A MULTI-RESOLUTION PD-SPH COUPLING APPROACH FOR STRUCTURAL FAILURE UNDER FLUID-STRUCTURE INTERACTION
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摘要: 流固耦合破坏是一类涉及结构变形与破坏以及复杂自由表面现象的强非线性力学问题. 结合近场动力学(peridynamics, PD)与光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)各自的优势并考虑其计算效率问题, 提出一种适用于分析流−固耦合破坏问题的多分辨率PD-SPH混合方法. 分别采用SPH和PD方法以不同的空间和时间分辨率对流体和结构进行离散与求解, 利用具有与流体粒子相同光滑长度的虚粒子处理流−固界面, 以高精度满足界面边界条件. 通过两个经典算例: 液柱静压力下弹性板的变形和溃坝流体冲击弹性闸门的变形问题, 表明提出的多分辨率PD-SPH方法兼具较高的计算精度和计算效率; 对含裂缝的Koyna重力坝水力劈裂问题进行模拟计算, 所得裂缝扩展路径与文献结果吻合, 说明该方法适用于涉及结构破坏的流固耦合问题仿真. 最后尝试采用该方法进行流体冲击作用下含裂纹混凝土板崩塌过程数值仿真, 准确描述混凝土板的断裂破坏和全过程中的流体运动. 多分辨率PD-SPH混合方法或可为流−固耦合作用下的结构损伤破坏仿真提供一种新选择.Abstract: Structural failure under fluid-structure interaction (FSI) is a type of strong nonlinear problem, which involves structural motion, deformation and failure as well as complex free-surface flows. Considering the respective advantages of peridynamics (PD) and smoothed particle hydrodynamics (SPH) as well as their computational efficiency, a multi-resolution PD-SPH coupling approach suitable for solving complicated FSI-concerned structural failure problems was proposed. The fluid and solid are discretized and solved by using SPH and PD approaches with different spatial and temporal resolutions, respectively. To achieve the precise satisfaction of interface boundary conditions, the fluid-structure interface is treated by using virtual particle technology, in which the same smoothing length of virtual particles as fluid particles is adopted. The modeling and analysis for two benchmark tests: large deformation of an elastic plate with hydrostatic pressure, and dam-break flow through an elastic gate, show that the presented multi-resolution PD-SPH coupling strategy and approach is suitable for simulating fluid-structure-interaction problems with satisfactory accuracy and efficiency. Further, the process of hydraulic fracture in Koyna gravity dam with an initial crack is simulated, and the cracking path in the simulation agrees well with available literature results, which indicates that the proposed coupling approach is appropriate for solving FSI-concerned structural failure problems. Finally, the proposed coupling strategy and numerical approach is employed to investigate the collapse process of a concrete slab due to fluid flow impacting, and the whole process of the concrete slab fracture as well as the motion of the fluid are captured with high accuracy. The results show that the proposed multi-resolution PD-SPH coupling approach may provide a potential alternative to simulate the process of structural failure under fluid-structure interaction.
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图 3 多分辨率PD-SPH耦合计算流程
Figure 3. Flow chart for multi-resolution PD-SPH coupling calculation
图 4 液柱静压力下铝板变形的初始条件(单位: m)
Figure 4. Initial condition for the aluminum plate under hydrostatic pressure (unit: m)
图 6 t = 5 s时工况III的流体压力场与板的挠度场
Figure 6. Fluid pressure and plate deflection field in case-III at t = 5 s
图 7 FSI系统归一化总能量时间历程
Figure 7. Time histories for normalized total energy of FSI system
图 9 溃坝流体冲破弹性闸门的初始条件示意图(单位: mm)
Figure 9. Schematic sketch for initial conditions in the dam-break flow through an elastic gate (unit: mm)
图 10 不同时刻弹性闸门变形和自由液面演变
Figure 10. Elastic gate deformation and change of fluid free surface
图 11 弹性闸门自由端水平位移时程
Figure 11. Time histories of horizontal displacements at the free end of elastic gate
图 16 水流冲击混凝土板模型(单位: m)
Figure 16. Model of water impacting on a concrete slab (unit: m)
图 17 水流冲击作用下混凝土板崩塌过程
Figure 17. Collapse process of concrete slab subjected to impact of water flow
表 1 液柱静压力下铝板变形问题工况布置
Table 1. The setup of different cases for aluminum plate deformation with hydrostatic pressure
Cases $\dfrac{{d{x_{\text{F}}}}}{{d{x_{\text{S}}}}}$ $d{x_{\text{S}}}{\text{/m}}$ $\dfrac{{\Delta {t_{\text{F}}}}}{{\Delta {t_{\text{S}}}}}$ $ \Delta {t_{\text{S}}}{\text{/s}} $ I 1.0 6.25 × 10−3 5.0 1.0 × 10−6 II 2.0 6.25 × 10−3 10.0 1.0 × 10−6 III 4.0 6.25 × 10−3 20.0 1.0 × 10−6 
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表 2 溃坝流体冲破弹性闸门问题工况布置
Table 2. The setup of different cases for dam-break flow through an elastic gate
Cases $\dfrac{{d{x_{\text{F}}}}}{{d{x_{\text{S}}}}}$ $d{x_{\text{S}}}{\text{/m}}$ $\dfrac{{\Delta {t_{\text{F}}}}}{{\Delta {t_{\text{S}}}}}$ $ \Delta {t_{\text{S}}}{\text{/s}} $ I 1.0 1.0 × 10−3 1.0 5.0 × 10−6 II 2.0 1.0 × 10−3 1.0 5.0 × 10−6 III 2.0 1.0 × 10−3 4.0 5.0 × 10−6
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