约束多体系统动力学分析的改进的离散零空间算法

通过对已有离散零空间矩阵计算方法的改进,构造了改进的离散零空间等效变换公式,该公式可不依赖于特定的积分方法,能简洁、方便的与多种数值积分方法相结合。基于改进公式,提出了改进的离散零空间算法框架,并将该框架与一般变分积分法结合,构造了约束多体系统动力学分析的改进的离散零空间算法。通过曲柄滑块机构的数值实验,验证了改进的离散零空间等效变换公式的正确性,示例了其与数值积分算法的良好结合性,说明了改进算法的可行性和有效性。     

多体系统动力学方程的无违约数值计算方法

多体系统动力学方程为3阶微分代数方程,已有的约束违约稳定法存在位移违约问题,数值仿真准确性和稳定性不足。本文将求解高阶微分代数方程的降阶理论、ε嵌入处理方式与隐式龙格库塔法相结合,提出了直接满足位移约束条件的多体系统动力学方程的无违约算法,避免了约束违约问题。该方法先将多体动力学方程转化为2阶微分代数方程,并与位移约束方程联立;再应用ε嵌入隐式龙格库塔法进行数值求解。应用两种方法分别对单摆机构进行数值仿真,结果表明本文的方法不仅能适应较大步长,且准确性和稳定性均优于约束违约稳定法。     

基于龙格库塔法的多输出物理信息神经网络模型

物理信息神经网络(physics-informed neural networks, PINN)由于嵌入了物理先验知识,可以在少量训练数据的情况下获得自动满足物理约束的代理模型,受到了智能科学计算领域的广泛关注.但是, PINN的离散时间模型(PINN-RK)无法同时近似多个物理量相互耦合的偏微分方程系统,限制了其处理复杂多物理场的能力.为了打破这一限制,文章提出了一种基于龙格库塔法的多输出物理信息神经网络(multi-output physics-informed neural networks based on the Runge-Kutta method, MO-PINN-RK), MO-PINN-RK模型在离散时间模型的基础上采用了并行输出的神经网络结构,通过将神经网络划分为多个子网络,建立了多个神经网络输出层.采用不同输出层近似不同物理量的方式, MO-PINN-RK模型不仅可以同时表征多个物理量,而且还能够实现求解偏微分方程系统的目的.另外, MO-PINN-RK克服了PINN离散时间模型仅适用于一维空间的局限性,将其应用范围扩展到了更为普遍的多维空间.为了验证MO-PIN...     

带约束非线性多体系统动力学方程数值分析方法

Lagrange方法是建立带约束多体系统动力学方程的普遍方法之一 ,其方程的形式为微分 代数方程组 ,数值计算与数值分析是研究多体系统动力学特性的重要方法。本文利用缩并法给出了带约束多体系统动力学方程的隐式数值计算方法和Lyapunov指数的计算方法。将数值仿真、Lya punov指数计算和Poincare映射有机结合 ,分析非线性多体系统动力学行为。通过一个算例 ,说明该方法的有效性     

具有奇异位置的多体系统动力学方程的隐式算法

本文研究了在运动过程中具有奇异位置的多体系统动力学方程的隐式算法，给出了隐式算法所用的Ｊａｃｏｂｉ矩阵，并建立了该矩阵中各子矩阵间的计算关系，提高了计算效率，计算结果表明隐式算法的计算速度和精度明显优于显式算法。     

带约束多体系统动力学方程的隐式算法

研究了带约束多体系统隐式算法,用子矩阵的形式推导出了多体系统正则方程的Ｊａｃｏｂｉ矩阵,它适用于多种隐式算法并给出了隐式Ｒｕｎｇｅ－Ｋｕｔｔａ算法,最后用一算例表明了隐式算法的计算效率和精度明显优于算法。     

多体系统动力学约束Hamilton方程多步块方法

针对多体系统动力学Hamilton体系正则微分-代数方程,基于等距节点、Chebyshev节点、Legendre节点等非等距节点,在时间区间上建立r-级多步块求解格式,得到单步区间各节点的非线性代数方程,求解过程利用Newton迭代.以双连杆机械臂系统为例,使用r-级多步块格式进行数值仿真,通过改变步长、仿真时间以及节...     

多体系统Euler-Lagrange方程组的一类新数值分析方法

针对受完整约束的多体系统,首先指出其动力学Euler-Lagrange方程组是高指标(index>2)的微分代数方程组;不同于传统的直接增广法和直接消去法,文中提出了一类将微分代数方程直接视为非线性代数方程组求解的新的数值分析方法;最后,以典型的单摆模型为例给出了新算法与其他方法的比较,结果表明新算法优于BDF方法及违约修正方法。     

树形多体系统动力学的隐式数值算法

研究了树形多体系统动力学的隐式算法．用矩阵形式给出了多体系统的正则方程及其右端函数的Ｊａｃｏｂｉ矩阵，并给出该矩阵的分块算法和对角隐式Ｒｕｎｇｅ－Ｋｕｔａ法（ＤＩＲＫＭ）以及隐式辛Ｒｕｎｇｅ－Ｋｕｔａ法（ＩＳＲＫＭ）．该算法便于编程计算，能提高计算效率，保持长期计算的稳定性．并用算例说明该算法的有效性     

多体系统动力学设计灵敏度分析直接微分法

针对受完整约束的多体系统动力学微分／代数方程数学模型动态最优化设计问题，建立了通用的目标函数和约束方程，并以此为基础，用直接微分方法系统地推导出了计算设计灵敏度的通用公式，最后通过平面机械臂模型对理论结果和相应算法进行了验证．     

约束多体系统动力学正则方程的约束变尺度方法

对约束多体系统动力学的正则方程建立了最优化问题模型,采用辛差分格式,提出相应的最优化问题的约束变尺度法,该方法有效地提高了计算稳定性,算例说明了方法的有效性。     

A new algorithm for solving differential/algebraic equations of multibody system dynamics

I.Intr0ductionTheequationsofmoti0nofconstrainedmultibodysystemdynamicscanbewrittenasfollows11lwherelistimeparameter*q6R'isgeneralizedcoordinatesvectorofsystem,M(q,t):RnXR-R"xnisgeneralizedmassn1atrixofsystem,k6RmisLagrangemultipliervector,fo(q,t):RnXR-R"(…     

Comparative study on multibody vehicle dynamics models based on subsystem synthesis method using Cartesian and joint coordinates

The subsystem synthesis method has been developed in order to improve computational efficiency for a multibody vehicle dynamics model. Using the subsystem synthesis method, equations of motion of the base body and each subsystem can be solved separately. In the subsystem synthesis method, various coordinate systems can be used and various integration methods can be applied in each subsystem, as long as the effective mass matrix and the effective force vector are properly produced. In this paper, comparative study has been carried out for the subsystem synthesis method with Cartesian coordinates and with joint relative coordinates. Two different integration methods such as an explicit integrator and an explicit implicit integrator are employed. In order to see the accuracy and computational efficiency from the different models based on the different coordinate systems and different integration methods, a rough terrain run simulations has been carried out with a 6 × 6 off-road multibody vehicle model.     

Singularity-free augmented Lagrangian algorithms for constrained multibody dynamics

After a general review of the methods currently available for the dynamics of constrained multibody systems in the context of numerical efficiency and ability to solve the differential equations of motion in singular positions, we examine the acceleration based augmented Lagrangian formulations, and propose a new one for holonomic and non-holonomic systems that is based on the canonical equations of Hamilton. This new one proves to be more stable and accurate that the acceleration based counterpart under repetitive singular positions. The proposed algorithms are numerically efficient, can use standard conditionally stable numerical integrators and do not fail in singular positions, as the classical formulations do. The reason for the numerical efficiency and better behavior under singularities relies on the fact that the leading matrix of the resultant system of ODEs is sparse, symmetric, positive definite, and its rank is independent of that of the Jacobian of the constraint equations. The latter fact makes the proposed method particularly suitable for singular configurations.     

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.     

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｙｎａｍｉｃｅｑｕａｔｉｏｎｓｏｆｍｏｔｉｏｎｏｆｍｕｌｔｉｂｏｄｙｓｙｓｔｅｍｓｗｉｔｈｃｏｎｓｔｒａｉｎｔｓａｒｅｔｈｅｆｏｌｌｏｗｉｎｇｄｉｆｆｅｒｅｎｔｉａｌ／ａｌｇｅｂｒａｉｃｅｑｕａｔｉｏｎｓ,ｉ．ｅ．,Ｅ...     

Screw-matrix method in dynamics of multibody systems

In the present paper the concept of screw in classical mechanics is expressed in matrix form, in order to formulate the dynamical equations of the multibody systems. The mentioned method can retain the advantages of the screw theory and avoid the shortcomings of the dual number notation. Combining the screw-matrix method with the tool of graph theory in Roberson/Wittenberg formalism. We can expand the application of the screw theory to the general case of multibody systems. For a tree system, the dynamical equations for eachj-th subsystem, composed of all the outboard bodies connected byj-th joint can be formulated without the constraint reaction forces in the joints. For a nontree system, the dynamical equations of subsystems and the kinematical consistency conditions of the joints can be derived using the loop matrix. The whole process of calculation is unified in matrix form. A three-segment manipulator is discussed as an example. This work is supported by the National Natural Science Fund.