【作者】 李超；

【导师】 李九红；

【作者基本信息】 西安理工大学 ， 结构工程， 2008， 硕士

【摘要】 作为20世纪建立的最有效的工程数值分析工具,有限元法不仅自身理论得到了迅猛发展,并日益受到工程界的重视。但由于网格生成的制约,使其应用受到限制。无网格法的出现,给数值方法开辟了新的途径。本文在阐述无网格法的基本原理以及无网格伽辽金法(EFG)的基础上,并通过对比分析现有的两种主要的无网格法与有限元耦合方法,结合无网格伽辽金法,建立了基于过渡单元的耦合方法。同时通过分析对比无网格法与有限元法的本质区别,提出了广义单元的概念,并建立了基于广义单元的EFG—FEM耦合方法,并把广义单元耦合法引入求解弹性接触问题中,并且编制了相应的FORTRAN程序,通过算例分析,主要得出以下结论:1.通过建立过渡单元,建立了无网格伽辽金法(EFG)与有限元法耦合的新的过渡函数,利用FORTRAN语言编制了无网格伽辽金法(EFG)与有限元法的耦合程序,并进行了悬臂梁算例分析,说明了EFG—FEM耦合法具有较高的计算精度,且其求解精度略高于有限元法。2.无网格法在处理边界条件方面是明显不如有限元法方便的,因此利用有限元法来克服无网格法的缺陷是十分必要的。3.通过对比无网格法与有限元法本质区别的基础上提出广义单元的概念,并在此基础上提出了广义单元耦合法,该方法在有限元与无网格的交界面处不用再设置过渡单元,而只需要设置共用结点,简化了程序的编制以及计算过程。4.结合线性规划法提出广义单元耦合—线性规划法求解接触问题,通过圆柱与刚性平面接触算例分析,验证了本文方法应用于求解接触问题的可行性。本文提出的无网格—有限元耦合方法及所得成果,有助于无网格法的进一步发展和研究。更多还原

【Abstract】 Being one of the most effective project numerical analysis tool established in the 20th century, the Element Finite Method not only developed in its own theory largely, but also be received the engineering value day by day. Since the limitation of mesh generation, it’s application and popularization are restricted. With the appearance of Meshless Method(MLM), a new way of numerical analysis is worked out.This paper studies the basic theory of Meshless and the Element -free Galerkin Method(EFG), along with the study and the analysis of the two main Coupled Meshless-Finite Element Method has been established, the author establishes the Coupled Meshless-Finite Element Method based on Transition Element. Meanwhile ,through the analysis of the essence difference the Meshless Method from the Finite Element, the concept Generalized Element has been proposed, and the Coupled Meshless-Finite Element Method based on Generalized Element has been proposed, then the author use this method to solve the Contact Question. The corresponding program by FORTRAN language is carried out. Trough result of the numerical -example, mainly draws the conclusion:1. After the transition element established, the new transient function is established, meanwhile the corresponding program by FORTRAN language is carried out and the cantilever beam is calculated as example to show the coupling method had higher computation precision than FEM.2. Meshless Method is inferior to FEM in processing the boundary condition, therefore it is extremely essential to study the coupled method of them.3. The concept of Generalized Element is proposed after the contract of the essence difference the Meshless Method from the Finite Element and the coupled method base on Generalized Element is established. This method does not need the Transition Element in the border of FEM and MLM, and only needs to establish the public point, so the program is simplified as well as the computation process.4. The generalized unit coupling - linear programming Method base on linear programming Method is proposed to solve Contact Question, through the example of the column and the rigid plane Contact Question, confirms that the method is feasible.The Coupled Meshless-Finite Element Method and its achievements proposed in this paper are helpful to the further development and research of Meshless Method.更多还原