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基于近场动力学的薄板弯曲大变形及断裂分析

申国哲 王瑞阳 夏阳 郑国君

申国哲, 王瑞阳, 夏阳, 郑国君. 基于近场动力学的薄板弯曲大变形及断裂分析. 力学学报, 2023, 55(2): 285-293 doi: 10.6052/0459-1879-22-519
引用本文: 申国哲, 王瑞阳, 夏阳, 郑国君. 基于近场动力学的薄板弯曲大变形及断裂分析. 力学学报, 2023, 55(2): 285-293 doi: 10.6052/0459-1879-22-519
Shen Guozhe, Wang Ruiyang, Xia Yang, Zheng Guojun. Large deformation and fracture analysis of thin plate bending based on peridynamics. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 285-293 doi: 10.6052/0459-1879-22-519
Citation: Shen Guozhe, Wang Ruiyang, Xia Yang, Zheng Guojun. Large deformation and fracture analysis of thin plate bending based on peridynamics. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 285-293 doi: 10.6052/0459-1879-22-519

基于近场动力学的薄板弯曲大变形及断裂分析

doi: 10.6052/0459-1879-22-519
基金项目: 国家自然科学基金(12072065)和辽宁省应用基础研究计划(2022JH2/101300224)资助项目
详细信息
    通讯作者:

    郑国君, 副教授, 主要研究方向为车身结构轻量化. E-mail: gj_zheng@dlut.edu.cn

  • 中图分类号: O346.1

LARGE DEFORMATION AND FRACTURE ANALYSIS OF THIN PLATE BENDING BASED ON PERIDYNAMICS

  • 摘要: 薄板结构仅在较小的荷载下就能产生较大的位移、旋转, 甚至引发结构产生裂纹并扩展, 进而发生结构整体断裂, 因此, 建立薄板结构在大变形过程中的裂纹扩展及断裂仿真模型, 具有重要的工程实际意义. 文章建立了用于薄板结构几何大变形和断裂分析的近场动力学(PD)和连续介质力学(CCM)耦合模型. 首先基于冯·卡门假设, 采用更新的拉格朗日法得到薄板在几何大变形增量步下的虚应变能密度增量公式, 并利用虚功原理和均质化假设求出几何大变形微梁键的本构模型参数; 接着分别建立几何大变形薄板PD模型与CCM模型的虚应变能密度增量, 并建立了薄板几何大变形PD-CCM耦合模型; 最后模拟了薄板结构在横向变形作用下的渐进断裂过程, 得到与实验结果高度一致的仿真结果, 验证了所提出的几何非线性PD-CCM耦合模型的精度. 结果表明: 本文所提出的薄板PD-CCM耦合模型具有简单高效, 无需考虑材料参数限制和边界效应的特点, 可以很好地用于预测薄板结构在几何大变形过程中的局部损伤和结构断裂, 有利于薄板结构的断裂安全评价和理论发展.

     

  • 图  1  矩形板单元

    Figure  1.  Rectangular plate element

    图  2  PD板模型

    Figure  2.  Peridynamic plate model

    图  3  断裂表面示意图

    Figure  3.  Schematic of the fracture surface

    图  4  PD-CCM板耦合模型

    Figure  4.  PD-CCM plate coupling model

    图  5  带有预置裂纹的钢板

    Figure  5.  Steel plate with preset cracks

    图  6  预置裂纹的钢板渐进撕裂过程

    Figure  6.  Progressive tearing process of steel with preset cracks

    图  7  钢板撕裂的载荷-位移对比曲线

    Figure  7.  Load-displacement comparison curve of steel plate tearing

    图  8  带有预置裂纹的纸张

    Figure  8.  Paper with preset cracks

    图  9  含预置裂纹纸张的渐进撕裂过程

    Figure  9.  Progressive tearing process of paper with preset cracks

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出版历程
  • 收稿日期:  2022-11-02
  • 录用日期:  2023-01-08
  • 网络出版日期:  2023-01-09

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