一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。     

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.     

STATIC STUDY OF CANTILEVER BEAM STICTION UNDER ELECTROSTATIC FORCE INFLUENCE

I. INTRODUCTION For capacitor-like microelectromechanical systems (MEMS) structure[1??6], the voltage betweenthe structure and substrate causes attractive force. The sources of the voltage can be an arti?ciallymounted device[2 , 7??9] or the temporar…     

基于运动约束解过约束并联机构变形协调方程

提出利用运动约束关系来间接求解过约束并联机构变形协调方程．首先介绍了该方法的原理，接着分别针对平面和空间过约束并联机构，详述该方法的解决步骤，结果验证了该方法的正确性，从中还可看出该方法在求解复杂过约束并联机构时非常简洁，最后介绍了采用该方法解决多度过约束问题．     

多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

完整系统的多刚体系统离散时间传递矩阵法研究

基于多刚体系统离散时间传递矩阵法，采用提高计算精度的方法，研究具有大运动、非线性特征的完整系统在平面、空间中的动力学响应。提出了对部分变量重新赋值的违约修正方法，计算机仿真表明了其有效性。多刚体系统离散时间传递矩阵法不须进行违约修正，体现了该方法建模灵活性较强、程式化程度较高的优点。     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

单侧摩擦约束夹杂物的瞬态弹性波散射的时域边界元分析--反平面情况

应用时域边界元法研究了瞬态SH波对单侧摩擦约束夹杂物的散射问题，假设摩擦遵守库仑定量，当入射SH波足够强时界面会出现局部滑移，发现了一种有效的迭代技术以确定边界上的未知区域（滑移和粘着区）。算例计算了无限域中圆柱埋置夹杂物对瞬态SH波的散射问题。     

Lyapunov stable penalty methods for imposing holonomic constraints in multibody system dynamics

This paper presents stability and convergence results on a novel approach for imposing holonomic constraints for a class of multibody system dynamics. As opposed to some recent techniques that employ a penalty functional to approximate the Lagrange multipliers, the method herein defines a penalized dynamical system using penalty-augmented kinetic and potential energies, as well as a penalty dependent constraint violation dissipation function. In as much as the governing equations are not typically cocreive, the usual convergence criteria for linear variational boundary value problems are not directly applicable. Still numerical simulations by various researchers suggest that the method is convergent and stable. Despite the fact that the governing equations are nonlinear, the theoretical convergence of the formulation is guaranteed if the multibody system is natural and conservative. Likewise, stability and asymptotic stability results for the penalty formulation are derived from well-known stability results available from classical mechanics. Unfortunately, the convergence theorem is not directly applicable to dissipative multibody systems, such as those encountered in control applications. However, it is shown that the approximate solutions of a typical dissipative system converge to a nearby collection of trajectories that can be characterized precisely using a Lyapunov/Invariance Principle analysis. In short, the approach has many advantages as an alternative to other computational techniques:

THE GENERAL METHOD FOR SOLVING DYNAMIC PROBLEMS

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