本文主要研究基于绝对节点坐标的柔性多体系统动力学建模和计算方法，主要工作包括：首先，给出了多体系统动力学基于绝对节点坐标单元的系统建模方法。利用Lagrange方程统一描述了三类大变形有限单元，包括绝对节点坐标索/梁单元、板/壳单元和6种三维实体单元（一次、二次插值类型的四面体、五面体和六面体单元）。提出了将柔性体节点的绝对坐标与刚体广义坐标直接组集的处理约束的方法，减少了系统的广义坐标数和约束方程数，从而降低了系统动力学方程的求解规模。针对柔性体中的碰撞检测问题，提出了将体间的碰撞检测转化为基本几何体包括球、长方体、圆柱和三角面片之间的三维面-面碰撞检测的方法，统一解决了柔性体和柔性体、柔性体和刚体、刚体和刚体之间的碰撞检测问题。其次，根据多体系统微分代数方程积分时的非线性迭代矩阵的块结构和稀疏性，提出了两次运用基于一维变带宽存储的线性方程组高效求解算法和结构并行计算方法。利用线性方程组的求解算法并结合面向对象的编程思想，设计并实现了包含三类绝对节点坐标单元的多体系统动力学求解器THUSolver。该求解器包括多体系统动力学方程求解、静力学方程求解和扰动方程的特征值求解三个模块，可对大变形、非线性及复杂接触的大规模多体系统动力学问题进行模拟仿真。利用结构并行计算方法将系统分为若干个子结构后进行并行计算，提高了动力学方程的计算效率。最后，利用本文研制的多体系统动力学求解器THUSolver对11个数值和工程算例进行了仿真研究，包括单缸引擎中活塞环和气缸壁的碰撞模型、单缸引擎柔性连杆和船用柴油发动机曲柄的实体单元模型、移动带状板材的板单元模型、大型天线索杆式伸展臂模型等。这些算例验证了绝对节点坐标单元计算的正确性以及本文所研究的接触算法和求解算法的有效性，同时也表明与传统有限元方法相比，用绝对节点坐标方法对大变形柔性多体系统进行动力学分析具有一定的优势。
In this paper, flexible multibody system dynamics modeling and its calculation method based on absolute nodal coordinates have been studied, the main work includes:Firstly, a systematical modeling method of multibody system dynamics based on absolute nodal coordinate elements was given. By applying Lagrange equations, large deformation finite elements, including the absolute nodal coordinate cable/beam elements, plate/shell elements and the six kinds of three-dimensional solid elements (linear, secondary interpolation type of tetrahedral, pentahedral and hexahedral element), were uniformly described. A method of directly assembling nodal absolute coordinates into rigid body’s general coordinates was proposed to reduce the number of system generalized coordinates and constraint equations, thereby reducing the solution size of system motion equation. With regard to the collision detection problem in flexible bodies, a method was proposed to convert collision detection between the bodies into the three-dimensional surface-surface collision detection between basic geometries including the sphere, the cuboid, the cylinder and the triangular patches, that supplied a uniform solution of the collision detection between the flexible and flexible, flexible and rigid body, rigid body and rigid body.Secondly, the method of twice using linear equations solving algorithm based on one-dimensional variable-bandwidth storage and the structure parallel computing method were proposed by using the block structure and sparsity of the nonlinear Jacobian iteration matrix when solving differential algebraic equations of multibody system. A multibody system dynamics solver was designed and developed by using linear equations solving algorithm and object oriented programming. This solver has the function of dynamic analysis, static analysis and eigenvalue analysis, and it can simulate dynamics of large scale flexible multibody systems including large deformation nonlinearity and complex contact. By using structure parallel computing method the system is divided into several sub-structure for parallel computing to improve the computational efficiency of dynamic equations.Finally, eleven numerical and engineering examples were studied by using this multibody system dynamic solver, including contact model between piston ring and cylinder wall in single cylinder engine, solid element models of flexible connecting rod in single cylinder engine and crank in large marine diesel engine model, plate element model of moving web and large antenna deployable articulated mast model. These Simulations demonstrated the absolute nodal coordinate elements’ computation accuracy and efficiency of contact algorithm and computation algorithm proposed in this paper. And they also proved that, compared to the traditional finite element method, the absolute nodal coordinate formulation has its advantage of dynamic analysis of large deformation flexible multibody system.
