Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Inertial parameter estimation and control of non-cooperative target with unilateral contact constraint

In this paper, the relative sliding motion between the target and the manipulator’s endeffector is considered and characterized as a unilateral contact constraint. A new possible solution is presented to estimate the inertial parameters of a non-cooperative target while the relative sliding motion exists. First, the detailed analysis of the dynamical model is presented, and a parameterexplicit linear time-varying model is obtained. Then, an extended state observer is constructed based on the new model, which can effectively estimate the unknown inertial parameters of the target when relative sliding motion exists. As the modified reactionless controller requires the knowledge of inertial parameters, a hybrid post-capture control scheme is also established based on the switch law between different controllers. The correctness and efficiency of the proposed algorithm are validated by numerical simulation, which proves a potential framework for the non-cooperative target postcapture operation.

考虑移动边界约束作用的薄壁件铣削动特性研究

针对薄壁件铣削过程工件约束边界复杂及动特性难预测等问题,创新性的提出了接触移动边界约束的概念,深入研究了接触移动边界约束对系统动特性的影响规律。首先,建立了考虑刀-工接触移动边界约束作用的薄板切削过程动力学模型,提取刀-工接触区域,分析了接触刚度力和阻尼力与接触参数的复杂影响关系。其次,预测了任意接触移动边界约束作用的薄板动态响应,形成了更为全面地任意边界约束选择方案,包括接触移动边界条件和经典边界条件。基于薄板理论建立系统运动学方程,综合考虑包括移动边界约束产生的能量项、常规任意边界约束产生的能量项以及薄板变形产生的能量项的组合。最后,通过不同案例以及有限元法,与现有文献中的数值、解析和实验等方法获得的结果作了大量对比,证明了本文提出方法的准确性。结果表明,接触移动约束效应对系统动态特性的影响不可忽视。

REDUCED AUGMENTED LAGRANGIAN BI-CONJUGATE GRADIENT METHOD FOR IMPACT-CONTACT PROBLEMS

To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditions, a new approach to enforcing surfacecontact constraints for the tran- sient nonlinear finite elementproblems, referred to as 'the reduced augmented Lagrangianbi-conjugate gradient method (ALCG)', is developed in this paper.Based on the nonlinear constrained optimization theory and iscompatible with the explicit time integration scheme, this approachcan also be used in implicit scheme naturally.

Generating Parametric G^n Blending Surface with Some Constraints

This paper presents a method of generating a parametric G^n blending surfacebased on reparameterizing the partial surface patches in the base surfaces on the basis of ErichHartmann method. This method is expressed as follows Firstly, the partial region near contact curvesin both base surfaces is reparameterized. The contact curves are used as the boundaries of thereparameterized partial region respectively. The reparameterized partial region in two base surfacesis called the reparameterized local base surfaces. Then the parametric G^n blending surface isgenerated by a linear combination of the reparameterized local base surface patches depending on oneof the common parameters. Therefore, generating a Parametric G^n Blending Surface between two basesurfaces is translated into generating a Parametric G^n Blending Surface between the tworeparameterized local base surfaces. This paper illustrates the method to generate the G^n blendingsurface with some constraints by generating a G^2 blending surface between the aerofoil and the bodyof a missile with the constraints of the forward and rear fringe curves. When the G^n blendingsurface with some constraints is generated, the partial region near contact curves in both basesurfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight aredefined by meeting the constraints through using an optimization method. Then the parametric G^nblending surface is generated by the linear combination of the reparameterized local base surfacepatches. The shape of the blending surface can be adjusted by changing the size of thereparameterized local base surface patches.

Multi-variable approach of contact-impact issue in variable topology system

Contact-impact processes occur at most cases in multibody systems. Sub-periods and sub-regional methods are frequently used recently, and different coordinates are introduced in both of the approaches. However, the sub-regional method seems to be more effective. Floating frame of reference formulation is widely used for contact treatment, which describes displacements by the rigid body motion and a small superposed deformation, and the coordinates depicting the deformation include finite element nodal coordinates and modal coordinates, the former deals with the contact/impact region, and the later describes the non-contact region. In this paper, free interface substructure method is used in modeling, and the dynamic equation of a single body is derived. Then, using the Lagrange equation of the first kind, the dynamic equations of multibody systems are established. Furthermore, contact-impact areas are treated through additional constraint equations and Lagrange multipliers. Using such approach, the number of system coordinates and the dimensions of mass matrix are significantly reduced with the modal truncation, therefore both of the efficiency and accuracy are guaranteed. Finite element method in the local contact region can deal with contact/impact between arbitrarily complex interfaces, whereas, additional contact constraints used in the nodal description region can avoid the customized parameters that are used in the continuous force model. C 2013 The Chinese Society of Theoretical and Applied Mechanics.[doi： 10.1063/2.1301307]

Coherent Application of a Contact Structure to Formulate Classical Non-Equilibrium Thermodynamics

This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.

Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

接触问题有限元分析方法综述

从直接迭代法、接触约束法和数学规划法等方面综述接触问题有限元分析的基本方法 .直接迭代法是一种“试验误差”方法 ,概念清楚 ,实施方便 ,但计算工作量较大 ,而且不能保证迭代一定收敛 .接触约束法主要利用罚函数方法或Lagrange乘子法将接触问题转化为无约束问题求解 .数学规划法利用接触问题的互补条件、非穿透条件等 ,将其归结为二次规划 (线性互补 )问题求解 ,这是一种非迭代类解法 ,收敛平稳、迅速 ,计算工作量较小 .

流体固体动力耦合分析的有限元法

应用有限元法探讨了流体、固体接触界面由无限接触点对组成,并以接触点对的瞬态接触内力作为待定变量的流体固体动力耦合模型的数值求解方法。分析了流体、固体域插值函数的特点,用二维八节点等参元及流固接触面上的接触点对单元,对流固耦合系统进行了离散化处理;并采用变分原理推导了反映流体固体动力相互作用机理的接触约束矩阵(或称动力耦合矩阵),建立了有限元控制方程,给出了完整的数值计算方法,研编了动力耦合系统的分析程序。数值计算结果与经典理论解误差很小,验证了动力耦合模型和有限元求解方法的正确性及其较高的计算精度。

基于多接触约束的动力学仿真计算效率

在进行基于虚拟样机技术的机械系统动力学分析时,如果系统包含多接触约束,计算效率往往低下,甚至导致模型求解失败,本质原因之一是当前非实际接触约束仍然要参与当前迭代计算,使求解模型的雅可比矩阵的规模比实际求解需要的规模大得多,从而可能引起该矩阵的条件数增大,使求解效率降低。基于此,针对多接触动力学系统计算效率问题,通过分析求解模型中雅可比矩阵构成的本质,提出采用消隐或激活接触约束的方法对雅可比矩阵降维,从而降低当前迭代步的解算规模,达到提高仿真效率的目的。仿真试验结果表明,消隐或激活接触约束的方法在不损失仿真精度的基础上,大大减少了多接触动力学模型的求解时间,提高了求解效率。

基于接触面几何的接触问题解法

给出了一种基于接触面几何的接触问题解法。该方法将变形体与变形体或刚体之间的接触面利用离散的解析曲面来描述。利用曲面的几何特性来给定接触体间的约束条件,并将之直接引入求解方程来求解接触问题。与传统的拉格朗日乘子法及罚函数法相比,该解法没有增加接触问题的自由度数目,且避免了应用罚函数法时的罚数的选择问题。算例表明,该方法准确有效。

作大范围运动柔性梁的一种碰撞动力学求解方法

研究作大范围运动柔性梁的碰撞动力学问题。针对梁碰撞前、碰撞过程、碰撞后三个阶段,分别建立各阶段的动力学方程。基于柔性多体系统刚柔耦合动力学理论,建立梁无碰撞时的刚柔耦合动力学方程。结合冲量动量法和接触约束法提出一种碰撞动力学求解方法,先以冲量动量法实现运动转换得到协调的碰撞初始条件,再以接触约束法求解碰撞过程。导出系统的刚柔耦合碰撞动力学方程,给出了接触、分离判据,实现三个不同阶段的转换与动力学求解。编制仿真软件,对实例进行动力学仿真,得到系统不同阶段的动力学响应。研究表明,所提碰撞求解方法可以较方便地用于计算柔性多体系统的碰撞问题。梁的柔性、大范围运动及碰撞效应相互耦合,碰撞行为对于柔性多体系统碰撞过程和碰撞后的全局动力学性态均产生较大的影响。

流体—固体瞬态动力耦合有限元分析研究

本文应用有限元法探讨了流体与固体的瞬态动力耦合分析 .利用拉氏乘子法 ,给出了流体与固体接触面上一种接触约束单元 ,将流体与固体动力耦合内力作为基本未知量 ,使流体域与固体域有机地联系成一整体 ,从而实现了流体—固体动力耦合系统的统一分析 .文中还推导了流固动力耦合系统的有限元控制方程 ,编制了计算程序 .数值计算结果验证了耦合模型的正确性及其较高的计算精度 ,并表明固体的变形效应对于流体—固体系统的动力响应是显著的 .

含非理想空间棱柱铰的多体系统接触分析

传统的接触分析方法通过物体间的相对运动确定接触位置.将这种方法用于多体系统中铰内的接触分析时,无论铰内间隙是否十分微小都必须解除铰的运动学约束,从而导致求解效率和求解精度方面的诸多弊端.基于铰约束反力与铰内接触力之间的力系等效关系,以及铰内可能接触点运动之间内在的运动学关系,以矩形截面的棱柱铰为例,提出了一种对空间棱柱铰进行摩擦接触分析的方法,可在不解除铰的运动学约束的前提下得到铰内接触模式和接触力.数值算例验证了方法的可行性.

橡胶复合材料结构非线性有限元分析

用非线性有限元法对一种典型的橡胶复合材料结构——轮胎的力学性能进行了分析。给出了轮胎滚动边界值问题的数学描述和有限元列式及相应的求解策略。取旋转刚体构形为参考构形，得到消去时间变量的惯性场和控制方程。用增量约束方法处理轮胎滚动接触问题可以达到收敛快、精度高。研究了滚动参数对轮胎总体和局部变形和受力的影响。计算结果与已有数据和试验相吻合，对轮胎设计和汽车动力学有指导意义。

岩体节理在动荷作用下的有限元分析

本义用约束节理单元法模拟应力波在节理处的传递过程。推导了动态约束节理单元的有限单元方程和数值分析公式以及碰撞、放释条件，并针对奥地利某公路隧洞工程进行了爆炸应力波在节理岩体中传播的有限元分析。

扬子块体与华北块体在海区的接触关系——来自上下源、长排列多道地震剖面的新认识

在新一轮南黄海区域地质地震调查工作中,针对地震地质条件和勘探目标,设计了新的地震资料采集技术方案——上下源延迟激发+长排列接收,获得了强反射界面之下的深部地层有效反射,揭示了千里岩断裂两侧分布着向南逆冲的构造推覆带.结合重力、磁力反演成果认为,千里岩隆起区为扬子块体与华北块体碰撞接触带,扬子块体向北运动与华北块体碰撞后楔入到华北块体之中.

对接机构隔框锁的接触碰撞动力学研究及仿真

为了给空间对接飞行器提供地面试验的参考依据 ,验证隔框锁结构设计的正确性和对接过程的可行性 ,本文针对隔框锁实例 ,在其运动平面内以均匀 B样条曲线拟合锁钩外轮廓 ,并建立起接触碰撞动力学微分方程和仿真模型。分析了刚体碰撞的过程、刚性接触的单边约束条件和考虑变形接触的法向力计算方法。文章还提出了基于几何引擎的接触点的实时判别算法 ,并给出了对接完成后锁钩的接触力、动能及动量的仿真曲线图。计算过程稳定、所得结果合理 ,具有重要的参考价值。

空间物体点接触纯滚动的几何意义

空间物体间点接触纯滚动的相互作用一般包含非完整约束,而约束所限制的虚位移通常采用速度水平的Appell-Chetaev条件给出,因此点接触纯滚动约束对应的几何意义并不直观。作者从多体系统中两物体沿其轮廓面做点接触纯滚动的问题出发,探讨此类非完整约束对应的几何意义。首先,提出两物体保持点接触的充分必要条件,并以球–面系统为例推导接触时的约束方程。然后,由空间物体点接触纯滚动的几何和速度约束,推导此时满足的两种几何限制条件。结果表明,采用两种几何条件获得的虚位移与速度约束的Appell-Chetaev条件相同。因此,可以认为保持点接触纯滚动的空间两物体在位形空间受到两种几何条件的约束限制。