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非齐次弹性力学问题双互易边界元方法研究

潘先云 余江鸿 周枫林

潘先云,余江鸿,周枫林. 非齐次弹性力学问题双互易边界元方法研究 [J]. 应用数学和力学,2022,43(9):1004-1015 doi: 10.21656/1000-0887.420208
引用本文: 潘先云,余江鸿,周枫林. 非齐次弹性力学问题双互易边界元方法研究 [J]. 应用数学和力学,2022,43(9):1004-1015 doi: 10.21656/1000-0887.420208
PAN Xianyun, YU Jianghong, ZHOU Fenglin. Research on the Dual Reciprocity Boundary Element Method for Non-Homogeneous Elasticity Problems[J]. Applied Mathematics and Mechanics, 2022, 43(9): 1004-1015. doi: 10.21656/1000-0887.420208
Citation: PAN Xianyun, YU Jianghong, ZHOU Fenglin. Research on the Dual Reciprocity Boundary Element Method for Non-Homogeneous Elasticity Problems[J]. Applied Mathematics and Mechanics, 2022, 43(9): 1004-1015. doi: 10.21656/1000-0887.420208

非齐次弹性力学问题双互易边界元方法研究

doi: 10.21656/1000-0887.420208
基金项目: 国家自然科学基金(11602082);湖南省教育厅科学研究项目(19B145);湖南省自然科学基金(2021JJ30211;2021JJ50043)
详细信息
    作者简介:

    潘先云(1996—),男,硕士生 (E-mail:1395779254@qq.com)

    周枫林(1986—),男,副教授,博士,硕士生导师 (通讯作者. E-mail:edwal0zhou@163.com)

  • 中图分类号: O343

Research on the Dual Reciprocity Boundary Element Method for Non-Homogeneous Elasticity Problems

  • 摘要:

    基于弹性力学边界元方法理论,将边界元法与双互易法结合,采用指数型基函数对非齐次项进行插值得到双互易边界积分方程。将边界积分方程离散为代数方程组,利用已知边界条件和方程特解求解方程组,得出域内位移和边界面力。指数型基函数的形状参数是由插值点最近距离的最小值决定,采用这种形状参数变化方案,分析径向基函数(RBF)插值精度以及插值稳定性。再次将指数型基函数应用到双互易边界元法中,分析双互易边界元方法下计算精度及稳定性,验证了指数型插值函数作为双互易边界元方法的径向基函数解决弹性力学域内体力项问题的有效性。

  • 图  1  正方体RBF插值点位置

    Figure  1.  Positions of RBF interpolation points in a cube

    图  2  正方体RBF插值精度

    Figure  2.  Accuracies of the cube RBF interpolation

    图  3  正方体RBF矩阵条件数

    Figure  3.  The condition number of the cube RBF matrix

    图  4  球体插值点位置

    Figure  4.  The sphere interpolation point positions

    图  5  边界上面力的相对误差

    Figure  5.  Relative errors of the surface force on the boundary

    图  6  RBF矩阵条件数

    Figure  6.  The condition number of the RBF matrix

    图  7  弯管几何图示(单位:mm)

    Figure  7.  The geometric model of an elbow pipe (unit: mm)

    图  8  弯管插值点位置

    Figure  8.  Positions of interpolation points of the elbow pipe

    图  9  取样点位置

    Figure  9.  Positions of sampling points

    图  10  边界上面力的相对误差

    Figure  10.  Relative errors of the surface force on the boundary

    图  12  取样点面力结果

    Figure  12.  Surface force results at sampling points

    图  13  取样点位移结果

    Figure  13.  Displacement results at sampling points

    图  11  RBF矩阵条件数

    Figure  11.  The condition number of the RBF matrix

    图  14  几何尺寸图 (单位:mm)

    Figure  14.  Geometric dimensions (unit: mm)

    图  15  载荷和约束

    Figure  15.  Loads and constraints

    图  16  有限元单元离散

    Figure  16.  Finite element discretization

    图  17  取样点位置

    Figure  17.  Sampling point positions

    图  18  取样点的位移

    Figure  18.  Displacements of sampling points

    表  1  取样点坐标

    Table  1.   Coordinates of sampling points

    numbercoordinatenumbercoordinate
    1(−0.9,0.160339,−4.364 77E−5)8(−0.2,0.896487,0.00340492)
    2(−0.8,0.285303,0.000256563)9(−0.1,0.99639,0.00353746)
    3(−0.7,0.393038,0.000830132)10(0,1.09467,0.00435635)
    4(−0.6,0.495195,0.00159942)11(0.1,1.19221,0.00445896)
    5(−0.5,0.596386,0.00213329)12(0.2,1.28571,0.00584447)
    6(−0.4,0.695987,0.00304904)13(0.3,1.37162,0.00800908)
    7(−0.3,0.796319,0.003251)14(0.4,1.45135,0.0105322)
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出版历程
  • 收稿日期:  2021-07-26
  • 修回日期:  2022-02-16
  • 网络出版日期:  2022-07-15
  • 刊出日期:  2022-09-30

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