粘接–映射混合算法及其对颗粒材料中板的振动特性分析
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摘要
结构与颗粒材料相互作用广泛存在于各工程领域,其研究过程中涉及的连续–离散耦合计算方法面对诸多挑战.本文提出了粘接–映射混合算法来研究连续体与离散介质耦合动力学问题.将连续体模型划分为内部区域及与颗粒接触的边界区域.边界区域采用粘接算法模拟连续体外部形状并使用高效的球形接触判断准则;提出一种包含Rayleigh阻尼映射的有限元映射质点弹簧算法来精确计算连续体内部区域内力和变形.二者相结合构成粘接–映射混合算法,并引入计算机集群和GPU(图形处理器)并行技术,对埋没于颗粒材料中受激振动固支方板的连续–离散耦合动力学问题进行了数值仿真研究.结果表明,粘接–映射混合算法有利于双层级并行算法的程序实现及优化,并在连续–离散耦合界面进行快速接触判断的同时实现对颗粒材料中方板位移、变形、振动形态等参数的研究.通过定幅扫频和定频变幅方式考察激振力频率和幅值对振动板非线性动力学行为的影响并观察到二倍周期现象,同时给出了该连续–离散耦合系统中颗粒体系的能量耗散特性.
The interaction between structure and granular materials exists widely in various engineering fields, and the research method of this continuum-discrete coupling problems faces numerous challenges. The composite-mapping hybrid algorithm is presented to research dynamics of continuum-discrete coupling problems. The continuum model is divided into the inner region and the border region of particle contact. In the border region, the composite spheres method is applied to construct the profile of continuum efficiently in order to facilitate fast contact detection between the continuum and particles. In the inner region, the finite element mapping method is introduced to precisely calculate the internal force and deformation of continuum, and the method also contains Rayleigh damping mapping processes. The program with the composite-mapping hybrid algorithm is developed based on the compute cluster and GPU parallel computing technique.The numerical simulation of the square vibration plate which supported at four fixed edges and buried in particles is doneto study continuum-discrete coupling dynamics problems. The results show that the proposed composite-mapping hybrid algorithm is appropriate for realization of the compute cluster and GPU paralleled computing technique and improvement of computational efficiency. In analysis on buried plate problems, motion and deformation of the plate can be easily and accurately measured by means of the algorithm. Simultaneously, contact detection can be achieved rapidly in the interface between continuum and discrete, and mechanical parameters of displacement, deformation and vibration modes can also be calculated. The influence of excitation frequency and amplitude on square plate's nonlinear vibration has been studied through excitation with constant amplitude-changing frequency and with constant frequency-changing amplitude, and the period-doubling has been found. Meanwhile, the energy dissipation of granular media in this continuum-discrete coupling system is provided.
The interaction between structure and granular materials exists widely in various engineering fields, and the research method of this continuum-discrete coupling problems faces numerous challenges. The composite-mapping hybrid algorithm is presented to research dynamics of continuum-discrete coupling problems. The continuum model is divided into the inner region and the border region of particle contact. In the border region, the composite spheres method is applied to construct the profile of continuum efficiently in order to facilitate fast contact detection between the continuum and particles. In the inner region, the finite element mapping method is introduced to precisely calculate the internal force and deformation of continuum, and the method also contains Rayleigh damping mapping processes. The program with the composite-mapping hybrid algorithm is developed based on the compute cluster and GPU parallel computing technique.The numerical simulation of the square vibration plate which supported at four fixed edges and buried in particles is doneto study continuum-discrete coupling dynamics problems. The results show that the proposed composite-mapping hybrid algorithm is appropriate for realization of the compute cluster and GPU paralleled computing technique and improvement of computational efficiency. In analysis on buried plate problems, motion and deformation of the plate can be easily and accurately measured by means of the algorithm. Simultaneously, contact detection can be achieved rapidly in the interface between continuum and discrete, and mechanical parameters of displacement, deformation and vibration modes can also be calculated. The influence of excitation frequency and amplitude on square plate's nonlinear vibration has been studied through excitation with constant amplitude-changing frequency and with constant frequency-changing amplitude, and the period-doubling has been found. Meanwhile, the energy dissipation of granular media in this continuum-discrete coupling system is provided.
引文
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2 Morfidis K.Vibration of Timoshenko beams on three-parameter elastic foundation.Computers and Structures,2010,88:294-308
3 Nakamura N.A practical method for estimating dynamic soil stiffness on surface of multi-layered soil.Earthquake Engineering&Structural Dynamics,2010,34(11):1391-1406
4 Hua X,Curtis J,Guo Y,et al.The internal loads,moments,and stresses in rod-like particles in a low-speed,vertical axis mixer.Chemical Engineering Science,2015,134(1):581-598
5 Laurent B,Cleary PW.Comparative study by PEPT and DEM for flow and mixing in a ploughshare mixer.Powder Technology,2012,228(3):171-186
6季顺迎.计算颗粒力学及工程应用.北京:科学出版社,2018(Ji Shunying.Computational Granular Mechanics and Its Engineering Applications.Beijing:Sciences Press,2018(in Chinese))
7 Nakashima H,Oida A.Algorithm and implementation of soil-tire contact analysis code based on dynamic FE-DE method.Journal of Terramechanics,2004,41(2):127-137
8 Lisjak A,Grasselli G.A review of discrete modeling techniques for fracturing processes in discontinuous rock masses.Journal of Rock Mechanics and Geotechnical Engineering,2014,6:301-314
9 Chung YC,Lin CK,Chou PH,et al.Mechanical behaviour of a granular solid and its contacting deformable structure under uniaxial compression-Part I:Joint DEM-FEM modelling and experimental validation.Chemical Engineering Science,2016,144:404-42010唐志平,胥建龙.离散元与壳体有限元结合的多尺度方法及其应用.计算力学学报,2007,24(5):591-596(Tang Zhiping,Xu Jianlong.A combined discrete/cylindrical shell finite element multiscale method and its application.Chin J Comput Mech,2007,24(5):591-
596(in Chinese))
11 Gao W,Zang MY,Xu W.An approach to freely combining 3d discrete and finite element methods.International Journal of Computational Methods,2014,11(01):1350051
12文龙飞,王理想,田荣.动载下裂纹应力强度因子计算的改进型扩展有限元法.力学学报,2018,50(3):599-610(Wen Longfei,Wang Lixiang,Tian Rong.Accurate computation on dynamic SIFs using improved XFEM.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):599-610(in Chinese))
13 Jin F,Zhang C,Hu W,et al.3D mode discrete element method:Elastic model.International Journal of Rock Mechanics&Mining Sciences,2011,48(1):59-66
14张青波,李世海,冯春.四节点矩形弹簧元及其特性研究.岩土力学,2012,33(11):3497-3502(Zhang Qingbo,Li Shihai,Feng Chun.Study of four-node rectangular spring element and its properties.Rock and Soil Mechanics,2012,33(11):3497-3502(in Chinese))
15冯春,李世海,刘晓宇.基于颗粒离散元法的连接键应变软化模型及其应用.力学学报,2016,48(1):76-85(Feng Chun,Li Shihai,Liu Xiaoyu,Particle-dem based linked bar strain softening model and its application.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):76-85(in Chinese))
16 Jiang T,Yu Y,He H,et al.Macroscopic shock plasticity of brittle material through designed void patterns.Journal of Applied Physics,2016,119(9):1853
17 Yu Y,Wang W,He H,et al.Mesoscopic deformation features of shocked porous ceramic:Polycrystalline modeling and experimental observations.Journal of Applied Physics,2015,117(12):686
18 Gusev AA.Physically admissible rules of evolution for discrete representations of continuous media.Journal of Non-Crystalline Solids,2006,352(42-49):4880-4883
19 Ferellec JF,Mcdowell GR.A method to model realistic particle shape and inertia in DEM.Granular Matter,2010,12(5):459-467
20钱劲松,陈康为,张磊.粒料固有各向异性的离散元模拟与细观分析.力学学报,2018,50(5):1041-1050(Qian Jinsong,Chen Kangwei,Zhang Lei.Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1041-1050(in Chinese))
21 Lu G,Third JR,M¨uller CR.Discrete element models for nonspherical particle systems:From theoretical developments to applications.Chemical Engineering Science,2015,127:425-465
22刘璐,龙雪,季顺迎.基于扩展多面体的离散单元法及其作用于圆桩的冰载荷计算.力学学报,2015,47(6):1046-1057(Liu Lu,Long Xue,Ji Shunying.Dilated polyhedra based discrete element method and its application of ice load on cylindrical pile.Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):1046-1057(in Chinese))
23 Podlozhnyuk A,Pirker S,Kloss C.Efficient implementation of superquadric particles in discrete element method within an opensource framework.Computational Particle Mechanics,2017,4(1):101-118
24王嗣强,季顺迎.考虑等效曲率的超二次曲面单元非线性接触模型.力学学报,2018,50(5):1081-1092(Wang Siqiang,Ji Shunying.Non-linear contact model for super-quadric element considering the equivalent radius of curvature.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1081-1092(in Chinese))
25 Pazdniakou A.Lattice spring models.Transport in Porous Media,2012,93(2):243-262
26 Zhao GF.Modelling 3D jointed rock masses using a lattice spring model.International Journal of Rock Mechanics&Mining Sciences,2015,78:79-90
27 Nishiura D,Sakaguchi H.Parallel-vector algorithms for particle simulations on shared-memory multiprocessors.Journal of Computational Physics,2011,230(5):1923-1938
28 Gusev AA.Finite element mapping for spring network representations of the mechanics of solids.Physical Review Letters,2004,93(3):034302
29 Ram′?rez R,P¨oschel T,Brilliantov NV,et al.Coefficient of restitution of colliding viscoelastic spheres.Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1999,60:4465
30孙其诚,王光谦.颗粒物质力学导论.北京:科学出版社,2009(Sun Qicheng,Wang Guangqian.Introduction to the Mechanics of Granular Materials.Beijing:Science Press,2009(in Chinese))
31 Iwashita K,Oda M.Micro-deformation mechanism of shear banding process based on modified distinct element method.Powder Technology,1999,109(1):192-205
32 Iwashita K,Oda M.Rolling resistance at contacts in simulation of shear band development by DEM.Journal of Engineering Mechanics,1998,124(3):285-292
33 Wong CX,Daniel MC,Rongong JA.Energy dissipation prediction of particle dampers.Journal of Sound&Vibration,2009,319(1):91-118
2 Morfidis K.Vibration of Timoshenko beams on three-parameter elastic foundation.Computers and Structures,2010,88:294-308
3 Nakamura N.A practical method for estimating dynamic soil stiffness on surface of multi-layered soil.Earthquake Engineering&Structural Dynamics,2010,34(11):1391-1406
4 Hua X,Curtis J,Guo Y,et al.The internal loads,moments,and stresses in rod-like particles in a low-speed,vertical axis mixer.Chemical Engineering Science,2015,134(1):581-598
5 Laurent B,Cleary PW.Comparative study by PEPT and DEM for flow and mixing in a ploughshare mixer.Powder Technology,2012,228(3):171-186
6季顺迎.计算颗粒力学及工程应用.北京:科学出版社,2018(Ji Shunying.Computational Granular Mechanics and Its Engineering Applications.Beijing:Sciences Press,2018(in Chinese))
7 Nakashima H,Oida A.Algorithm and implementation of soil-tire contact analysis code based on dynamic FE-DE method.Journal of Terramechanics,2004,41(2):127-137
8 Lisjak A,Grasselli G.A review of discrete modeling techniques for fracturing processes in discontinuous rock masses.Journal of Rock Mechanics and Geotechnical Engineering,2014,6:301-314
9 Chung YC,Lin CK,Chou PH,et al.Mechanical behaviour of a granular solid and its contacting deformable structure under uniaxial compression-Part I:Joint DEM-FEM modelling and experimental validation.Chemical Engineering Science,2016,144:404-42010唐志平,胥建龙.离散元与壳体有限元结合的多尺度方法及其应用.计算力学学报,2007,24(5):591-596(Tang Zhiping,Xu Jianlong.A combined discrete/cylindrical shell finite element multiscale method and its application.Chin J Comput Mech,2007,24(5):591-
596(in Chinese))
11 Gao W,Zang MY,Xu W.An approach to freely combining 3d discrete and finite element methods.International Journal of Computational Methods,2014,11(01):1350051
12文龙飞,王理想,田荣.动载下裂纹应力强度因子计算的改进型扩展有限元法.力学学报,2018,50(3):599-610(Wen Longfei,Wang Lixiang,Tian Rong.Accurate computation on dynamic SIFs using improved XFEM.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):599-610(in Chinese))
13 Jin F,Zhang C,Hu W,et al.3D mode discrete element method:Elastic model.International Journal of Rock Mechanics&Mining Sciences,2011,48(1):59-66
14张青波,李世海,冯春.四节点矩形弹簧元及其特性研究.岩土力学,2012,33(11):3497-3502(Zhang Qingbo,Li Shihai,Feng Chun.Study of four-node rectangular spring element and its properties.Rock and Soil Mechanics,2012,33(11):3497-3502(in Chinese))
15冯春,李世海,刘晓宇.基于颗粒离散元法的连接键应变软化模型及其应用.力学学报,2016,48(1):76-85(Feng Chun,Li Shihai,Liu Xiaoyu,Particle-dem based linked bar strain softening model and its application.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):76-85(in Chinese))
16 Jiang T,Yu Y,He H,et al.Macroscopic shock plasticity of brittle material through designed void patterns.Journal of Applied Physics,2016,119(9):1853
17 Yu Y,Wang W,He H,et al.Mesoscopic deformation features of shocked porous ceramic:Polycrystalline modeling and experimental observations.Journal of Applied Physics,2015,117(12):686
18 Gusev AA.Physically admissible rules of evolution for discrete representations of continuous media.Journal of Non-Crystalline Solids,2006,352(42-49):4880-4883
19 Ferellec JF,Mcdowell GR.A method to model realistic particle shape and inertia in DEM.Granular Matter,2010,12(5):459-467
20钱劲松,陈康为,张磊.粒料固有各向异性的离散元模拟与细观分析.力学学报,2018,50(5):1041-1050(Qian Jinsong,Chen Kangwei,Zhang Lei.Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1041-1050(in Chinese))
21 Lu G,Third JR,M¨uller CR.Discrete element models for nonspherical particle systems:From theoretical developments to applications.Chemical Engineering Science,2015,127:425-465
22刘璐,龙雪,季顺迎.基于扩展多面体的离散单元法及其作用于圆桩的冰载荷计算.力学学报,2015,47(6):1046-1057(Liu Lu,Long Xue,Ji Shunying.Dilated polyhedra based discrete element method and its application of ice load on cylindrical pile.Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):1046-1057(in Chinese))
23 Podlozhnyuk A,Pirker S,Kloss C.Efficient implementation of superquadric particles in discrete element method within an opensource framework.Computational Particle Mechanics,2017,4(1):101-118
24王嗣强,季顺迎.考虑等效曲率的超二次曲面单元非线性接触模型.力学学报,2018,50(5):1081-1092(Wang Siqiang,Ji Shunying.Non-linear contact model for super-quadric element considering the equivalent radius of curvature.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1081-1092(in Chinese))
25 Pazdniakou A.Lattice spring models.Transport in Porous Media,2012,93(2):243-262
26 Zhao GF.Modelling 3D jointed rock masses using a lattice spring model.International Journal of Rock Mechanics&Mining Sciences,2015,78:79-90
27 Nishiura D,Sakaguchi H.Parallel-vector algorithms for particle simulations on shared-memory multiprocessors.Journal of Computational Physics,2011,230(5):1923-1938
28 Gusev AA.Finite element mapping for spring network representations of the mechanics of solids.Physical Review Letters,2004,93(3):034302
29 Ram′?rez R,P¨oschel T,Brilliantov NV,et al.Coefficient of restitution of colliding viscoelastic spheres.Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1999,60:4465
30孙其诚,王光谦.颗粒物质力学导论.北京:科学出版社,2009(Sun Qicheng,Wang Guangqian.Introduction to the Mechanics of Granular Materials.Beijing:Science Press,2009(in Chinese))
31 Iwashita K,Oda M.Micro-deformation mechanism of shear banding process based on modified distinct element method.Powder Technology,1999,109(1):192-205
32 Iwashita K,Oda M.Rolling resistance at contacts in simulation of shear band development by DEM.Journal of Engineering Mechanics,1998,124(3):285-292
33 Wong CX,Daniel MC,Rongong JA.Energy dissipation prediction of particle dampers.Journal of Sound&Vibration,2009,319(1):91-118