constraint through bilinear approach, i.e., Hirota method and Wronskian technique. We show that the potential can be a summation of squares of wave functions and these wave functions can precisely be described as Wronskians.     

Resource constraint scheduling with a fractional shared resource

We consider a scheduling problem motivated by mining in remote off-grid areas. In this model, mines have pre-assigned mineral processing jobs and their own machine for executing these jobs. Each job also needs a certain amount of electricity in order to get completed. The electricity, on the other hand, is of limited supply and must be shared between the mines. We present a mathematical formulation of the problem and a Lagrangian relaxation based heuristic. Computational results which compares our heuristic with genetic algorithm and simulated annealing are also presented.     

Behavioral portfolio selection with loss control

In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world, gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound for losses) in the bad states. Examples are given to illustrate the general results.