Numerical Simulation of Behavior of Cable Wave under High-speed Impact via SPH Algorithm
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摘要: 针对高速冲击下钢索波动行为问题, 分别采用人工黏性与镜像粒子法相结合的SPH算法和FEM对冲击过程进行数值模拟, 得到了高速冲击下钢索应力波的传播规律。结果对比可知: 钢索中心处产生形变时粒子相互挤压, 内外两侧部分粒子产生反应力; 外侧产生断裂时, 波峰处粒子产生相切于应力传递方向较大主应力, 且中心带粒子呈圆弧状分布; 内侧未断裂时, 部分粒子产生绝对值较大的反应力; 完全断裂后, 中心处粒子主应力方向指向冲击方向; 冲击应力随着冲击角度的增大而减小, 随着摩擦因数的增大而增大。通过理论验证了仿真模型的准确性, 具有重要的工程借鉴价值。两种算法的系统总能量损耗相似, 但采用SPH算法对进行数值模拟计算的精度更高, 效率更高, 表明了SPH算法的优越性。Abstract: Aiming at the wave behavior of steel cable under high-speed impact, SPH algorithm combining with artificial viscosity and mirror particle method and FEM method are used to simulate the impact process, and the propagation law in stress wave of steel cable under high-speed impact is obtained. The results show that when the deformation occurs at the center of the cable, the particles squeeze each other, and some particles on both sides produce reaction forces. When the fracture occurs in the outside, the particles at the wave crest are tangent to each other and the main stress is larger in the direction of stress transfer, and the particles in the central zone are distributed in an arc shape. When the inner side is not broken, some particles produce larger absolute reaction force. After complete fracture, the main stress direction of the particle at the center points to the impact direction. The impact stress decreases with the increasing of impact angle and increases with the increasing of friction coefficient. The accuracy of the model is verified by theoretical comparison, which has engineering reference. The total energy loss of the two algorithms is similar, but the SPH method is more accurate and efficient, which shows the superiority of SPH method.
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Key words:
- steel cable /
- high-speed impact /
- SPH algorithm /
- FEM /
- numerical simulation
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表 1 不同金属材料Mie-Gruneisen状态方程中的参数
材料 ρ0/(kg·m-3) Γ c0/(m·s-1) λ 钢 7 890 1.587 3 075 1.294 铝 2 790 2.000 5 330 1.340 铜 8 960 2.000 3 940 1.489 表 2 不同冲击速度下的钢索波动参数(SPH算法)
冲击速度/ (m·s-1) 波速名称 理论值/ (m·s-1) 仿真值/ (m·s-1) 误差/% 260 纵波 5188.75 5 000.00 3.64 横波 559.75 555.60 0.74 弯折波 505.88 476.20 5.87 270 纵波 5188.75 5 000.00 3.64 横波 574.01 569.64 0.79 弯折波 517.53 488.86 5.54 280 纵波 5188.75 5 002.00 3.60 横波 588.10 588.20 0.02 弯折波 529.00 501.00 5.29 290 纵波 5188.75 5 001.00 3.62 横波 602.02 593.21 1.47 弯折波 540.21 513.22 5.00 300 纵波 5 188.75 5 000.01 3.64 横波 615.78 606.11 1.57 弯折波 551.37 526.30 4.55 表 3 不同冲击速度下的钢索波动参数(FEM算法)
冲击速度/ (m·s-1) 波速名称 理论值/ (m·s-1) 仿真值/ (m·s-1) 误差/% 260 纵波 5188.75 4 877.43 6.00 横波 559.75 498.18 10.89 弯折波 505.88 447.70 11.50 270 纵波 5188.75 4 876.39 6.02 横波 574.01 517.76 9.80 弯折波 517.53 456.72 11.75 280 纵波 5188.75 4 877.42 6.00 横波 588.10 525.58 10.63 弯折波 529.00 466.95 11.73 290 纵波 5188.75 4 877.43 6.00 横波 602.02 535.80 11.00 弯折波 540.21 473.76 12.30 300 纵波 5188.75 4 877.94 5.99 横波 615.78 549.90 10.70 弯折波 551.37 486.97 11.68 -
[1] 张志春, 卞强, 展文豪, 等. 高速冲击问题的SPH粒子接触算法三维数值计算[J]. 兵器装备工程学报, 2018, 39(9): 1-6 doi: 10.11809/bqzbgcxb2018.09.001ZHANG Z C, BIAN Q, ZHAN W H, et al. High velocity impact simulation using SPH contact algorithm[J]. Journal of Ordnance Equipment Engineering, 2018, 39(9): 1-6 (in Chinese) doi: 10.11809/bqzbgcxb2018.09.001 [2] 肖毅华, 张浩锋, 胡德安, 等. 基于改进PIB搜索法的SPH方法在高速冲击模拟中的应用[J]. 振动与冲击, 2015, 34(23): 88-92 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201523017.htmXIAO Y H, ZHANG H F, HU D A, et al. Application of SPH with modified PIB search algorithm to high-velocity impact simulation[J]. Journal of Vibration and Shock, 2015, 34(23): 88-92 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201523017.htm [3] 赵光明, 宋顺成. 非线性侵彻动力过程的再生核质点法[J]. 爆炸与冲击, 2010, 30(4): 355-360 https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ201004004.htmZHAO G M, SONG S C. An improved reproducing kernel particle method for nonlinear dynamical penetration process[J]. Explosion and Shock Waves, 2010, 30(4): 355-360 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ201004004.htm [4] ZHANG Z L, LIU M B. Smoothed particle hydrodynamics with kernel gradient correction for modeling high velocity impact in two-and three-dimensional spaces[J]. Engineering Analysis with Boundary Elements, 2017, 83: 141-157 doi: 10.1016/j.enganabound.2017.07.015 [5] SUN P N, TOUZÉ D L, OGER G, et al. An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 2: extension of the scheme to cylindrical coordinates and simulations of 3D axisymmetric problems with experimental validations[J]. Journal of Computational Physics, 2021, 426: 109936 doi: 10.1016/j.jcp.2020.109936 [6] WANG W, WU Y J, WU H, et al. Numerical analysis of dynamic compaction using FEM-SPH coupling method[J]. Soil Dynamics and Earthquake Engineering, 2021, 140: 106420 doi: 10.1016/j.soildyn.2020.106420 [7] MARKAUSKAS D, KRUGGEL-EMDEN H. Coupled DEM-SPH simulations of wet continuous screening[J]. Advanced Powder Technology, 2019, 30(12): 2997-3009 doi: 10.1016/j.apt.2019.09.007 [8] SCAZZOSI R, GIGLIO M, MANES A. FE coupled to SPH numerical model for the simulation of high-velocity impact on ceramic based ballistic shields[J]. Ceramics International, 2020, 46(15): 23760-23772 doi: 10.1016/j.ceramint.2020.06.151 [9] YOUNG J, TEIXEIRA-DIAS F, AZEVEDO A, et al. Adaptive Total Lagrangian Eulerian SPH for high-velocity impacts[J]. International Journal of Mechanical Sciences, 2021, 192: 106108 doi: 10.1016/j.ijmecsci.2020.106108 [10] VARAS D, ZAERA R, LÓPEZ-PUENTE J. Numerical modelling of the hydrodynamic ram phenomenon[J]. International Journal of Impact Engineering, 2009, 36(3): 363-374 doi: 10.1016/j.ijimpeng.2008.07.020 [11] VARAS D, LÓPEZ-PUENTE J, ZAERA R. Numerical analysis of the hydrodynamic ram phenomenon in aircraft fuel tanks[J]. AIAA Journal, 2012, 50(7): 1621-1630 doi: 10.2514/1.J051613 [12] VARAS D, ZAERA R, LÓPEZ-PUENTE J. Numerical modelling of partially filled aircraft fuel tanks submitted to Hydrodynamic Ram[J]. Aerospace Science and Technology, 2012, 16(1): 19-28 doi: 10.1016/j.ast.2011.02.003 [13] ST-GERMAIN P, NISTOR L, TOWNSEND R, et al. Smoothed-particle hydrodynamics numerical modeling of structures impacted by tsunami bores[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2014, 140(1): 66-81 doi: 10.1061/(ASCE)WW.1943-5460.0000225 [14] 初文华, 明付仁, 张健. 三维SPH算法在冲击动力学中的应用[M]. 北京: 科学出版社, 2017: 16CHU W H, MING F R, ZHANG J. Application of three-dimensional SPH algorithm in impact dynamics[M]. Beijing: Science Press, 2017: 16 (in Chinese) [15] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994, 110(2): 399-406 doi: 10.1006/jcph.1994.1034 [16] SHIN Y S, LEE M, LAM K Y, et al. Modeling mitigation effects of watershield on shock waves[J]. Shock and Vibration, 1998, 5: 782032 [17] LIBERSKY L D, PETSCHEK A G, CARNEY T C, et al. High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response[J]. Journal of Computational Physics, 1993, 109(1): 67-75 doi: 10.1006/jcph.1993.1199