【作者】 周小义；

【导师】 邓安福；

【作者基本信息】 重庆大学 ， 岩土工程， 2008， 博士

【摘要】 数值流形方法用于计算结构或材料的位移和变形,能对连续变形与非连续变形问题进行统一求解,对问题具有较高的求解精度,是目前岩土工程数值分析方法的一个研究热点。本文针对数值流形方法理论体系及其在岩土工程中的应用,并结合一些学者已有的研究成果,开展了对数值流形方法部分研究工作。本论文的研究工作及取得的成果主要有以下几个方面:(1)研究了覆盖位移函数对刚度矩阵形成的影响,提出了将覆盖位移函数的基本级数函数基中x、y由材料的绝对坐标改进为以流形单元的形心坐标为原点的相对坐标的建议来改善刚度矩阵的局部性态,以利于求解计算。同时指出了选择合理的坐标原点以便充分发挥覆盖位移函数的全阶项对总平衡方程组成时刚度矩阵和荷载矩阵的贡献,使求解精度得到提高。(2)基于广义变分原理的理论体系,利用罚函数法,推导了梁板单元分析的修正泛函;构造了梁板流形单元及相应的流形单元格式(位移函数、应变矩阵和刚度矩阵等)。(3)针对工程中广泛应用中厚板的弯曲分析问题,以数值流形方法的基本思想为基础,建立了Winkler弹性地基上Mindlin板的数值流形方法;对工程中分析弹性地基上的中厚板弯曲问题具有一定的参考意义。(4)利用数值流形方法对隧道工程中衬砌结构进行了尝试性的分析,提出了结合规则网格和有限网格并行、高低阶覆盖位移函数混合计算的思想,以达到前处理和程序计算、计算效率和求解精度的协调。(5)通过对目前数值流形方法中采用的几种本构模型的研究,提出了适用于非线性分析的数值流形方法。文中本构模型采用非线性弹性模型(Duncan-Chang模型和K-G模型),为数值流形方法进行岩土工程非线性分析提供了有益的数值分析方法。(6)在前人研究的基础上,构造了六面体有限覆盖的三维流形单元,推导了三维流形单元覆盖位移函数、应变矩阵、刚度矩阵、荷载矩阵等表达式。通过算例分析及与解析解和ANASYS计算结果的比较,表明该思路是有效可行的。(7)自编了较大型的面向对象计算机程序,该程序采用C++语言在VC++平台中编制,能对数值流形方法的一般问题(如文中所涉及的相关问题等)进行计算,具有较好的程序前后处理功能,并通过算例验证了程序是有效和合理的。更多还原

【Abstract】 Numerical manifold method is used for calculating the displacement and the deformation of the structure or the material, and it is capable of uniformly dealing with the problem of continuous deformation and discontinuous deformation. It has higher calculation precision for problem and is pop method of research for the numerical method in geotechnical engineering.Aiming at the theory and application of numerical manifold method, and combining the previous research work, this dissertation have researched the theory and application of numerical manifold method. The main works and research findings are written as following :(1) Have research the effects of cover displacement function to the stiffness matrix, put forward that x, y of basic progression functions has changed from the absolute value of coordinate in material region to opposite value of center coordinate in manifold element for amending the local character of the stiffness matrix in favor of solution, propose that the correct original coordinate is chose to exert the contribution of all order in the stiffness matrix and the stress matrix of equilibrium equations for increasing of precision in calculation.(2) Establish the modified functional of the analysis of the beam element and plate element, base on the generalized variational principle and penalty function method. Then, it is used to create the beam and plate manifold element and the format of manifold element( such as displacement function, strain matrix and stiffness matrix etc).(3) Aim at the bending problem of the moderately thick plate, the numerical manifold method of the Mindlin plate on the Winkler foundation is put forward, based on the principle of the numerical manifold method. It is significative to some bending problem of the moderately thick plate on the elastic foundation in engineering analysis.(4) Do some tentative analysis of the tunnel lining by numerical manifold method. the idea is given that combining regular mesh with finite element mesh and using low-order and high-order cover displacement function in numerical manifold method, it make preprocess and program analysis, precision and efficiency for coordination.(5) Give the numerical manifold method for nonlinear analysis by researching the consitistutive models used in numerical manifold method presently. Nonlinear models(Duncan-Chang model and K-G model )are used in this paper, and useful numerical analytic method is provided for nonlinear analysis of numerical manifold method in geotechnical engineering.(6) Construct the three-dimensional manifold element covering hexahedron, provide cover displacement function, strain matrix, stiffness matrix and stress matrix of the three-dimensional manifold element by the previous research work. With the example computation analysis and comparison with analytical solution and ANSYS computation result, the method is proved to be effective.(7) Programmed the Object-Oriented program with C++ language in VC++ platform. It is capable for calculating the common problem of manifold method (such as these correlative problems in the paper etc), and has better preprocess and postprocess function. The program is proved to be effictive and feasible by example.更多还原