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基于键型近场动力学非连续Galerkin有限元法的爆炸毁伤模拟

成嘉禾 顾鑫 章青

成嘉禾, 顾鑫, 章青. 基于键型近场动力学非连续Galerkin有限元法的爆炸毁伤模拟[J]. 应用数学和力学, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338
引用本文: 成嘉禾, 顾鑫, 章青. 基于键型近场动力学非连续Galerkin有限元法的爆炸毁伤模拟[J]. 应用数学和力学, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338
CHENG Jiahe, GU Xin, ZHANG Qing. Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics[J]. Applied Mathematics and Mechanics, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338
Citation: CHENG Jiahe, GU Xin, ZHANG Qing. Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics[J]. Applied Mathematics and Mechanics, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338

基于键型近场动力学非连续Galerkin有限元法的爆炸毁伤模拟

doi: 10.21656/1000-0887.430338
基金项目: 

国家自然科学基金项目 12172121

国家自然科学基金项目 U1934206

中央高校科研业务费 B210201031

详细信息
    作者简介:

    成嘉禾(1997—),男,硕士生(E-mail: jexooooo@163.com)

    顾鑫(1991—),男,副研究员,硕士生导师(E-mail: xingu@hhu.edu.cn)

    通讯作者:

    章青(1963—),男,教授,博士生导师(通讯作者. E-mail: lxzhangqing@hhu.edu.cn)

  • (我刊编委章青来稿)
  • 中图分类号: O242;O342

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics

  • (Contributed by ZHANG Qing, M. AMM Editorial Board)
  • 摘要: 近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.
    (Contributed by ZHANG Qing, M. AMM Editorial Board)
    1)  (我刊编委章青来稿)
  • 图  1  传统有限元的连续网格(左)与非连续Galerkin有限元的网格(右)[22]

    Figure  1.  The continuous mesh of traditional finite elements (left) and the mesh of non-continuous Galerkin finite element (right)[22]

    图  2  含预制裂纹玻璃板及其外荷载

    Figure  2.  The pre-cracked glass panel and its external load

    图  3  本文方法(左)与Ha等[26]方法(右)得到的裂纹扩展模式(t=46 μs)

    Figure  3.  The crack propagation modes obtained with the present method (left) and the method of Ha et al. [26] (right) (t=46 μs)

    图  4  本文方法(上)与Ha等[26]方法(下)得到的裂纹在分叉点演变情况

      为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.

    Figure  4.  The evolution of crack bifurcation points obtained with the present method (top) and the method of Ha et al.[26] (bottom)

    图  5  左右两边固定约束(左)与四周固定约束(右)的几何模型

    Figure  5.  Geometric models with fixed constraints on the left and right sides (left) and fixed constraints on all sides (right)

    图  6  对边固定混凝土板迎爆面(上)与背爆面(下)的毁伤情况

    Figure  6.  The damages of the front surface (top) and the back surface (bottom) of the concrete slab fixed on the opposite sides

    图  7  四边固定混凝土板迎爆面(上)与背爆面(下)的毁伤情况

    Figure  7.  The damages of the front surface (top) and the back surface (bottom) of the concrete slab fixed on 4 sides

    图  8  0.5 m,0.6 m爆距下,起爆11.5 ms时刻混凝土板迎爆面(左)与背爆面(右)的毁伤情况

    Figure  8.  The damages of the front surface (left) and the back surface (right) of the concrete slab at 11.5 ms after detonation at 0.5 m, 0.6 m blast distances

    图  9  0.1 kg,0.3 kg炸药当量下,起爆11.5 ms时刻混凝土板迎爆面(左)与背爆面(右)的毁伤情况

    Figure  9.  The damages of the front surface (left) and the back surface (right) of the concrete slab at 11.5 ms after detonation for 0.1 kg, 0.3 kg explosive equivalents

    表  1  计算时间对比

    Table  1.   The computation time comparison

    Δx=1 mm Δx=0.5 mm Δx=0.25 mm
    present method 54 s 246 s 1 350 s
    conventional bond-based PD method 104 s 522 s 3 277 s
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-10-25
  • 修回日期:  2023-01-07
  • 刊出日期:  2023-04-01

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