基于T样条的变网格等几何薄板动力学分析  

DYNAMIC ANALYSIS OF VARIABLE MESH ISOGEOMETRIC THIN PLATE BASED ON T-SPLINE

作　　者：王悦 崔雅琦 於祖庆 兰朋[1] 陆念力[1] Wang Yue;Cui Yaqi;Yu Zuqing;Lan Peng;Lu Nianli(School of Mechatronics Engineering,Harbin Institute of Technology,Harbin 150001,China;College of Mechanical&Electrical Engineering,Hohai University,Changzhou 213002,Jiangsu,China)

机构地区：[1]哈尔滨工业大学机电工程学院,哈尔滨150001 [2]河海大学机电工程学院,江苏常州213002

出　　处：《力学学报》2021年第8期2323-2335,共13页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11802072);湖南省科技重大专项(2018GK1040)资助项目。

摘　　要：具有大位移、大变形的薄板在接触碰撞等工况下,其局部应变会产生剧烈变化.为了保证对其进行动力学分析的精度和计算效率,本文整合计算机辅助设计(CAD)与计算机辅助工程(CAE)系统,提出了一种基于T样条曲面的变网格柔性系统等几何分析方法.首先,建立基于T样条曲面单元的基尔霍夫薄板运动学模型,并根据非线性格林-拉格朗日应变建立由T样条曲面单元离散的薄板弹性模型.其次,通过在T网格中的局部区域插入节点的方式,达到T样条曲面网格局部更新的目的.利用T样条混合函数细化算法得到计算新广义变量的转换矩阵,并结合广义α法创建了变自由度系统动力学方程的求解算法,形成了系统的T样条单元局部细化算法.最后,静力学算例与柔性单摆模型分别验证了T样条薄板弹性模型的正确性,以及T样条薄板单元在动力学分析上的精度和收敛性.通过对受冲击柔性薄板的动力学分析表明,本文所提出T样条单元及局部细化算法可以只在接触碰撞等应变剧烈变化的区域实现局部网格细化,从而控制系统自由度数,提高计算效率.The local strain of a thin plate with large displacement and large deformation will change dramatically under contact and collision working conditions. In order to ensure the accuracy and computational efficiency of flexible thin plate system’s dynamic analysis, this investigation integrates computer aided design(CAD) and computer aided engineering(CAE) systems, and proposes an isogeometric analysis(IGA) method for variable mesh flexible multibody system based on T-spline surface elements. Firstly, the kinematic description of a Kirchhoff thin plate based on T-spline surface elements is modeled, and the elastic model of a thin plate discretized by T-spline surface elements is established according to the nonlinear Green-Lagrange strain. Secondly, the goal of updating mesh of T-spline surface locally is achieved by inserting knots into the local region of the corresponding T-mesh. The transformation matrix, which is used to calculate the new generalized coordinates, generalized velocities and generalized accelerations of the refined system,is obtained by using the T-spline blending function refinement algorithm. The calculating solution algorithm for the dynamic equation of the system with variable degrees of freedom is created by combining the generalized α method with geometry update routine, and thus the local mesh refinement algorithm for the surface which is modeled by Tspline is formed. Finally, statics examples and flexible pendulum model verify the correctness for the elastic model of Kirchhoff thin plate based on T-spline surface, as well as computation precision and convergence for the proposed method in the dynamics analysis respectively. The dynamic analysis of the impacted flexible thin plate shows that the T-spline element and local refinement algorithm proposed in this paper can realize local mesh update only in the area where the strain changes violently, such as contact and collision, so as to control the degree of freedom of the system and improve the computational efficiency.

关 键 词：T样条 基尔霍夫薄板 等几何分析 多柔体系统动力学 

分 类 号：O313.7[理学—一般力学与力学基础]