非线性动力学中基于T样条的局部变网格等几何实体单元  

T-spline based isogeometric solid element with locally varying mesh in nonlinear dynamics

作　　者：王悦 兰朋 陆念力 於祖庆 付松 Yue Wang;Peng Lan;Nianli Lu;Zuqing Yu;Song Fu(School of Mechatronics Engineering,Harbin Institute of Technology,Harbin,150001,China;State Key Laboratory of Green Building in Western China,Xi’an University of Architecture&Technology,Xi’an,710055,China;School of Mechanical and Electrical Engineering,Xi’an University of Architecture and Technology,Xi’an,710055,China;College of Mechanical&Electrical Engineering,Hohai University,Changzhou,213022,China)

机构地区：[1]School of Mechatronics Engineering,Harbin Institute of Technology,Harbin,150001,China [2]State Key Laboratory of Green Building in Western China,Xi’an University of Architecture&Technology,Xi’an,710055,China [3]School of Mechanical and Electrical Engineering,Xi’an University of Architecture and Technology,Xi’an,710055,China [4]College of Mechanical&Electrical Engineering,Hohai University,Changzhou,213022,China

出　　处：《Acta Mechanica Sinica》2024年第2期162-181,共20页力学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant No.12272123);the Applied Fundamental Research Program of Changzhou(Grant No.CJ20220058);the Opening Fund of State Key Laboratory of Green Building in Western China(Grant No.LSKF202327);the Independent research project of State Key Laboratory of Green Building in west China(Grant No.LSZZ202209);the Fellowship of China Postdoctoral Science Foundation(Grant No.2022M720955).

摘　　要：为了解决三维空间中的非线性动力学问题,本文提出了一种新的等几何实体单元,并通过张量分析中的坐标变换得到其非线性应变场.为了使所提出的单元能够无缝地应用于计算机辅助设计(CAD)和计算机辅助工程(CAE)系统中,采用三变量T样条作为等几何实体单元的基函数.借助Bézier投影法,提出了基于T样条的等几何实体单元的局部网格更新算法.在重要区域对网格进行局部细化以获得准确的结果,在重要区域以外对冗余单元进行粗化以提高计算效率.因此,非线性动力学分析中的计算效率和计算精度得到了平衡.三个静力学数值算例验证单元弹性模型的正确性.通过柔性摆仿真算例研究该单元的动力学特性.通过实验测试该单元解决非线性动力学实际问题的能力.应用局部网格更新算法进行柔性摆与障碍物碰撞接触的仿真.通过对计算结果和计算耗时的分析,研究基于局部变网格T样条的实体单元在非线性动力学问题中的有效性.To solve nonlinear dynamic problems in three-dimensional space,this investigation presents a new isogeometric solid element and nonlinear strain field of the proposed element through coordinate transformation in tensor analysis.In order to make the proposed element can be used seamlessly in computer aided design(CAD)and computer aided engineering(CAE)systems,trivariate T-spline is adopted as the basis function of the isogeometric solid element.Local mesh update algorithms are developed for T-spline based isogeometric solid element in virtue of Bézier projection method.Mesh is refined locally in important regions to obtain accurate results and redundant elements are coarsened beyond important regions to improve computational efficiency.Therefore,the computational efficiency and the computational accuracy are balanced in nonlinear dynamics analysis.Three statics numerical examples are set to test the correctness of the elemental elastic model.A flexible pendulum simulation is performed to study the dynamics characteristic of the proposed element.An experiment is implemented to test the proposed element’s ability to solve nonlinear dynamics problems.A simulation that a flexible pendulum contacts with a stick is performed and local mesh update algorithms are employed.The computation results and computation time are analyzed to research the effectiveness of the proposed locally varying mesh T-spline based solid element in nonlinear dynamics problems.

关 键 词：非线性动力学 实体单元 张量分析 坐标变换 投影法 BÉZIER 变网格 三变量 

分 类 号：O342[理学—固体力学]