柔性多体系统变形体离散方法研究

A Reasonable discretization method of the deformation body will play an important role in the flexible multibody systems. The assumed mode method and finite element method are most widely used at present. The assumed mode method cannot used to deal with large deformation, because its theory is based on the assumption of small deformation. Finite element method also has its drawbacks, low computational efficiency, element easily distorted, cannot maintain high-order continuous. So, Seeking new discretization methods is the project's aim, the efficient discretization theory of deformation bodies of flexible multibody systems is established by theoretical analysis and numerical simulation. The project will mainly focus on the following topics:.1. The Non-Uniform Rational B-Spline interpolation method which is widely used in computer aided design will be introduced to describe the deformable body of computer aided analysis, and then new discretization methods of deformation bodies can be proposed..2. The discretization methods of deformation bodies will be used to describe the displacement field which is based on the absolute nodal coordinate formulation. After that, the general continuum mechanics approach and the elastic line approach are used to formulate the elastic forces. Finally, the dynamic model which is based on the absolute nodal coordinate formulation is established..3. The dynamic simulation software for flexible multibody systems will be developed, and the dynamic behaviors of different discretization methods will be compared with each other.

一种合理的变形体离散方法将对柔性多体系统动力学产生举足轻重的作用。目前运用较广的有假设模态法和有限元法，假设模态法基于线性小变形假设，在处理大变形问题时存在缺陷；而有限元法也存在计算效率低，单元容易发生畸变、不能保持高阶连续等缺陷。针对目前柔性体变形场描述方法存在的缺陷,本课题拟通过理论分析与数值模拟提出高效的变形体离散理论。本课题的主要研究内容为:1、将计算机辅助设计中广泛应用的非均匀有理B样条插值方法引入到计算机辅助分析的变形体描述，从而提出新的变形体离散方法；2、将变形体离散方法用于描述基于绝对节点坐标法的柔性体位移场，同时给出求解弹性力的连续介质力学方法和弹性线方法，并最终建立基于绝对节点坐标法的动力学模型。3、研制出柔性多体系统动力学仿真软件，并分析变形体不同离散方法对系统动力学性态的影响。

一种合理的变形体离散方法将对柔性多体系统动力学产生举足轻重的作用。目前运用较广的有假设模态法和有限元法，假设模态法基于线性小变形假设，在处理大变形问题时存在缺陷；而有限元法也存在计算效率低，单元容易发生畸变、不能保持高阶连续等缺陷。针对目前柔性体变形场描述方法存在的缺陷，本课题通过理论分析与数值模拟提出高效的变形体离散理论。本项目的主要研究内容有：. 1. 在浮动坐标系方法中引入Bezier插值方法和B样条插值方法，并与目前应用广泛的有限元法和假设模态法构造柔性体变形场统一的表达形式，采用Bezier插值方法、B样条插值方法、假设模态法和有限元法对柔性梁变形场进行描述，通过第二类Lagrange方程建立中心刚体-柔性悬臂梁模型的动力学方程，并将动力学仿真结果与已有文献的仿真和实验进行对比，验证Bezier插值方法和B样条插值方法的准确性以及可推广性。将Bezier插值方法、B样条插值方法、假设模态法和有限元法推广到n个柔性铰和n根柔性杆组成的空间多杆刚柔耦合系统动力学模型的变形场描述中。基于递推的齐次变换矩阵方法和Lagrange动力学建模方法，建立柔性多体系统刚柔耦合动力学方程，并通过仿真实例说明变形场离散方法的正确性。. 2. 给出适用于几何非线性大变形问题的绝对节点坐标法，采用有限元法对基于绝对节点坐标法三维梁单元的位移场进行描述，同时给出求解弹性力的弹性线方法，并与已有连续介质力学方法进行比较，从理论分析以及动力学仿真上说明该方法的优越性。最后通过工程实例履带式车辆动力学仿真进一步阐述上述结论。. 3. 基于1、2两项研究内容的基础，编制动力学仿真软件，并选用稳定高效的微分-代数方程组的数值算法，基于变形体不同离散方法对柔性多体系统动力学问题进行仿真，分析变形体不同离散方法对系统动力学性态的影响，进而验证了方法的可行性和优越性。