Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.

A linear complementarity model for multibody systems with frictional unilateral and bilateral constraints

The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed. For bilateral constraints, frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions. With the time-stepping impulse-velocity scheme, the measure differential equations are discretized. The equations of horizontal linear complementarity problems （HLCPs）, which are used to compute the impulses, are constructed by decomposing the absolute function and the filled-in relay function. These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints, or HLCPs for frictional bilateral constraints. Finally, a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem （NCP）. An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.

New method for oblique impact dynamics research of a flexible beam with large overall motion considering impact friction force

A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid modeling method, dynamic equations of the system, which include all states（before, during, and after the collision）are obtained. Simulation results of a concrete example are compared with the results obtained from two other models： a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.

A VARIATIONAL-HEMIVARIATIONAL INEQUALITY IN CONTACT PROBLEM FOR LOCKING MATERIALS AND NONMONOTONE SLIP DEPENDENT FRICTION

We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.

The Rolling Wheel Equations without Magic: A Combined Slip-Stiction Approach by the Udwadia-Kalaba Formulation with Constraints Relaxation for a Smooth Simulation

The Udwadia-Kalaba formulation is proposed to model the dynamics of the rolling wheel. A unified approach that addresses both the slip and the stiction in the contact section is considered. Purely rolling constraints are associated with stiction and are suitably lifted as slip occurs. An extended formulation for the Uwadia-Kalaba equations of motion is introduced for that matter. It resorts to the weighted minimum norm and the weighted semi-least-squares solutions of the constraints equations. This not only allows a bias on constraints, by an appropriate description of weight functions based on friction, it also leads to a smooth activation or deactivation of selected constraints without rewriting the equations of motion or upsetting their numerical integration.

“抱团取暖”可以应对“寒冬”吗? 贸易政策不确定性与企业协同创新 ——来自中美贸易摩擦的经验证据

基于2018年美国政府发起的对华贸易战,运用广义双重差分模型考察贸易政策不确定性对企业协同创新的影响及其作用渠道与经济后果。研究发现:贸易政策不确定性通过加剧融资约束、降低风险承担能力的作用渠道驱动中国企业选择“抱团取暖”,即以“协同创新”的方式谋求技术突破和研发攻关以抵御外部风险。调节效应检验结果发现:当上市公司属于高新技术企业时,贸易政策不确定性对协同创新的驱动效应更为显著;数字化转型为企业间创新要素的聚拢和流动提供了便利,较高的知识产权保护力度降低了企业协同创新中知识被模仿和窃取的风险,因此两者均能够强化贸易政策不确定性对企业协同创新的驱动作用。进一步区分协同创新的主体后发现:当企业面临贸易政策不确定性时,更倾向于选择与供应链上下游企业、高校及科研机构进行协同创新。并且,贸易政策不确定性在促使企业选择协同创新后可显著提升企业未来一期、二期、三期的全要素生产率,从而证实“抱团取暖”的协同创新方式确实能够帮助企业安稳度过“寒冬”。本文丰富了协同创新的驱动机制研究,也为企业在急剧变化的外部贸易环境中以“抱团”方式寻求理性出路提供了参考与借鉴。

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.

含干摩擦-刚性间隙约束振动系统的动力学特性研究

建立了含干摩擦-刚性约束的单自由度振动系统动力学模型,给出在考虑干摩擦和碰撞耦合条件下分段光滑振动系统动力学约束条件,同时引入非线性刚度因素,通过协同仿真的方法得出系统响应周期运动类型和分布区域,重点讨论了质量块发生速度黏滞和位移黏滞的动力学特征,并对低频小间隙参数域内的基本周期转迁规律进行了量化表征。研究表明,质量块与皮带之间发生的速度黏滞响应主要受激励频率影响;由于干摩擦的存在,质量块与约束面首次发生碰撞的速度更为复杂;质量块与刚性约束之间的碰撞振动响应与间隙δ和激励频率ω同时存在很强的关联关系,在低频小间隙参数域涌现了丰富的动力学响应特征。

贸易摩擦中反补贴措施对中国出口企业创新的影响研究——基于中国相关上市公司数据的实证分析

贸易摩擦背景下两个或多个国家之间会发生贸易争端和冲突,反补贴措施就是贸易摩擦中一种常见的非关税贸易措施手段。基于中国贸易救济信息网、中国海关数据库、国泰安数据库的数据,实证检验了反补贴措施对中国出口企业创新的影响。研究结果表明:反补贴措施促进了出口企业创新;企业所处行业的市场集中度以及融资约束情况对反补贴措施与企业创新之间的关系具有调节作用。进一步分析表明,在高出口广度企业、高生产率企业及民营企业中,反补贴措施对企业创新的正向影响更加明显。以上研究结果在进行了一系列稳健性检验后仍显著,论证了贸易摩擦中反补贴措施对企业创新的正向影响,为我国出口企业有效应对反补贴措施提供了实证证据。

板材冲压成形有限元数值模拟界面摩擦约束处理方法

基于弹塑性大变形板材冲压成形增量有限元法,采用线性弹簧单元提出一种空间三维板材冲压成形等效界面摩擦力的处理方法.这种方法的优点是可以反映界面摩擦力的同步、被动产生效果,同时它还可以保证约束后刚度矩阵的对称性.将提出的摩擦约束处理算法引入自主开发的板材成形模拟软件FASTAMP,计算了汽车油底壳的成形过程,计算结果的厚度分布与实际冲压件吻合比较好,验证了等效界面摩擦力约束处理方法的有效性.

考虑摩擦约束时面板温度应力的有限元分析

本文介绍了用有限元法模拟接触摩擦的方法 ,并计算分析了堆石体的摩擦约束对面板温度应力的影响 .研究分析表明 ,摩擦约束引起的平均拉应力最大值出现在靠近趾板的中下部 ,当摩擦角小于坝坡角时 ,面板内不会产生贯穿的拉应力 ,摩擦角大于坝坡角时 ,拉应力分布的数值存在上限 ,达到上限值之后 ,板内平均拉应力不再随温度变化而增大 .提高坝坡平整度 ,减小堆石体对面板的约束是避免贯穿裂缝的有效措施 .

板材冲压成形变形局部化与动边界摩擦约束

提出适于具有强烈弯曲效应的大应变、大位移与界面摩擦三重非线性空间曲壳有限元列式；给出一种动边界摩擦约束的元级代数消元方法．就板材在方盒型冲头作用下的冲压胀形过程，引入几种现代非经典塑性本构理论以及空单元技术；研究了成形过程中的变形局部化与断裂问题．

带摩擦约束的塑性形变理论的广义变分不等方程

非线性弹塑性力学的变分不等式原理是解决金属塑性加工中非线性问题的有效的、合理的理论基础针对带Ｃｏｕｌｏｍｂ摩擦约束的塑性形变理论引进Ｌａｇｒａｎｇｅ乘子，从最小势能的角度出发构造了考虑摩擦效应这一能导致变分不等形式的广义能量泛函，把一般的有条件的变分原理化为无条件的变分原理来唯一确定，并且得出了Ｌａｇｒａｎｇｅ乘子所代表的物理意义。

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.

摩擦约束不完全变分不等原理及其微粒群优化解法

利用不完全变分不等原理,将摩擦约束纳入问题的能量泛函,同时放松体积不可压缩的约束条件ε_(ii)=0,用罚因子处理体积应变。实际算例表明,不完全变分不等原理不但能计算速度场,而且能直接计算变形力,且所得到的变形力比滑移线场结合极值方法获得的解析解更接近试验结果。在有限变形情况下,仍能得到变形力的理想结果。同时,利用微粒群优化方法,直接求解变分问题的能量泛函,避开了变分不等式的求解困难问题。针对优化求解过程中出现解的随机性,利用求平均值方法,使求解过程稳定,有效地改善了求解结果,并由此扩展了微粒群算法的应用领域。

材料性能对搅拌摩擦焊焊缝成形的影响

采用左螺纹圆柱搅拌头对O态和T4态2024铝合金进行搅拌摩擦焊接试验,研究了材料性能对搅拌摩擦焊焊缝成形的影响,并用软性约束分析了材料性能对焊核尺寸的影响。试验结果表明:焊缝形貌受焊核周边金属约束的影响,约束程度与材料力学性能和温度有关。O态2024铝合金对接焊时,软性约束体对塑性金属横向迁移的约束小,焊核面积和焊核宽度较T4态2024铝合金的焊核面积和焊核宽度大。两种热处理状态2024铝合金对接焊时,强度和硬度较高的T4态2024铝合金置于返回边时,在焊缝两侧、前进边的软性约束体对塑性金属的约束较返回边的软性约束体对塑性金属的约束强,焊核向返回边偏移;由于在返回边有更多的塑性金属,使其沿焊缝厚度方向向上的运动趋势增强,因此返回边的焊核高度较前进边的焊核高度高。对T4态2024铝合金进行适当的预热,会增强焊缝金属的塑化程度,使其向焊缝两侧的迁移运动趋势增强,焊核宽度及面积增大。

刚塑性广义变分不等原理及其在平面应变分析中的应用

首先利用Lagrangian乘子法,从势能角度出发构造了考虑摩擦效应这一能导致变分不等形式的广义能量泛函,把一般的有条件的变分原理化为无条件的变分原理来唯一确定,得出了各Lagrangian乘子所代表的物理意义,建立了刚塑性理论中的Coulomb摩擦约束的广义变分不等原理。而后基于退化的摩擦约束广义变分等式原理,对长矩形板镦粗进行了塑性加工工步分析。所得结果与经典上限法结果相吻合。

平转连续梁桥主梁现浇施工中的摩阻效应

采用平转施工的连续梁桥,其转体梁段一般使用支架现浇的方式制作。在转体梁段分段长度较长的情况下,现浇梁体和模板接触面会产生较大的摩阻力和切向黏结应力,阻碍梁体的自由变形,因而增大预应力箱梁的应力损失。采用有限元分析软件,分析了现浇梁与底模支架之间的摩阻系数和模板约束情况,计算了预应力筋张拉时主梁最大悬臂状态各单元应力。结果表明:一定情况下此摩阻和约束效应对梁体有效预应力的影响是不能忽视的。

轮胎—松软地面相互作用有限元分析

采用改进的可变约束法 ,给出了松软地面条件下轮胎、地面相互作用处理方法。研究了稳态驱动条件下轮胎、松软地面之间相互作用 ,分析了接地印迹上摩擦接触特性及轮胎内部应力分布特性。结果表明 ,本方法能够处理轮胎和松软地面之间相互作用问题 。