多场耦合问题的协同求解方法研究与应用
|
摘要
多场耦合问题是指在一个系统中,由两个或者两个以上的场相互作用而产生的一种现象,它在自然界或机电产品中广泛存在。随着市场竞争的白热化,多场耦合问题在继电器、微机电系统、发动机、燃气涡轮、压力容器等机电产品中越来越多地表现出来,工程实践中迫切需要一种比较好的方法来求解多场耦合问题。传统研究多侧重于对特定多场耦合问题的建模和求解策略的探讨,本文则对一般的多场耦合问题进行了理论研究,提出了分析这种问题的协同求解方法,并对该方法的关键技术进行了深入的研究。
首先对一般多场耦合问题的数学模型和耦合关系进行了理论研究。在对七种基本场的数学模型和其间的十四种耦合关系进行分析的基础上,给出了基本场和耦合场的数学模型的统一描述。对耦合关系进行研究,分别从耦合区域、耦合强度、耦合途径、耦合方程和耦合机理等方面出发,定义了五种耦合关系。使用这五种耦合关系对工程中常见的十个种基本耦合场进行了研究,并具体分析了微机电系统中的多场耦合问题。
其次提出了多场耦合问题的协同求解方法,并对其关键技术进行了研究。在传统分区解法的基础上,给出了协同求解方法的基本思路,并从数学和计算实施的角度给出了求解步骤。接着研究了协同求解方法的四个关键技术:(1)结点数据映射技术。综合三种插值法(快速壳法、滑动最小二乘法和反距离移动平均法)的优点,提出了一种先用快速壳法插值内点,再依次使用滑动最小二乘法和反距离移动平均法插值外点的混合法。给出了混合法的MATLAB实施流程,并用该程序对一个热应力问题进行计算,从稳定性、精度和计算速度方面对几种方法进行了比较,证明了混合法的优越性;(2)任务协同技术。以一个MEMS问题作为稳态耦合场协同求解的例子,分析了电场、温度场和结构场以及结点载荷插值模块的任务划分,并详细阐述了其协同求解流程;又以一个感应加热问题作为瞬态耦合场协同求解的例子,阐述了其实施流程及文件系统的构成;最后对一般的多场耦合问题,提出了任务和任务关系的数学模型,并给出了一种基于WEB的任务协同算法。(3)并行加速算法。该算法从某单场求解后的映射点开始,同时启动预测线和仿真线,并根据下一个预测点的预测值与仿真值的差距决定是否跳跃。在阐述了该算法的总体思想后,讨论了其涉及的三个关键技术:结点分区技术、分片预估技术和分层抽样技术。以感应加热问题为例,使用单步跳跃策略和多步跳跃策略进行仿真试验,结果表明本算法具有高精度和高效率的特点。(4)协同求解平台技术。基于J2EE技术提出了其功能体系结构,然后提出了一种联合Rational Rose ,Weblogic Workshop和SQLServer开发J2EE平台的新方法AUP,使用该方法构建了本文的多场协同求解平台MPCIDS,并给出了的MPCIDS原型系统。
作为协同求解方法实施的一个综合性的例子,本文最后在MPCIDS上研究了一个集成电控模块的热弹耦合振动问题。首先分别建立了振动分析和热分析的数字模型,并使用试验进行验证,修正了数字模型。接着对该问题依次进行了稳态仿真和瞬态仿真,并把仿真结果与其它热弹耦合振动问题进行了比较,结果表明,当温度持续上升时,处于不同位置的两类继电器的固有频率和加速度响应会出现不同的变化。
与已有的研究相比,本文的工作有以下几点贡献:[1]建立了耦合场的数学模型,定义了五种耦合关系,并对常见的十种基本耦合场分析了其耦合关系[2]在分区法的基础上提出了协同求解方法,并对其四个关键技术进行了深入研究,较好的解决了一般多场耦合问题的求解策略和求解效率问题。[3]使用协同求解方法分析了集成电控模块中的热弹耦合振动,得到了一些有意义的结论。
Multiphysics problems(MPPS) are phenomena produced by interaction between two or more fields in a system, which exist widely in nature or mechan-electron products. With the heating competition of markets, MPPS are brought out more and more in mechan-electron products such as delays, MEMS, engines, gas turbins, and so an efficient approach to solve MPPS is urgent in demand in practice. Conventional research focused mainly on modeling and solving tragedy of specific problems. Focusing on general problems, this thesis proposes a collaborative approach to solve MPPS, and study the key technologies of this approach.
Firstly the theory of mathematical models and coupling relations of general MPPS is studied. Based on analysis of models of seven basic fields and fourteen coupling relations between them, unified description of mathematical models of basic fields and coupled fields are given. Then the coupling relation are studied and five kinds of coupling relations are defined according to coupling region,coupling strength,coupling approach,coupling equation and coupling mechanism. Subsequently, ten general coupled fileds in engineering are studied with these five coupling relations and as a sample, MPPS of MEMS is studied.
Subsequently a collaborative solving approach to MPPS is proposed. Firstly the basic idea of collaborative solving approach is brought out, and then,based on the conventional partitioned method, a mathematical example is given to explain why the approach is approtiate. Then the arithmetic is described from mathematical respect and computational implement respect. Following this, four key technologies of the collaborative solving approach are studied. (1) Node Mapping Technology. Combing the advantage of three interpolating method:rapid shell method, moving least square method, inverse moving averaging method, a method to map nonmatched mesh,named fixed method, is prposed, which interpolates inner nodes by rapid shell method ,and then interpolates outer nodes by moving least square method and finally by inverse moving averaging method. The computational implement of this method is depicted witi MATLAB, and a thermal stress problem is solved by mixed method. The result shows that its’stability, accuracy and efficiency are satisfactory. (2) Task Collaborative Technology. As a sample of static coupled fields, MEMS is broke into electricity field, temperature field and structure field. The collaborative solving flow is described in detail. And then, as a sample of transient coupled fields, an induction heating problem is solved by collaborative solving method, in which the file system is depicited detaily. Finally, general mathematical models of task and task relation are given, and a task collaboration arithmetic based on WEB is proposed. (3) Parallel Accelerating Technology. At a mapping point after a single filed is solved, prediction line and simulaition line start, and the calculating will jump a step when the difference between prediction value and simulation value is little enough. Having described the general thoughts of this arithmetic, the thesis discusses three related key technologies: node partition technology, sliced prediction technology and layered sampling technology. Taking a induction heating problem for example, single-step jump strategy and multi-step jump strategy are implemented, and the result shows that this arithmetic is of high accuracy and efficiency. (4) Collaborative Solving Platform Technology. Based on J2EE technology, the function framework of this platform is proposed, and then a method to develop J2EE platform, named AUP, is proposed, which combines Rational Rose, Weblogic Workshop and SQLServer. By this method, a multiphysics collaborative solving platform named MPCIDS is constructed and the prototype of MPCIDS is given.
As a general sample of collaborative solving method, this thesis studies a thermal-elastic coupled vibration problem on MPCIDS. Firstly the mathematical models of vibration anlysis and thermal analysis are constructed and modified by test. And then static simulation and transient simulation are done. The simulation result shows that two kinds of the inherent frequency and acceleration response of relays at different places vary differently when temperature arises.
Comparing with the former researches, the contributions of this thesis are as follows: (1) It constructes mathematical of coupled fields, and defines six kinds of coupling relation, and analyses the coupling relation of ten basic coupled fileds. (2) Based on the partitioned method, it proposes a collaborative solving method, and its’four key technologies are studied in depth, which solves the solving trategy and efficiency of general multiphysics problems. [3] It solves a thermal-elastic coupled vibration problem of integrated electricity controlled module, and draws up some meaningful conclusion.
首先对一般多场耦合问题的数学模型和耦合关系进行了理论研究。在对七种基本场的数学模型和其间的十四种耦合关系进行分析的基础上,给出了基本场和耦合场的数学模型的统一描述。对耦合关系进行研究,分别从耦合区域、耦合强度、耦合途径、耦合方程和耦合机理等方面出发,定义了五种耦合关系。使用这五种耦合关系对工程中常见的十个种基本耦合场进行了研究,并具体分析了微机电系统中的多场耦合问题。
其次提出了多场耦合问题的协同求解方法,并对其关键技术进行了研究。在传统分区解法的基础上,给出了协同求解方法的基本思路,并从数学和计算实施的角度给出了求解步骤。接着研究了协同求解方法的四个关键技术:(1)结点数据映射技术。综合三种插值法(快速壳法、滑动最小二乘法和反距离移动平均法)的优点,提出了一种先用快速壳法插值内点,再依次使用滑动最小二乘法和反距离移动平均法插值外点的混合法。给出了混合法的MATLAB实施流程,并用该程序对一个热应力问题进行计算,从稳定性、精度和计算速度方面对几种方法进行了比较,证明了混合法的优越性;(2)任务协同技术。以一个MEMS问题作为稳态耦合场协同求解的例子,分析了电场、温度场和结构场以及结点载荷插值模块的任务划分,并详细阐述了其协同求解流程;又以一个感应加热问题作为瞬态耦合场协同求解的例子,阐述了其实施流程及文件系统的构成;最后对一般的多场耦合问题,提出了任务和任务关系的数学模型,并给出了一种基于WEB的任务协同算法。(3)并行加速算法。该算法从某单场求解后的映射点开始,同时启动预测线和仿真线,并根据下一个预测点的预测值与仿真值的差距决定是否跳跃。在阐述了该算法的总体思想后,讨论了其涉及的三个关键技术:结点分区技术、分片预估技术和分层抽样技术。以感应加热问题为例,使用单步跳跃策略和多步跳跃策略进行仿真试验,结果表明本算法具有高精度和高效率的特点。(4)协同求解平台技术。基于J2EE技术提出了其功能体系结构,然后提出了一种联合Rational Rose ,Weblogic Workshop和SQLServer开发J2EE平台的新方法AUP,使用该方法构建了本文的多场协同求解平台MPCIDS,并给出了的MPCIDS原型系统。
作为协同求解方法实施的一个综合性的例子,本文最后在MPCIDS上研究了一个集成电控模块的热弹耦合振动问题。首先分别建立了振动分析和热分析的数字模型,并使用试验进行验证,修正了数字模型。接着对该问题依次进行了稳态仿真和瞬态仿真,并把仿真结果与其它热弹耦合振动问题进行了比较,结果表明,当温度持续上升时,处于不同位置的两类继电器的固有频率和加速度响应会出现不同的变化。
与已有的研究相比,本文的工作有以下几点贡献:[1]建立了耦合场的数学模型,定义了五种耦合关系,并对常见的十种基本耦合场分析了其耦合关系[2]在分区法的基础上提出了协同求解方法,并对其四个关键技术进行了深入研究,较好的解决了一般多场耦合问题的求解策略和求解效率问题。[3]使用协同求解方法分析了集成电控模块中的热弹耦合振动,得到了一些有意义的结论。
Multiphysics problems(MPPS) are phenomena produced by interaction between two or more fields in a system, which exist widely in nature or mechan-electron products. With the heating competition of markets, MPPS are brought out more and more in mechan-electron products such as delays, MEMS, engines, gas turbins, and so an efficient approach to solve MPPS is urgent in demand in practice. Conventional research focused mainly on modeling and solving tragedy of specific problems. Focusing on general problems, this thesis proposes a collaborative approach to solve MPPS, and study the key technologies of this approach.
Firstly the theory of mathematical models and coupling relations of general MPPS is studied. Based on analysis of models of seven basic fields and fourteen coupling relations between them, unified description of mathematical models of basic fields and coupled fields are given. Then the coupling relation are studied and five kinds of coupling relations are defined according to coupling region,coupling strength,coupling approach,coupling equation and coupling mechanism. Subsequently, ten general coupled fileds in engineering are studied with these five coupling relations and as a sample, MPPS of MEMS is studied.
Subsequently a collaborative solving approach to MPPS is proposed. Firstly the basic idea of collaborative solving approach is brought out, and then,based on the conventional partitioned method, a mathematical example is given to explain why the approach is approtiate. Then the arithmetic is described from mathematical respect and computational implement respect. Following this, four key technologies of the collaborative solving approach are studied. (1) Node Mapping Technology. Combing the advantage of three interpolating method:rapid shell method, moving least square method, inverse moving averaging method, a method to map nonmatched mesh,named fixed method, is prposed, which interpolates inner nodes by rapid shell method ,and then interpolates outer nodes by moving least square method and finally by inverse moving averaging method. The computational implement of this method is depicted witi MATLAB, and a thermal stress problem is solved by mixed method. The result shows that its’stability, accuracy and efficiency are satisfactory. (2) Task Collaborative Technology. As a sample of static coupled fields, MEMS is broke into electricity field, temperature field and structure field. The collaborative solving flow is described in detail. And then, as a sample of transient coupled fields, an induction heating problem is solved by collaborative solving method, in which the file system is depicited detaily. Finally, general mathematical models of task and task relation are given, and a task collaboration arithmetic based on WEB is proposed. (3) Parallel Accelerating Technology. At a mapping point after a single filed is solved, prediction line and simulaition line start, and the calculating will jump a step when the difference between prediction value and simulation value is little enough. Having described the general thoughts of this arithmetic, the thesis discusses three related key technologies: node partition technology, sliced prediction technology and layered sampling technology. Taking a induction heating problem for example, single-step jump strategy and multi-step jump strategy are implemented, and the result shows that this arithmetic is of high accuracy and efficiency. (4) Collaborative Solving Platform Technology. Based on J2EE technology, the function framework of this platform is proposed, and then a method to develop J2EE platform, named AUP, is proposed, which combines Rational Rose, Weblogic Workshop and SQLServer. By this method, a multiphysics collaborative solving platform named MPCIDS is constructed and the prototype of MPCIDS is given.
As a general sample of collaborative solving method, this thesis studies a thermal-elastic coupled vibration problem on MPCIDS. Firstly the mathematical models of vibration anlysis and thermal analysis are constructed and modified by test. And then static simulation and transient simulation are done. The simulation result shows that two kinds of the inherent frequency and acceleration response of relays at different places vary differently when temperature arises.
Comparing with the former researches, the contributions of this thesis are as follows: (1) It constructes mathematical of coupled fields, and defines six kinds of coupling relation, and analyses the coupling relation of ten basic coupled fileds. (2) Based on the partitioned method, it proposes a collaborative solving method, and its’four key technologies are studied in depth, which solves the solving trategy and efficiency of general multiphysics problems. [3] It solves a thermal-elastic coupled vibration problem of integrated electricity controlled module, and draws up some meaningful conclusion.
引文
[1]张秋光.场论.北京:地质出版社,1988.
[2]陈恕行.现代偏微分方程导论.北京:科学出版社,2005.
[3]蒋叔豪.偏微分方程数值解.杭州:浙江大学出版社,1985.
[4]刘更,刘天祥,谢琴.无网格法及其应用.西安:西北工业大学出版社,2005.
[5]刘顺隆,郑群.计算流体力学.哈尔滨:哈尔滨工程大学出版社,1998.
[6]李志印,熊小辉,吴家鸣.计算流体力学常用数值方法简介.广东造船,2004(3):5-8.
[7]曾攀.有限元分析及其应用.北京:清华大学出版社,2004.
[8]姚寿广.边界元法数值方法及其工程应用.北京:国防工业出版社,1995.
[9]王福军.计算流体动力学分析.北京:清华大学出版社,2004.
[10]宋康祖.紧支函数无网格方法研究.博士学位论文,清华大学工程力学系,2000.
[11] http://www.ansys.com
[12] http://www.mscsoftware.com/
[13] http://www.physica.com
[14] http://www.femlab.com.cn/
[15] http://www.flormerics.com
[16] http://www.algor.com
[17] http://www.spectrum.com
[18]林胜勇.MEMS中多能量场耦合问题数值方法研究[硕士论文].西安:西北工业大学,2001.
[19] M. Roos, E. Batawi, U. Harnisch, etc. Efficient simulation of fuel cell stacks with the volume averaging method.Journal of Power Sources, 2003(118):86-95.
[20] M. Furmanczyk, P. Wilkerson, and A. Przekwas. Multiphysics Modeling of Integrated Microfluidic -Thermoelectric Cooling for Stacked 3D ICs. 19th IEEE SEMI-THERM Symposium,2003, 35-41.
[21]郑晓静.电磁固体力-磁-电作用的耦合效应.兰州大学学报(自然科学版),1999,35(3):17-21.
[22]朱林利,郑晓静.基于Boltzmann方程在外加电场和磁场作用下热传导及电磁热弹性理论.兰州大学学报(自然科学版).2005,41(2):104-108.
[23]何丽红,郑晓静.风-沙-电多场耦合模型及其对风沙流结构的影响.兰州大学学报(自然科学版).2005,41(3):87-92.
[24]邱高伟,郑晓静.热扩散和电场对风沙流发展过程的影响.应用数序和力学,2007,28(2):165-175.
[25]冯国泰,黄家骅,李海滨.涡轮发动机三维多场耦合数值仿真的数学模型.上海理工大学学报,2001,23(3):190-192.
[26]李海滨,冯国泰,王松涛.涡轮三维叶栅的气热耦合数值模拟.工程热物理学报,2003,24(5):770-772.
[27]梁卫国.盐类矿床水压致裂水溶开采的多场耦合理论及应用研究.岩石力学与工程学报,2005,24(6):1090-1090.
[28]薛强,冯夏庭,刘建军.填埋气体运移过程的多场耦合模型及仿真分析.系统仿真学报,2005,17(1):20-24.
[29]陆军,李恒,苏燕兵等.垂直Bridgman法多组元晶体生长的多场耦合模型.西安交通大学学报,2006,40(5):582-586.
[30]戴庆华,戴宏亮,王熙.多场耦合下压电圆筒的热电弹性瞬态响应.深圳大学学报理工版,2006,23(2):122-127.
[31]洪深泽,董定福,王树军等.热锻成形过程温度场的热力耦合数值模拟.机械工程学报,1996,32(1):62-67.
[32]杨兰和.煤炭地下气化干馏气渗流运动多场耦合数值模拟.西安交通大学学报,2002,36(7):752-756.
[33]张敦福,王锡平,赵俊峰.悬臂输送管道流-固耦合动力学系统的直接解法.机械工程学报,2004,40(3):195-198.
[34]刘建军,刘先贵.开发过程中三场耦合的数学模型.特种油气藏,2001,8(2):31-33.
[35] O.Sigmund. Design of multiphysics actuators using topology optimization-Part I: One-material structures. Computer methods in applied mechanics and engineering, 2001(190):6577-6604.
[36] O.Sigmund. Design of multiphysics actuators using topology optimization-PartⅡ: two-material structures. Computer methods in applied mechanics and engineering, 2001(190):6605-6627.
[37] John Michopoulos,Charbel Farhat,Elias Houstis.Dynamic-Data-Driven Real-Time Computational Mechanics Environment. ICCS 2004,LNCS 3038,2004,693-700.
[38] J. Michopoulos, C. Farhat, E. Houstis,etc.Dynamic Data Driven Methodologies for multiphysics system modeling and simulation.ICCS 2005,LNCS3515,2005,616-623.
[39] J. Michopoulos, P. Tsompanopoulou, E. Houstis. On a data-dviven environment for multiphysics applications. Future generation computer systems. 2005(21):953-968.
[40] A.V.Smirnov. Multi-physics modeling environment for continuum and discrete dynamics.2004,1-12.
[41] T.Belytschko,R.Mullen. Stability of explicit-implicit mesh partitions in time integration. Int. J. Number. Methods Emgrg. ,1978(12):1575-1586.
[42] T.Belytschko, T.Yen, R.Mullen. Mixed methods for time integration. Comput. Methods Appl. Mech. Engrg. , 1979(17/18):259-275.
[43] T.J.R. Hughes, W.K. Liu. Implicit-explicit finite elements in transient analysis:Ⅰ. Stablity theory;Ⅱ. Implementation and numerical examples. J. Appl. Mech., 1978(45):371-378.
[44] T.J.R. Hughes, K.S. Pister, R.L. Taylor. Implicit-explicit finite elements in nonlinear transient analysis. Comput. Methods Appl. Mech. Engrg. , 1979(17/18):159-182.
[45] T.J.R. Hughes, R.S. Stephenson. Stability of implicit-explicit finite elements in nonlinear transient analysis. Int. J. Engrg. Sci. , 1981(19):295-302.
[46] C.A. Felippa, K.C. Park. Staggered transient analysis procedures for coupled-field mechanincal systems:formulation. Comput. Methods Appl. Mech. Engrg. , 1980 (24): 61-111.
[47] C. A. Felippa, J. A. Deruntz. Finite element analysis of shock-induced hull cavitation. Comput. Methods Appl. Mech. Engrg. , 1984(44):297-337.
[48] C. A. Felippa, T. L. Geers. Partitioned analysis of coupled mechanincal systems. Eng.Comput. 1988(5):123-133.
[49] Carlos A.Felippa, K.C.Park, Charbel Farhat. Partitioned analysis of coupled mechanical systems. Computer methods in applied mechanics and engineering,2001(190):3247-3270.
[50] Charles Lawrence. An overview of three approaches to multidisciplinary aeropropulsion simulations.1997,NASA TM-107443.
[51] M N Sanhinkaya. Inverse dynamic analysis of multiphysics systems. MechE, 2004 (218): 13-26.
[52] C. Walshaw, M. Cross, and K. McManus.Multiphase mesh partitioning for parallel computational mechanincs codes.ICCS2002,LNCS 2330.2003,943-952.
[53] Michael Raulli , Kurt Maute. Optimization of fully coupled electrostatic–fluid–structure interaction problems. Computers & Structures.2005(83):221-233.
[54]张凯,彭云峰.一种微构件的多物理场耦合求解方法.机械设计与制造,2006(2):1-3.
[55]王东方,潘琼瑶,郑百林等.柴油机气缸盖多场耦合三维有限元分析.力学季刊,2005,26(3):511-516.
[56]周萍,刘朝东,周乃君等.石油焦煅烧回转窑内多场耦合数值仿真与操作参数的优化,潭素技术,2006,25(2):1-5.
[57]朱文峰,林忠钦,来新民.基于多场耦合的车门铰链凸焊过程有限元仿真.焊接学报,2005,26(1):64-68.
[58]康永林,宋仁伯,董洪波等.60Si2Mn半固态轧制有限元模拟.机械工程学报,2002, 38(6): 83-87.
[59]邓文君,夏伟,周照耀.正交切削高强耐磨铝青铜的有限元分析.机械工程学报,2004, 40(3):71-75.
[60]倪正顺,帅词俊,钟掘.基于热力耦合的热挤压模具结构参数优化设计.中国机械工程,2004,15(9):757-759.
[61]宋广胜,刘相华,王国栋等.齿轮钢淬火过程多场耦合分析.特殊钢,2007,28(1):7-9.
[62]郑百林,潘琼瑶,王锋.柴油机活塞热机耦合三维有限元分析.同济大学学报(自然科学版),2006,34(11):1534-1538.
[63]王文龙,梁慧敏,翟国富.密封点此继电器接触系统机电热耦合仿真分析.机电元件,2007,27(1):3-6.
[64]李迎,俞小莉,李婷等.活塞-缸套瞬态耦合传热的有限元仿真.浙江大学学报(工学版),2007,41(2):347-350.
[65] C. Bailey, H.Lu, D.Wheeler. Computational modeling techniques for reliability of electronic components on printed circuit boards. Applied Numerical Mathematics,2002(40):101-117.
[66] C.Bailey, G.A.Taylor, M.Cross, etc. Discretisation procedures for multi-physics phenomena. Journal of Computational and Applied Mathematics,1999(103):3-17.
[67] Mats Leijon, Hans Bernhoff, Olov ?gren,etc. Multiphysics simulation of wave energy to electric energy conversion by permanent magnet linear generator. IEEE transactions on energy conversion,2005,20(1):219-224.
[68] Michael T.Heath ,Xiangming Jiao. Academic Channenges in Large-Scale Multiphysics Simulations.ICCS 2005,LNCS3515,52-59.
[69]陈云敏,叶肖伟,张民强等.多场耦合作用下重金属离子在粘土中的迁移性状试验研究.岩土工程学报,2005,27(12):1371-1375.
[70] James R. Stewart, H.Carter Edwards. A framework approach for developing parallel adaptive multiphysics applications. Finite Elements in Analysis and Design, 2004(40):1599-1617.
[71] Charles Boivin, Carl Ollivier-Gooch. A toolkit for numerical simulation of PDEs. II.Solving generic multiphysics problems. Computer methods in applied mechanics and engineering,2004(193):3891-3918.
[72] R. Sahu, M.J. Panthaki ,W.H. Gerstle. An Object-Oriented Framework for Multidisciplinary, Multi-Physics, Computational Mechanics. Engineering with Computers, 1999(15):105-125.
[73] P.CHOW, C.ADDISON. An overview on current multiphysics software strategies for coupled applications with interacting physics on parallel and distributed computers. Eleventh International Conference on Domain Decomposition Mehtods,1999, 396-401.
[74] Dany Kemmler, Panagiotis Adamidis, Wenqing Wang.Solving coupled geoscience problems on high performance computing platforms.ICCS 2005,LNCS3515,2005,1064-1071.
[75] P. Adamidis, A. Beck, U. Becker-Lemgau,etc. Steel strip production- a pilot application for coupled simulation with several calculation systems. Journal of Materials processing Technology,1998(80-81):330-336.
[76] S. Giurgea, T. Chevalier, J.-L. Coulomb,etc. Unified physics properties description in a multiphysics open platform. IEEE transactions on magnetics, 2003,39(3):1642-1645.
[77]高行山,赵亚溥,吕胜利等.微机电系统多场耦合仿真分析.动力学与控制学报,2004, 2(1):70-74.
[78]李海滨,冯国泰.叶轮机械中的多场耦合分析技术.航空发动机,2002(2):51-56.
[79]龚光彩,梅炽,周萍.关于多场耦合问题的几个概念探讨.湖南大学学报(自然科学版),1999,26(6):71-77.
[80] Piperno S, Farhat C, Larrouturou B. Partitioned procedures for the transient solution of coupled aeroelastic problems. Comp Mteh Appl Mech Eng, 1995(124):79-112.
[81] Piperno S. Explicit/implicit fluid-structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. Int J Num Meth Fluids, 1997(25):1207-1226.
[82] Rugonyi S, Bathe K J . On the analysis of fully-coupled fluid flows with structural interatcitons-a Coupling and Condensation Procedure. Int J of Comp Civil and Struct Engineering ,2000(1):29-41.
[83] Rugonyi S, Bathe K J. On finite element analysis of fluid flows fully coupled with structural interactions. Computer Modeling and Simulation in Engineering, 2001(2):195-212.
[84] K. C. Park. Partitioned transient analysis procedures for coupled-field problems: stability analysis. J. Appl. Mech. , 1980(47):370-376.
[85] K. C. Park, C. A. Felippa. Partitioned transient analysis procedures for coupled- field problems: accuracy analysis. J. Appl. Mech. , 1980(47):919-926.
[86] K.C. Park,C.A.Ft.elippa,J.A.DeRuntz,Stabilizaiton of staggered solution procedures for fluid-structure interaction analysis. Computational Methods for Fluid-Structure Interaction Problems,AMD vol.26,American Society of Mechanical Engineers,NewYork,1977,pp.95-124.
[87]刘雯林,何培英.三维散乱数据曲面重构技术综述.工程图学学报,2003(2): 143-148.
[88] K. Jansen, F. Shakib, and T. Hughes, Fast Projection Algorithm for Unstructured Meshes. 1992.
[89] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469-483.
[90] R.A. de By.R.A.d.B. , R.A.Knippers, etc. Principles of geographic information systems[M]. an introductory textbook. Enschede, The NetherIands, the International Institute for Aerospace Survey and Earth Sciences (ITC), 2001.
[91]周维垣,寇晓东.无单元法及其工程应用.力学学报,1998,30(2):193-202.
[92]结点载荷插值的混合法.计算机仿真,2006,23(8):73-75.
[93]杜子芳.抽样技术及其应用.北京:清华大学出版社,2005.
[94]胡文斌,郭荷清,华贲.基于web的建筑协同求解平台的研究.计算机系统应用,2004(11):17-19.
[95]朱万贵,葛昌跃,顾新建.面向大批量定制产品的协同求解平台研究.工程设计学报,2004,11(2):81-84.
[96]欧阳坚,张晓峰,沈海,等.一种基于WEB的VLSI协同求解平台.计算机工程与应用,2003(12):133-135.
[97]毕星,翟丽.项目管理.上海:复旦大学出版社,2000.
[98]宋伟,杨振峰,杨丽华.基于J2EE和MVC模式的Web应用程序开发方法.河北工业科技,2005,22(4):189-191.
[99]克罗尔,麦希萨克著,朱剑平译.敏捷与秩序:RUP最佳实践.北京:清华大学出版社,2006.
[100] http://www-306.ibm.com/software/rational/
[101] http://www.bea.com/
[102]熊光楞,李伯虎,柴旭光.虚拟样机技术.系统仿真学报,2001,13(1):114-117.
[103] Chang W P,Wan S M. Thermomechanincally coupled nonlinear vibration of plates. Int J Nonlinear Mech,1986,21(5):375-389.
[104] Chang W P,Jen S C. Nonlinear free vibration of heated orthotropic retangular plates. Int J Solid structure, 1986,22(3):267-281.
[105]戴德成.矩形板的非线性热弹耦合振动.振动工程学报,1990,8(2):65-72.
[106]张晓晴,树学锋.一类变厚度固支圆板热弹耦合的振动分析.太原理工大学学报, 2005, 36(6):673-675.
[107]王永岗,戴诗亮.扁球壳和扁锥壳的轴对称非线性热弹耦合振动.应用数学和力学, 2004,25(4):391-399.
[108]武新华,马晓峰.叶片热弹耦合场分析.汽轮机技术,2003,45(1):14-16.
[109]张晓晴,树学锋.几何非线性圆板的热弹耦合振动.太原理工大学学报,2000,31 (2):119-119.
[110]罗烈雷,吴晓,钟斌.复合材料圆柱壳非线性热弹耦合振动.振动与冲击,2001, 20(3): 75-78.
[2]陈恕行.现代偏微分方程导论.北京:科学出版社,2005.
[3]蒋叔豪.偏微分方程数值解.杭州:浙江大学出版社,1985.
[4]刘更,刘天祥,谢琴.无网格法及其应用.西安:西北工业大学出版社,2005.
[5]刘顺隆,郑群.计算流体力学.哈尔滨:哈尔滨工程大学出版社,1998.
[6]李志印,熊小辉,吴家鸣.计算流体力学常用数值方法简介.广东造船,2004(3):5-8.
[7]曾攀.有限元分析及其应用.北京:清华大学出版社,2004.
[8]姚寿广.边界元法数值方法及其工程应用.北京:国防工业出版社,1995.
[9]王福军.计算流体动力学分析.北京:清华大学出版社,2004.
[10]宋康祖.紧支函数无网格方法研究.博士学位论文,清华大学工程力学系,2000.
[11] http://www.ansys.com
[12] http://www.mscsoftware.com/
[13] http://www.physica.com
[14] http://www.femlab.com.cn/
[15] http://www.flormerics.com
[16] http://www.algor.com
[17] http://www.spectrum.com
[18]林胜勇.MEMS中多能量场耦合问题数值方法研究[硕士论文].西安:西北工业大学,2001.
[19] M. Roos, E. Batawi, U. Harnisch, etc. Efficient simulation of fuel cell stacks with the volume averaging method.Journal of Power Sources, 2003(118):86-95.
[20] M. Furmanczyk, P. Wilkerson, and A. Przekwas. Multiphysics Modeling of Integrated Microfluidic -Thermoelectric Cooling for Stacked 3D ICs. 19th IEEE SEMI-THERM Symposium,2003, 35-41.
[21]郑晓静.电磁固体力-磁-电作用的耦合效应.兰州大学学报(自然科学版),1999,35(3):17-21.
[22]朱林利,郑晓静.基于Boltzmann方程在外加电场和磁场作用下热传导及电磁热弹性理论.兰州大学学报(自然科学版).2005,41(2):104-108.
[23]何丽红,郑晓静.风-沙-电多场耦合模型及其对风沙流结构的影响.兰州大学学报(自然科学版).2005,41(3):87-92.
[24]邱高伟,郑晓静.热扩散和电场对风沙流发展过程的影响.应用数序和力学,2007,28(2):165-175.
[25]冯国泰,黄家骅,李海滨.涡轮发动机三维多场耦合数值仿真的数学模型.上海理工大学学报,2001,23(3):190-192.
[26]李海滨,冯国泰,王松涛.涡轮三维叶栅的气热耦合数值模拟.工程热物理学报,2003,24(5):770-772.
[27]梁卫国.盐类矿床水压致裂水溶开采的多场耦合理论及应用研究.岩石力学与工程学报,2005,24(6):1090-1090.
[28]薛强,冯夏庭,刘建军.填埋气体运移过程的多场耦合模型及仿真分析.系统仿真学报,2005,17(1):20-24.
[29]陆军,李恒,苏燕兵等.垂直Bridgman法多组元晶体生长的多场耦合模型.西安交通大学学报,2006,40(5):582-586.
[30]戴庆华,戴宏亮,王熙.多场耦合下压电圆筒的热电弹性瞬态响应.深圳大学学报理工版,2006,23(2):122-127.
[31]洪深泽,董定福,王树军等.热锻成形过程温度场的热力耦合数值模拟.机械工程学报,1996,32(1):62-67.
[32]杨兰和.煤炭地下气化干馏气渗流运动多场耦合数值模拟.西安交通大学学报,2002,36(7):752-756.
[33]张敦福,王锡平,赵俊峰.悬臂输送管道流-固耦合动力学系统的直接解法.机械工程学报,2004,40(3):195-198.
[34]刘建军,刘先贵.开发过程中三场耦合的数学模型.特种油气藏,2001,8(2):31-33.
[35] O.Sigmund. Design of multiphysics actuators using topology optimization-Part I: One-material structures. Computer methods in applied mechanics and engineering, 2001(190):6577-6604.
[36] O.Sigmund. Design of multiphysics actuators using topology optimization-PartⅡ: two-material structures. Computer methods in applied mechanics and engineering, 2001(190):6605-6627.
[37] John Michopoulos,Charbel Farhat,Elias Houstis.Dynamic-Data-Driven Real-Time Computational Mechanics Environment. ICCS 2004,LNCS 3038,2004,693-700.
[38] J. Michopoulos, C. Farhat, E. Houstis,etc.Dynamic Data Driven Methodologies for multiphysics system modeling and simulation.ICCS 2005,LNCS3515,2005,616-623.
[39] J. Michopoulos, P. Tsompanopoulou, E. Houstis. On a data-dviven environment for multiphysics applications. Future generation computer systems. 2005(21):953-968.
[40] A.V.Smirnov. Multi-physics modeling environment for continuum and discrete dynamics.2004,1-12.
[41] T.Belytschko,R.Mullen. Stability of explicit-implicit mesh partitions in time integration. Int. J. Number. Methods Emgrg. ,1978(12):1575-1586.
[42] T.Belytschko, T.Yen, R.Mullen. Mixed methods for time integration. Comput. Methods Appl. Mech. Engrg. , 1979(17/18):259-275.
[43] T.J.R. Hughes, W.K. Liu. Implicit-explicit finite elements in transient analysis:Ⅰ. Stablity theory;Ⅱ. Implementation and numerical examples. J. Appl. Mech., 1978(45):371-378.
[44] T.J.R. Hughes, K.S. Pister, R.L. Taylor. Implicit-explicit finite elements in nonlinear transient analysis. Comput. Methods Appl. Mech. Engrg. , 1979(17/18):159-182.
[45] T.J.R. Hughes, R.S. Stephenson. Stability of implicit-explicit finite elements in nonlinear transient analysis. Int. J. Engrg. Sci. , 1981(19):295-302.
[46] C.A. Felippa, K.C. Park. Staggered transient analysis procedures for coupled-field mechanincal systems:formulation. Comput. Methods Appl. Mech. Engrg. , 1980 (24): 61-111.
[47] C. A. Felippa, J. A. Deruntz. Finite element analysis of shock-induced hull cavitation. Comput. Methods Appl. Mech. Engrg. , 1984(44):297-337.
[48] C. A. Felippa, T. L. Geers. Partitioned analysis of coupled mechanincal systems. Eng.Comput. 1988(5):123-133.
[49] Carlos A.Felippa, K.C.Park, Charbel Farhat. Partitioned analysis of coupled mechanical systems. Computer methods in applied mechanics and engineering,2001(190):3247-3270.
[50] Charles Lawrence. An overview of three approaches to multidisciplinary aeropropulsion simulations.1997,NASA TM-107443.
[51] M N Sanhinkaya. Inverse dynamic analysis of multiphysics systems. MechE, 2004 (218): 13-26.
[52] C. Walshaw, M. Cross, and K. McManus.Multiphase mesh partitioning for parallel computational mechanincs codes.ICCS2002,LNCS 2330.2003,943-952.
[53] Michael Raulli , Kurt Maute. Optimization of fully coupled electrostatic–fluid–structure interaction problems. Computers & Structures.2005(83):221-233.
[54]张凯,彭云峰.一种微构件的多物理场耦合求解方法.机械设计与制造,2006(2):1-3.
[55]王东方,潘琼瑶,郑百林等.柴油机气缸盖多场耦合三维有限元分析.力学季刊,2005,26(3):511-516.
[56]周萍,刘朝东,周乃君等.石油焦煅烧回转窑内多场耦合数值仿真与操作参数的优化,潭素技术,2006,25(2):1-5.
[57]朱文峰,林忠钦,来新民.基于多场耦合的车门铰链凸焊过程有限元仿真.焊接学报,2005,26(1):64-68.
[58]康永林,宋仁伯,董洪波等.60Si2Mn半固态轧制有限元模拟.机械工程学报,2002, 38(6): 83-87.
[59]邓文君,夏伟,周照耀.正交切削高强耐磨铝青铜的有限元分析.机械工程学报,2004, 40(3):71-75.
[60]倪正顺,帅词俊,钟掘.基于热力耦合的热挤压模具结构参数优化设计.中国机械工程,2004,15(9):757-759.
[61]宋广胜,刘相华,王国栋等.齿轮钢淬火过程多场耦合分析.特殊钢,2007,28(1):7-9.
[62]郑百林,潘琼瑶,王锋.柴油机活塞热机耦合三维有限元分析.同济大学学报(自然科学版),2006,34(11):1534-1538.
[63]王文龙,梁慧敏,翟国富.密封点此继电器接触系统机电热耦合仿真分析.机电元件,2007,27(1):3-6.
[64]李迎,俞小莉,李婷等.活塞-缸套瞬态耦合传热的有限元仿真.浙江大学学报(工学版),2007,41(2):347-350.
[65] C. Bailey, H.Lu, D.Wheeler. Computational modeling techniques for reliability of electronic components on printed circuit boards. Applied Numerical Mathematics,2002(40):101-117.
[66] C.Bailey, G.A.Taylor, M.Cross, etc. Discretisation procedures for multi-physics phenomena. Journal of Computational and Applied Mathematics,1999(103):3-17.
[67] Mats Leijon, Hans Bernhoff, Olov ?gren,etc. Multiphysics simulation of wave energy to electric energy conversion by permanent magnet linear generator. IEEE transactions on energy conversion,2005,20(1):219-224.
[68] Michael T.Heath ,Xiangming Jiao. Academic Channenges in Large-Scale Multiphysics Simulations.ICCS 2005,LNCS3515,52-59.
[69]陈云敏,叶肖伟,张民强等.多场耦合作用下重金属离子在粘土中的迁移性状试验研究.岩土工程学报,2005,27(12):1371-1375.
[70] James R. Stewart, H.Carter Edwards. A framework approach for developing parallel adaptive multiphysics applications. Finite Elements in Analysis and Design, 2004(40):1599-1617.
[71] Charles Boivin, Carl Ollivier-Gooch. A toolkit for numerical simulation of PDEs. II.Solving generic multiphysics problems. Computer methods in applied mechanics and engineering,2004(193):3891-3918.
[72] R. Sahu, M.J. Panthaki ,W.H. Gerstle. An Object-Oriented Framework for Multidisciplinary, Multi-Physics, Computational Mechanics. Engineering with Computers, 1999(15):105-125.
[73] P.CHOW, C.ADDISON. An overview on current multiphysics software strategies for coupled applications with interacting physics on parallel and distributed computers. Eleventh International Conference on Domain Decomposition Mehtods,1999, 396-401.
[74] Dany Kemmler, Panagiotis Adamidis, Wenqing Wang.Solving coupled geoscience problems on high performance computing platforms.ICCS 2005,LNCS3515,2005,1064-1071.
[75] P. Adamidis, A. Beck, U. Becker-Lemgau,etc. Steel strip production- a pilot application for coupled simulation with several calculation systems. Journal of Materials processing Technology,1998(80-81):330-336.
[76] S. Giurgea, T. Chevalier, J.-L. Coulomb,etc. Unified physics properties description in a multiphysics open platform. IEEE transactions on magnetics, 2003,39(3):1642-1645.
[77]高行山,赵亚溥,吕胜利等.微机电系统多场耦合仿真分析.动力学与控制学报,2004, 2(1):70-74.
[78]李海滨,冯国泰.叶轮机械中的多场耦合分析技术.航空发动机,2002(2):51-56.
[79]龚光彩,梅炽,周萍.关于多场耦合问题的几个概念探讨.湖南大学学报(自然科学版),1999,26(6):71-77.
[80] Piperno S, Farhat C, Larrouturou B. Partitioned procedures for the transient solution of coupled aeroelastic problems. Comp Mteh Appl Mech Eng, 1995(124):79-112.
[81] Piperno S. Explicit/implicit fluid-structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. Int J Num Meth Fluids, 1997(25):1207-1226.
[82] Rugonyi S, Bathe K J . On the analysis of fully-coupled fluid flows with structural interatcitons-a Coupling and Condensation Procedure. Int J of Comp Civil and Struct Engineering ,2000(1):29-41.
[83] Rugonyi S, Bathe K J. On finite element analysis of fluid flows fully coupled with structural interactions. Computer Modeling and Simulation in Engineering, 2001(2):195-212.
[84] K. C. Park. Partitioned transient analysis procedures for coupled-field problems: stability analysis. J. Appl. Mech. , 1980(47):370-376.
[85] K. C. Park, C. A. Felippa. Partitioned transient analysis procedures for coupled- field problems: accuracy analysis. J. Appl. Mech. , 1980(47):919-926.
[86] K.C. Park,C.A.Ft.elippa,J.A.DeRuntz,Stabilizaiton of staggered solution procedures for fluid-structure interaction analysis. Computational Methods for Fluid-Structure Interaction Problems,AMD vol.26,American Society of Mechanical Engineers,NewYork,1977,pp.95-124.
[87]刘雯林,何培英.三维散乱数据曲面重构技术综述.工程图学学报,2003(2): 143-148.
[88] K. Jansen, F. Shakib, and T. Hughes, Fast Projection Algorithm for Unstructured Meshes. 1992.
[89] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469-483.
[90] R.A. de By.R.A.d.B. , R.A.Knippers, etc. Principles of geographic information systems[M]. an introductory textbook. Enschede, The NetherIands, the International Institute for Aerospace Survey and Earth Sciences (ITC), 2001.
[91]周维垣,寇晓东.无单元法及其工程应用.力学学报,1998,30(2):193-202.
[92]结点载荷插值的混合法.计算机仿真,2006,23(8):73-75.
[93]杜子芳.抽样技术及其应用.北京:清华大学出版社,2005.
[94]胡文斌,郭荷清,华贲.基于web的建筑协同求解平台的研究.计算机系统应用,2004(11):17-19.
[95]朱万贵,葛昌跃,顾新建.面向大批量定制产品的协同求解平台研究.工程设计学报,2004,11(2):81-84.
[96]欧阳坚,张晓峰,沈海,等.一种基于WEB的VLSI协同求解平台.计算机工程与应用,2003(12):133-135.
[97]毕星,翟丽.项目管理.上海:复旦大学出版社,2000.
[98]宋伟,杨振峰,杨丽华.基于J2EE和MVC模式的Web应用程序开发方法.河北工业科技,2005,22(4):189-191.
[99]克罗尔,麦希萨克著,朱剑平译.敏捷与秩序:RUP最佳实践.北京:清华大学出版社,2006.
[100] http://www-306.ibm.com/software/rational/
[101] http://www.bea.com/
[102]熊光楞,李伯虎,柴旭光.虚拟样机技术.系统仿真学报,2001,13(1):114-117.
[103] Chang W P,Wan S M. Thermomechanincally coupled nonlinear vibration of plates. Int J Nonlinear Mech,1986,21(5):375-389.
[104] Chang W P,Jen S C. Nonlinear free vibration of heated orthotropic retangular plates. Int J Solid structure, 1986,22(3):267-281.
[105]戴德成.矩形板的非线性热弹耦合振动.振动工程学报,1990,8(2):65-72.
[106]张晓晴,树学锋.一类变厚度固支圆板热弹耦合的振动分析.太原理工大学学报, 2005, 36(6):673-675.
[107]王永岗,戴诗亮.扁球壳和扁锥壳的轴对称非线性热弹耦合振动.应用数学和力学, 2004,25(4):391-399.
[108]武新华,马晓峰.叶片热弹耦合场分析.汽轮机技术,2003,45(1):14-16.
[109]张晓晴,树学锋.几何非线性圆板的热弹耦合振动.太原理工大学学报,2000,31 (2):119-119.
[110]罗烈雷,吴晓,钟斌.复合材料圆柱壳非线性热弹耦合振动.振动与冲击,2001, 20(3): 75-78.