地下结构断裂破坏分析的无网格流形方法研究
发布时间：2019-04-27 18:00
【摘要】：近年来无网格方法和数值流形方法以其新颖的计算思想和数值技术得到了力学与工程界的重视。无网格方法是近年来发展起来的一种新兴的数值方法，因其具有不需要网格，只需要节点信息、前处理简单、计算精度高等特点，已成为目前科学和工程计算方法的研究热点之一；而数值流形方法通过引入数学与物理双重网格和有限覆盖技术解决了材料连续与非连续性的数学统一表述的问题，使得连续变形分析与非连续变形分析得到了统一，非常适合于各种非连续、大变形等问题的分析模拟。然而，在处理复杂非连续问题时（如多裂纹扩展问题），这两种方法均有其各自的缺陷，例如无网格方法一般采用光线法（如可视、衍射准则）来处理域内的不连续问题，这样可能会由于插值点不足而导致试函数难以建立，产生数值解的不稳定性等问题；数值流形方法在处理复杂非连续问题时，由于双重网格的局限性，使得数值流形方法的覆盖系统生成算法十分复杂，严重影响了它的应用。为了克服无网格方法和数值流形方法在处理复杂非连续问题时遇到的困难，本文提出和发展了一种基于单位分解法和有限覆盖技术的、地下结构破坏过程模拟分析的无网格流形MSIM（Meshless ShepardInterpolation Method,简称MSIM）新方法。在该方法中，插值函数除了不受域内不连续面的影响外，还具有高阶完备性、一致性，且可以在需要的节点处具备Kronecker-Delta属性，能够方便准确地施加各种边界条件；克服了传统无网格方法在处理不连续问题时由于采用光线法所遇到的困难及数值流形方法由于网格的存在使得覆盖系统的生成异常复杂的问题。本文主要开展了以下工作： 1、基于单位分解和数值流形方法的有限覆盖理论，建立和发展了基于MSIM插值的、用于地下结构裂纹扩展和破坏过程分析的无网格流形MSIM方法，详细地介绍和推导了相关公式，给出了无网格流形MSIM方法中的不连续问题处理方法和无网格流形MSIM方法数值实现的具体步骤； 2、在无网格流形MSIM方法中引入了J积分法、虚拟裂纹扩展法及虚拟裂纹闭合法等目前常用的几种应力强度因子的计算方法，特别是把目前仅用于有限元计算的虚拟裂纹扩展法、虚拟裂纹闭合法引入到了无网格流形MSIM方法中，并对其相应的裂纹扩展准则选取和裂纹扩展步长的确定等进行了研究； 3、研究和发展了数学覆盖被不连续面切割后的无网格流形MSIM方法物理覆盖系统全自动生成理论与算法；基于Matlab平台，给出了无网格流形覆盖系统自动生成等无网格流形MSIM方法关键模块的实施技术，并编制了可应用于地下结构断裂破坏分析的无网流形MSIM方法的计算程序； 4、利用具有解析解答的或参考解答的含裂纹试件算例，，对J积分法、虚拟裂纹扩展法及虚拟裂纹闭合法等各种方法的计算精度和稳定性进行了对比分析研究，并在此基础上对具有试验或数值分析对照结果的各种裂纹扩展算例进行了裂纹扩展模拟分析研究，以验证和测试本文所发展的地下结构断裂破坏分析的无网流形MSIM理论和方法的正确性和可靠性； 5、结合套拱加固的隧道衬砌破坏试验，利用研制的无网格流形MSIM分析程序，对套拱加固后带裂缝衬砌的具体破坏过程进行了分析研究，进一步对本文理论和方法的正确性、有效性进行了验证。
[Abstract]:In recent years, the method of meshless method and the numerical manifold method have been paid more and more attention in the fields of mechanics and engineering with its novel calculation and numerical techniques. The meshless method is a new numerical method that has been developed in recent years, because it has the characteristics of no need of the grid, only the information of the nodes, the simple processing and the high calculation precision, and has become one of the hot spots of the current scientific and engineering calculation method. The numerical manifold method solves the problem of the continuous and non-continuous mathematical expression of the material by introducing the mathematical and physical double mesh and the finite covering technique, so that the continuous deformation analysis and the non-continuous deformation analysis are unified, and the numerical manifold method is very suitable for various non-continuous deformation analysis. Analysis and simulation of large deformation and other problems. in deal with complex non-continuous problems (e. g., multi-crack propagation problems), however, both of that two approach have their respective drawbacks, e. g., the meshless method generally uses a light method (e. g., a visual, diffraction criterion) to process discrete problems in the domain, so that the problem that the test function is difficult to establish due to the defect of the interpolation point and the instability of the numerical solution are solved; and when the numerical manifold method is used for processing the complex non-continuous problems, the method for covering the numerical manifold method is very complex due to the limitation of the double grid, It has a serious impact on its application. In order to overcome the difficulties of meshless method and numerical manifold method in dealing with complex non-continuous problems, this paper presents and develops a new method of Meshless Shearer Interpolation Method (MIMIM), which is based on the unit decomposition method and the finite coverage technique. in that method, the interpolation function has the high-order completeness and the consistency in addition to the influence of the discontinuous surface in the domain, and the Kronecker-Delta attribute can be provided at the required node, so that various boundary conditions can be conveniently and accurately applied; The problem that the traditional meshless method is difficult to meet with the light method and the numerical manifold method when the discontinuous problem is processed is overcome, and the problem that the generation of the overlay system is abnormal due to the existence of the grid is overcome. The following work is mainly carried out in this paper: 1. Based on the finite covering theory of the unit decomposition and the numerical manifold method, the MIMIM method based on MIMinterpolation is established and developed for the analysis of the crack propagation and the destruction process of the underground structure, and the relevant public information is introduced and derived in detail. The non-continuous problem processing method in the non-grid-manifold MSIM method and the concrete step of the numerical implementation of the non-grid-manifold MSIM method are given. step-by-step;2, J is introduced in the method of no-grid-manifold MSIM The calculation method of several stress intensity factors, such as the integration method, the virtual crack extension method and the virtual crack closed method, is a virtual crack extension method which is only used for finite element calculation, and the virtual crack closed method is introduced to the meshless manifold MSIM. In the method, the corresponding crack propagation criterion and the determination of the crack growth step size are carried out. 3. Research and develop the full-automatic generation theory and algorithm of the non-grid-manifold MSIM method physical covering system after the mathematical coverage is cut by the discontinuous surface; on the basis of the Mat In this paper, the implementation technology of non-grid-manifold MSIM method, such as automatic generation of non-grid-manifold covering system, is given, and a non-net-manifold MSIM method, which can be applied to the analysis of the fracture and failure of underground structures, is developed. meter The calculation accuracy and the stability of various methods such as the J integration method, the virtual crack extension method and the virtual crack closed method are carried out by using a crack-containing test case with an analytical solution or a reference solution. In this paper, a comparative analysis study is carried out, and on this basis, the crack propagation simulation analysis is carried out on various crack propagation examples with test or numerical analysis control results, so as to verify and test the theory and method of the non-net-manifold MSIM for the analysis of the fracture failure of the underground structure developed in this paper. Correct Based on the development of a non-grid-manifold MSIM analysis program, this paper makes an analysis and study on the concrete failure process of the crack lining after the reinforcement of the set arch, and further the correctness of the theory and method of this paper.
【学位授予单位】：同济大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU93
本文编号：2467196
[Abstract]:In recent years, the method of meshless method and the numerical manifold method have been paid more and more attention in the fields of mechanics and engineering with its novel calculation and numerical techniques. The meshless method is a new numerical method that has been developed in recent years, because it has the characteristics of no need of the grid, only the information of the nodes, the simple processing and the high calculation precision, and has become one of the hot spots of the current scientific and engineering calculation method. The numerical manifold method solves the problem of the continuous and non-continuous mathematical expression of the material by introducing the mathematical and physical double mesh and the finite covering technique, so that the continuous deformation analysis and the non-continuous deformation analysis are unified, and the numerical manifold method is very suitable for various non-continuous deformation analysis. Analysis and simulation of large deformation and other problems. in deal with complex non-continuous problems (e. g., multi-crack propagation problems), however, both of that two approach have their respective drawbacks, e. g., the meshless method generally uses a light method (e. g., a visual, diffraction criterion) to process discrete problems in the domain, so that the problem that the test function is difficult to establish due to the defect of the interpolation point and the instability of the numerical solution are solved; and when the numerical manifold method is used for processing the complex non-continuous problems, the method for covering the numerical manifold method is very complex due to the limitation of the double grid, It has a serious impact on its application. In order to overcome the difficulties of meshless method and numerical manifold method in dealing with complex non-continuous problems, this paper presents and develops a new method of Meshless Shearer Interpolation Method (MIMIM), which is based on the unit decomposition method and the finite coverage technique. in that method, the interpolation function has the high-order completeness and the consistency in addition to the influence of the discontinuous surface in the domain, and the Kronecker-Delta attribute can be provided at the required node, so that various boundary conditions can be conveniently and accurately applied; The problem that the traditional meshless method is difficult to meet with the light method and the numerical manifold method when the discontinuous problem is processed is overcome, and the problem that the generation of the overlay system is abnormal due to the existence of the grid is overcome. The following work is mainly carried out in this paper: 1. Based on the finite covering theory of the unit decomposition and the numerical manifold method, the MIMIM method based on MIMinterpolation is established and developed for the analysis of the crack propagation and the destruction process of the underground structure, and the relevant public information is introduced and derived in detail. The non-continuous problem processing method in the non-grid-manifold MSIM method and the concrete step of the numerical implementation of the non-grid-manifold MSIM method are given. step-by-step;2, J is introduced in the method of no-grid-manifold MSIM The calculation method of several stress intensity factors, such as the integration method, the virtual crack extension method and the virtual crack closed method, is a virtual crack extension method which is only used for finite element calculation, and the virtual crack closed method is introduced to the meshless manifold MSIM. In the method, the corresponding crack propagation criterion and the determination of the crack growth step size are carried out. 3. Research and develop the full-automatic generation theory and algorithm of the non-grid-manifold MSIM method physical covering system after the mathematical coverage is cut by the discontinuous surface; on the basis of the Mat In this paper, the implementation technology of non-grid-manifold MSIM method, such as automatic generation of non-grid-manifold covering system, is given, and a non-net-manifold MSIM method, which can be applied to the analysis of the fracture and failure of underground structures, is developed. meter The calculation accuracy and the stability of various methods such as the J integration method, the virtual crack extension method and the virtual crack closed method are carried out by using a crack-containing test case with an analytical solution or a reference solution. In this paper, a comparative analysis study is carried out, and on this basis, the crack propagation simulation analysis is carried out on various crack propagation examples with test or numerical analysis control results, so as to verify and test the theory and method of the non-net-manifold MSIM for the analysis of the fracture failure of the underground structure developed in this paper. Correct Based on the development of a non-grid-manifold MSIM analysis program, this paper makes an analysis and study on the concrete failure process of the crack lining after the reinforcement of the set arch, and further the correctness of the theory and method of this paper.
【学位授予单位】：同济大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU93
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