【作者】 宋少云；

【导师】 李世其；

【作者基本信息】 华中科技大学 ， 机械设计及理论， 2007， 博士

【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。更多还原

【Abstract】 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.更多还原