球颗粒三维离散元法仿真软件的改进研究
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摘要
为了提高课题组研制软件的性能,本文建立了局部坐标系下颗粒与边界接触判断的简化算法和在软件中引入OpenMP技术的方法,并改进了球颗粒样本生成方法。为了提高软件仿真模拟真实度、推动软件创新化发展,本文建立了VDA-3DS实体模型显示方法和三维虚拟环境设计方法。同时添加了多物理属性颗粒与多物理属性边界计算功能、多种情况下的人机交互显示功能、颗粒质量统计和流量统计功能、数据存储时步功能,并使用VC++6.0实现了上述算法和功能。本文还对改进后的软件进行了测试,通过测试结果的观察和比对,初步验证了本文所建立方法的可行性和有效性。
本文的工作对于完善课题组研制的三维离散元法计算仿真软件、推动该软件发展均有一定意义。
Discrete element method is a kind of numerical calculation method used to analyze the mechanical behavior of granular materials and the ruler of their sport, is put forward by Dr. Peter Cundall in the turn of the last century. The main idea of discrete element method takes the whole consisting of many discrete units, according to the contact between two discrete units, establishing mechanical model. The motion state of each discrete element is obtained by Newton’s second law, through introducing the time step, recursively computing granular materials movement process, and gaining behavior of the whole granular materials. Initially, the method is mainly used study of rock mechanics, but because of the limitations of the finite element method and the advantage of discrete element method, discrete element method has been continuously inherited and developed, After nearly three decades, through numerous experts, scholars and research institutions, discrete element method has been gradually developed, currently, in the studying of mining, agriculture, water conservancy and hydropower, it has widely used.
From space discrete element method can be divided into two-dimensional and three-dimensional. Commonly, oval, disc and polygon is used to simulate granular materials by two-dimensional discrete element method. Although the two-dimensional discrete element method is simple, efficient and etc, it becomes more mature day by day, however, establishing and analyzing mechanical model is limited to flat, so two-dimensional discrete element method, the scope of application still has its limitations. In recent years, three-dimensional discrete element method made discrete element method further developed. Granular material is commonly modeled used sphere unit, ellipsoid unit and block by three-dimensional discrete element method. Not only fully inheriting the advantages of two-dimensional discrete element method, but also greatly improving the accuracy of the calculation and simulation, it works well.
In the past, a new mechanical part must be designed, and then tested and improved, and be redesigned, retested and so on, it is a complex process which costs much. In order to solve this problem, our group develops digital software which can design component, simulate and analyze how the component works. After further development based the Pro / Engineer, it can analyze and optimize mechanical component. It cuts cost when design new component.
3D Software is designed according to three-dimensional discrete element method, although the three-dimensional discrete element method compared with two-dimensional discrete element method only increases one dimension, but the complexity of modeling, analysis and simulation multiples which makes developing and testing software more difficult. Prominent issues are many, for example: calculation is slow and inefficient, simulation is not realistic compared to Pro / Engineer, part of function is unachieved and etc. In this paper, I study issues above further based summing up and inheriting the experience of developing three-dimensional software.
Simulation of soil particle usually requires a large swatch, the software can’t generate enough particles if we take time step method. During generating these particles will move as a result of collisions, so it can’t achieve a similar stationary state as the soil. In order to meet need that generating large-scale particles and simulating soil, this paper uses the method that generates particles in a hexahedron or cylinder, all particles will be generated at one time by the method above, and in the subsequent time step, enlarging particles according to factor set by the user and the time when particles begin being enlarged. Particles will move because of collision while they are being enlarged, ultimately, they achieve steady-state uniform mixing. At the same time, this paper has also established the method that generating particles while feed port is moving. When feed port is moving, three-dimensional software computes out the position of the feed port by formula, and generates particles.
In order to improve the performance of three-dimensional software, in this paper, I established the algorithm of determining contact that spherical particle with disc and spherical surface. First, the border is converted to the local coordinate system which center is same to center of border, and then determining contact of particle with border in the local coordinate system, finally, convert the result to the global coordinate system according to Cramer's rule, computation number is reduced with this method in determining contact, to a certain extent can improve the performance of three-dimensional software. At the same time, this paper also details the OpenMP technique in three-dimensional software configuration and application, OpenMP technology is verified by testing and it is important and useful. Always, the physical properties is different between particle and border In the industry and agriculture, the model of generating multi-attribute particle and the model of determining contact of multi-attribute particle with multi-attribute border is established in this paper to meet the actual demand. The correction formula is used in the calculation to correct parameters in the mechanics model, and differentiate particles with color through OpenGL.
Although the three-dimensional software already has a sound theoretical basis, but there are still many function not been realized yet, affecting the process of testing and application, to make three-dimensional software more applicably, the following functions are added in this paper: switch simulation and display, switch display of numbering particle, switch display of partial’s location, check parameter, make statistics of particle flow, make statistics of particles’mass and store time step.
The way by which original three-dimensional software extract data is correct and it fit for simulation, but it is worse than Pro / Engineer software. In this paper, on the basis of long-term research and test, VDA-3DS entity-plan can be displayed. With this method, the plan drawn by Pro / Engineer software is saved as VDA format and be converted to 3DS format. A 3DS file read module is added in the three-dimensional software to get information of 3DS files and displays them, and these entity-plans can be translate and rotated, improving fidelity of simulation.
In this paper, introduction of virtual reality technology in three-dimensional software is an innovation, how to introduce virtual reality technology in face of three-dimensional software’s structure, function and etc is made a particular description, and through the sky-box building systems, the terrain generation system and user roaming model to create three-dimensional virtual environment, it makes a way for introducing virtual reality technology to three-dimensional software.
In the VC++6.0, fulfill all the above-mentioned algorithms and functions, and test developed software with software engineering method, proof relevant coding and building method correct.
本文的工作对于完善课题组研制的三维离散元法计算仿真软件、推动该软件发展均有一定意义。
Discrete element method is a kind of numerical calculation method used to analyze the mechanical behavior of granular materials and the ruler of their sport, is put forward by Dr. Peter Cundall in the turn of the last century. The main idea of discrete element method takes the whole consisting of many discrete units, according to the contact between two discrete units, establishing mechanical model. The motion state of each discrete element is obtained by Newton’s second law, through introducing the time step, recursively computing granular materials movement process, and gaining behavior of the whole granular materials. Initially, the method is mainly used study of rock mechanics, but because of the limitations of the finite element method and the advantage of discrete element method, discrete element method has been continuously inherited and developed, After nearly three decades, through numerous experts, scholars and research institutions, discrete element method has been gradually developed, currently, in the studying of mining, agriculture, water conservancy and hydropower, it has widely used.
From space discrete element method can be divided into two-dimensional and three-dimensional. Commonly, oval, disc and polygon is used to simulate granular materials by two-dimensional discrete element method. Although the two-dimensional discrete element method is simple, efficient and etc, it becomes more mature day by day, however, establishing and analyzing mechanical model is limited to flat, so two-dimensional discrete element method, the scope of application still has its limitations. In recent years, three-dimensional discrete element method made discrete element method further developed. Granular material is commonly modeled used sphere unit, ellipsoid unit and block by three-dimensional discrete element method. Not only fully inheriting the advantages of two-dimensional discrete element method, but also greatly improving the accuracy of the calculation and simulation, it works well.
In the past, a new mechanical part must be designed, and then tested and improved, and be redesigned, retested and so on, it is a complex process which costs much. In order to solve this problem, our group develops digital software which can design component, simulate and analyze how the component works. After further development based the Pro / Engineer, it can analyze and optimize mechanical component. It cuts cost when design new component.
3D Software is designed according to three-dimensional discrete element method, although the three-dimensional discrete element method compared with two-dimensional discrete element method only increases one dimension, but the complexity of modeling, analysis and simulation multiples which makes developing and testing software more difficult. Prominent issues are many, for example: calculation is slow and inefficient, simulation is not realistic compared to Pro / Engineer, part of function is unachieved and etc. In this paper, I study issues above further based summing up and inheriting the experience of developing three-dimensional software.
Simulation of soil particle usually requires a large swatch, the software can’t generate enough particles if we take time step method. During generating these particles will move as a result of collisions, so it can’t achieve a similar stationary state as the soil. In order to meet need that generating large-scale particles and simulating soil, this paper uses the method that generates particles in a hexahedron or cylinder, all particles will be generated at one time by the method above, and in the subsequent time step, enlarging particles according to factor set by the user and the time when particles begin being enlarged. Particles will move because of collision while they are being enlarged, ultimately, they achieve steady-state uniform mixing. At the same time, this paper has also established the method that generating particles while feed port is moving. When feed port is moving, three-dimensional software computes out the position of the feed port by formula, and generates particles.
In order to improve the performance of three-dimensional software, in this paper, I established the algorithm of determining contact that spherical particle with disc and spherical surface. First, the border is converted to the local coordinate system which center is same to center of border, and then determining contact of particle with border in the local coordinate system, finally, convert the result to the global coordinate system according to Cramer's rule, computation number is reduced with this method in determining contact, to a certain extent can improve the performance of three-dimensional software. At the same time, this paper also details the OpenMP technique in three-dimensional software configuration and application, OpenMP technology is verified by testing and it is important and useful. Always, the physical properties is different between particle and border In the industry and agriculture, the model of generating multi-attribute particle and the model of determining contact of multi-attribute particle with multi-attribute border is established in this paper to meet the actual demand. The correction formula is used in the calculation to correct parameters in the mechanics model, and differentiate particles with color through OpenGL.
Although the three-dimensional software already has a sound theoretical basis, but there are still many function not been realized yet, affecting the process of testing and application, to make three-dimensional software more applicably, the following functions are added in this paper: switch simulation and display, switch display of numbering particle, switch display of partial’s location, check parameter, make statistics of particle flow, make statistics of particles’mass and store time step.
The way by which original three-dimensional software extract data is correct and it fit for simulation, but it is worse than Pro / Engineer software. In this paper, on the basis of long-term research and test, VDA-3DS entity-plan can be displayed. With this method, the plan drawn by Pro / Engineer software is saved as VDA format and be converted to 3DS format. A 3DS file read module is added in the three-dimensional software to get information of 3DS files and displays them, and these entity-plans can be translate and rotated, improving fidelity of simulation.
In this paper, introduction of virtual reality technology in three-dimensional software is an innovation, how to introduce virtual reality technology in face of three-dimensional software’s structure, function and etc is made a particular description, and through the sky-box building systems, the terrain generation system and user roaming model to create three-dimensional virtual environment, it makes a way for introducing virtual reality technology to three-dimensional software.
In the VC++6.0, fulfill all the above-mentioned algorithms and functions, and test developed software with software engineering method, proof relevant coding and building method correct.
引文
[1] Cundall P A, Strack O L. A discrete numerical model for granular assembles[J]. Geotechnique, 1979, 29(1): 47~65
[2]刘凯欣,高凌天.离散元法研究的评述[J].力学进展, 2003, 33(4): 483~490
[3]刑纪波,王泳嘉.崩落采矿法放矿的离散元仿真[J].东北工学院学报, 1988(2): 148~153
[4]徐泳.用颗粒离散元法模拟料仓卸料过程[J].农业工程学报, 1999, 15(3): 65~69
[5]梁庆国,韩文峰,李雪峰等.极震区岩体地震动力破坏研究体系框架初探[J].地球科学进展, 2010, 25(1): 43~54
[6]赖森华.有底部结构崩落采矿法放矿动力学问题的研究[D].北京:北京科技大学, 1988.
[7]唐志平.三维离散元方法及其在冲击力学中的应用[J].中国种学, 2003, 33(11): 989~998
[8]黄昕.粘性炭素糊料冲击压实机理及其离散元数值仿真研究[D].长沙:中南大学, 2007.
[9] Zhang X, Vu-Quoc L. A method to extract the mechanical properties of particles in collision based on a new elasto-plastic normal force-displacement model[J]. Mechanics of Materials, 2002, 34: 779~794
[10] Asmar B N, Langston P A, Matchett A J, et al. Validation tests on a distinct element model of vibrating cohesive particle systems[J]. Computers and Chemical Engineering. 2002, 26: 785~802
[11]孙春宝.动筛跳汰过程的离散单元法模拟研究[D].沈阳:东北大学, 1994.7.
[12]付宏,乌兰,黄万风等.基于图元的三维离散元法边界建模方法[J].计算机集成制造系统, 2008, 14(12): 2328~2333
[13]苏堆田,侯克鹏,朱国辉.边坡稳定性分析中极限平衡法、三维有限元法和离散元法的联合应用研究[J].湖南有色金属, 2003, 19(6): 48~51
[14]于建群,付宏,李红等.离散元法及其在农业机械工作部件研究与设计中的应用[J].农业工程学报, 2005, 21(5):1~6
[15] John M, Mahmood K. An ellipse-based discete element model for granular materials[J]. International Journal for numerical and analytical methods in geomechanics, 1993(17): 603~623
[16]洪俊.伴随挤压破碎的发射药床散粒体系统动力学仿真研究[D].南京:南京理工大学, 2007.
[17] Vemuri B C, Chen L, Vu-Quou L, et al. Efficient and accurate collision detection for granular flow simulation[J]. Graphical Models and Image Processing, 1998, 60: 403~422
[18]杨全文,左树春,徐泳.颗粒离散元法的微机可视化程序设计[J].中国农业大学学报, 2002, 7(6): 10~13
[19] Buchholtz V, Poschel T. A vectorized algorithm for molecular dynamics of short-range interacting particles[J]. International Journal of Modern Physics C, 1993, 4(5): 1049～1057
[20]殷顺昌. OpenMP并行程序性能分析[D].长沙:国防科学技术大学, 2006.
[21]郑峰,李名世,蔡佳佳.基于OpenMP的并行遗传算法探讨[J].心智与计算, 2007(4): 396~402
[22]贾志刚.精通OpenGL[M].北京:电子工业出版社, 1998.
[23]彭晓明,王坚. OpenGL深入编程与实例揭密[M].北京:人民邮电出版社,1999.
[24]江早,王洪成. OpenGL VC/VB图形编程[M].北京:科学出版社, 2001.
[25]徐长青,许志闻,郭晓新.计算机图形学[M].北京:机械工业出版社, 2005.
[26] Ting J M. A robust algorithm for ellipse-based discrete element modeling of granular material[J]. Computers and Geotechnics, 1992, 13: 175~186
[27] Walton O R, Braun R L. Viscosity, Granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks[J]. Journal of Rheology, 1986, 30(5): 949~980
[28]乌兰.三维离散元法计算仿真软件的研究[D].长春:吉林大学, 2007.
[29] Rothenburg L, Bathurst R J. Numerical simulation of idealized granular assemblies with plane elliptical particles[J]. Computers and Geotechnics, 1991, 11: 315~329
[30] Dziugys A, Peters B. An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers[J]. Granular Matter 3, 2001, 231-265
[31] Koeppe J P, Enz M, Kakalios J. Phase diagram for avalanche stratification of granular material[J]. Submitted to Physical Review Letters, 1998.
[32] Cleary P W, Sawley M L. DEM modeling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge[J]. Applied Mathematical Modelling, 2002, 26: 89~111
[33] Fineberg J. Physics in a jumping sandbox[J]. Nature, 1996, 382(29): 763~764
[34] Vu-Quoc L, Zhang X. An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations[J]. Mechanics of Materials, 1999, 31: 235~269
[35] Yang Y, Schrock M D. Analysis of grain kernel rebound motion[J]. Transactions of the ASAE, 1994, 37(1): 27~31
[36] Xiao S L. Short communication contact detection algorithms for three Dimensional ellipsoids in discrete element modeling[J]. International journal for numerical and analytical methods in geomechanics. 1995, 9: 653~659
[37]李伟,朱德懋,胡选利等.不连续散粒体的离散单元法[J].南京航空航天大学学报, 1999, 31(1): 85-91
[38] Liu K,Zheng W, Gao L, Tanimura S. A numerical analysis for stress wave propagation of anisotropic solids by discrete element method[C]. In: Chiba A,Tanimura S,Hokamoto K,eds. Proceedings of the 4th International Symposiym on Impact Engineering. Kumamoto Japan, 2001-07-16-18, UK: Elsevier Science Ltd, 2001: 589~594
[39]商慧.三维离散元法计算仿真软件开发研究[D].长春:吉林大学, 2006.
[40] Campbell C S, Brennen C E. Computer simulation of granular shear flows[J]. Journal of Fluid Mechanics, 1985, 151: 167~188
[41]匡天君,滕远道,王乘等.基于MFC和OpenGL三维图形的开发[J].微计算机信息, 2004, 20(6): 115~116
[42]蔡佳佳,李名世,郑峰.多核微机基于OpenMP的并行计算[J].计算机技术与发展, 2007, 17(10): 87~91
[43] Sun Microsystems, Inc. OpenMP API用户指南[EB]. 2007.
[44]李运蒙.软件的开发与创新[J].青海师范大学学报, 2000, 4: 17~19
[45]周思越,龚振邦.虚拟现实定义的探讨[J].计算机仿真, 2006, 23(9): 219~222
[46]陈晶.虚拟现实技术及运用[C].海南省通信学会学术年会论文集, 2005.
[2]刘凯欣,高凌天.离散元法研究的评述[J].力学进展, 2003, 33(4): 483~490
[3]刑纪波,王泳嘉.崩落采矿法放矿的离散元仿真[J].东北工学院学报, 1988(2): 148~153
[4]徐泳.用颗粒离散元法模拟料仓卸料过程[J].农业工程学报, 1999, 15(3): 65~69
[5]梁庆国,韩文峰,李雪峰等.极震区岩体地震动力破坏研究体系框架初探[J].地球科学进展, 2010, 25(1): 43~54
[6]赖森华.有底部结构崩落采矿法放矿动力学问题的研究[D].北京:北京科技大学, 1988.
[7]唐志平.三维离散元方法及其在冲击力学中的应用[J].中国种学, 2003, 33(11): 989~998
[8]黄昕.粘性炭素糊料冲击压实机理及其离散元数值仿真研究[D].长沙:中南大学, 2007.
[9] Zhang X, Vu-Quoc L. A method to extract the mechanical properties of particles in collision based on a new elasto-plastic normal force-displacement model[J]. Mechanics of Materials, 2002, 34: 779~794
[10] Asmar B N, Langston P A, Matchett A J, et al. Validation tests on a distinct element model of vibrating cohesive particle systems[J]. Computers and Chemical Engineering. 2002, 26: 785~802
[11]孙春宝.动筛跳汰过程的离散单元法模拟研究[D].沈阳:东北大学, 1994.7.
[12]付宏,乌兰,黄万风等.基于图元的三维离散元法边界建模方法[J].计算机集成制造系统, 2008, 14(12): 2328~2333
[13]苏堆田,侯克鹏,朱国辉.边坡稳定性分析中极限平衡法、三维有限元法和离散元法的联合应用研究[J].湖南有色金属, 2003, 19(6): 48~51
[14]于建群,付宏,李红等.离散元法及其在农业机械工作部件研究与设计中的应用[J].农业工程学报, 2005, 21(5):1~6
[15] John M, Mahmood K. An ellipse-based discete element model for granular materials[J]. International Journal for numerical and analytical methods in geomechanics, 1993(17): 603~623
[16]洪俊.伴随挤压破碎的发射药床散粒体系统动力学仿真研究[D].南京:南京理工大学, 2007.
[17] Vemuri B C, Chen L, Vu-Quou L, et al. Efficient and accurate collision detection for granular flow simulation[J]. Graphical Models and Image Processing, 1998, 60: 403~422
[18]杨全文,左树春,徐泳.颗粒离散元法的微机可视化程序设计[J].中国农业大学学报, 2002, 7(6): 10~13
[19] Buchholtz V, Poschel T. A vectorized algorithm for molecular dynamics of short-range interacting particles[J]. International Journal of Modern Physics C, 1993, 4(5): 1049～1057
[20]殷顺昌. OpenMP并行程序性能分析[D].长沙:国防科学技术大学, 2006.
[21]郑峰,李名世,蔡佳佳.基于OpenMP的并行遗传算法探讨[J].心智与计算, 2007(4): 396~402
[22]贾志刚.精通OpenGL[M].北京:电子工业出版社, 1998.
[23]彭晓明,王坚. OpenGL深入编程与实例揭密[M].北京:人民邮电出版社,1999.
[24]江早,王洪成. OpenGL VC/VB图形编程[M].北京:科学出版社, 2001.
[25]徐长青,许志闻,郭晓新.计算机图形学[M].北京:机械工业出版社, 2005.
[26] Ting J M. A robust algorithm for ellipse-based discrete element modeling of granular material[J]. Computers and Geotechnics, 1992, 13: 175~186
[27] Walton O R, Braun R L. Viscosity, Granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks[J]. Journal of Rheology, 1986, 30(5): 949~980
[28]乌兰.三维离散元法计算仿真软件的研究[D].长春:吉林大学, 2007.
[29] Rothenburg L, Bathurst R J. Numerical simulation of idealized granular assemblies with plane elliptical particles[J]. Computers and Geotechnics, 1991, 11: 315~329
[30] Dziugys A, Peters B. An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers[J]. Granular Matter 3, 2001, 231-265
[31] Koeppe J P, Enz M, Kakalios J. Phase diagram for avalanche stratification of granular material[J]. Submitted to Physical Review Letters, 1998.
[32] Cleary P W, Sawley M L. DEM modeling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge[J]. Applied Mathematical Modelling, 2002, 26: 89~111
[33] Fineberg J. Physics in a jumping sandbox[J]. Nature, 1996, 382(29): 763~764
[34] Vu-Quoc L, Zhang X. An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations[J]. Mechanics of Materials, 1999, 31: 235~269
[35] Yang Y, Schrock M D. Analysis of grain kernel rebound motion[J]. Transactions of the ASAE, 1994, 37(1): 27~31
[36] Xiao S L. Short communication contact detection algorithms for three Dimensional ellipsoids in discrete element modeling[J]. International journal for numerical and analytical methods in geomechanics. 1995, 9: 653~659
[37]李伟,朱德懋,胡选利等.不连续散粒体的离散单元法[J].南京航空航天大学学报, 1999, 31(1): 85-91
[38] Liu K,Zheng W, Gao L, Tanimura S. A numerical analysis for stress wave propagation of anisotropic solids by discrete element method[C]. In: Chiba A,Tanimura S,Hokamoto K,eds. Proceedings of the 4th International Symposiym on Impact Engineering. Kumamoto Japan, 2001-07-16-18, UK: Elsevier Science Ltd, 2001: 589~594
[39]商慧.三维离散元法计算仿真软件开发研究[D].长春:吉林大学, 2006.
[40] Campbell C S, Brennen C E. Computer simulation of granular shear flows[J]. Journal of Fluid Mechanics, 1985, 151: 167~188
[41]匡天君,滕远道,王乘等.基于MFC和OpenGL三维图形的开发[J].微计算机信息, 2004, 20(6): 115~116
[42]蔡佳佳,李名世,郑峰.多核微机基于OpenMP的并行计算[J].计算机技术与发展, 2007, 17(10): 87~91
[43] Sun Microsystems, Inc. OpenMP API用户指南[EB]. 2007.
[44]李运蒙.软件的开发与创新[J].青海师范大学学报, 2000, 4: 17~19
[45]周思越,龚振邦.虚拟现实定义的探讨[J].计算机仿真, 2006, 23(9): 219~222
[46]陈晶.虚拟现实技术及运用[C].海南省通信学会学术年会论文集, 2005.