【作者】 王雪；

【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】 随着计算科学及软件技术的发展,有限元法从理论基础到误差估计都已十分成熟,但其内在固有的局限性使它在许多领域失效而难以应用,例如在高度大变形问题、动态裂纹扩展问题、高速撞击引起的几何畸变等问题中,有限元法存在困难或者不能解决。无网格方法以其新颖的数值思想、先进的数值技术,得到了学术界的初步认可和广泛关注。在处理裂纹扩展时,只需要通过自由裂纹面或者裂纹线的延伸来模拟,这大大简化了裂纹模拟的过程,因此在裂纹扩展问题上无网格方法具有其独特的优势。其中基于移动最小二乘近似(MLS)理论的无网格伽辽金方法(EFGM),以其精度高、稳定性好和收敛速度快等特点成为最具有发展前景的一种。本文首先分析研究了无网格方法在国内外的发展历史及现状,并对现行的一些重要无网格方法作了概括性评述;归纳总结了目前比较流行的无网格近似方法、不连续性的处理、离散化方法及基本边界条件的实现等。详细推导了无网格伽辽金方法的刚度方程,得出了详细的数值求解计算公式,用MATLAB编制了无网格方法计算通用程序。通过对两个典型算例的数值解与精确解的对比,可以看出本文计算结果具有较高的精度,验证了无网格伽辽金法的可行性,并对目前无网格伽辽金法(EFGM)中基函数的选取、影响域半径的大小等作了详细的研究,并得出其取值或选择的基本规律。其次,本文编制了求解线弹性弹性断裂力学问题的二维无网格Galerkin法程序,选取带有部分扩展基的基函数,分别采用J积分法和远场围线积分法,成功的求解出了单边裂纹有限板和单边斜裂纹有限板的位移场和应力场,其结果与大型有限元软件(ANSYS)的计算结果吻合良好;同时用所求得的裂纹尖端的应力场位移场推导出了应力强度因子,并模拟了单边裂纹有限板的裂纹扩展。算例论证了该方法具有简捷、高效的特点,从而为结构断裂分析提供了一条有效的途径。最后,对影响断裂力学问题计算精度的因素,如权函数、基函数、不连续性的处理、积分路径、衍射法则参数、节点分布程度、部分扩展基函数在影响域内节点数目等作了详细的研究,并得出其取值或选择的基本规律。基于以上的研究,将无网格求解断裂力学的程序用于复杂应力状态下开洞混凝土墙体实际问题及复杂应力状态下重力坝的位移场和应力场计算,得到了满意的结果,可为工程设计提供参考。属性不符更多还原

【Abstract】 As the development of computational science and software technique,the Finite Element Method (FEM) has become much powerful both in the estimation of error and foundation of theory.However,because of the FEM’s inherent defect,it can not be used in many fields.For example,the FEM become powerless or can not solve the problems such as tremendous distortion,dynamic crack propagation,geometry aberration by high-speed bump,and so on. Under such a conditions.the element free method become been recognized and gain more and more attention because of its original idea and advanced technology in the numerical calculation.Firstly ,this paper investigate the history and actuality that element free method developed in the world,and analyzes the advantage and disadvantage of the element free method,and then outlines some popular methods in element free method such as the approximation method, discontinuity disposal method and essential boundary conditions disposal method. Stiffness equation of EFGM are derived.General program of the EFGM is programmed by MATLAB software.Through to two example computation solution and the exact solution contrast.The accuracy and a the precision of the procedure are conformed.Aimed at the basis function choice, Shape function, essential boundary conditions and obtain of the domain of influence in the most popular method-element free Galerkin method (EFGM),this paper studys particularly and gives out the basic rules.Secondly, by using the theory of linear elastic fracture mechanics,the J-integral method and the contour integral method,a new type of weight function basing on partially enriched basis function,analysis of displacement and stress field is given for finite plates with single edge crack and single inclined edge crack.Furthermore,the caculation esults of the meshless methord is approached to the calculation result of two analysis software of ANSYS.Based on the stress field of crack tip,stress intensity factor is solved,and simulated crack propagation.The analysis of crack propagation is dramatically simplified.The examples reveal the effectiveness of the present method. Finally,this paper studies particularly the influences of the weight function,the basis functions,the extent of distribution nodes,the discontinuities guidelines,the integral contours,the lamd with diffraction rules and the distrubution of nodes and gives out the basic rules.Meantime,Stress field and displacement feld of concrete wall with holes under complicated stress and Gravity dam are simulated by the program of EFGM to solve fracture mechanics problems and the result is not only satisfactoried but also available for the application in engineering.更多还原