地下結(jié)構(gòu)斷裂破壞分析的無網(wǎng)格流形方法研究
發(fā)布時間：2019-04-27 18:00
【摘要】：近年來無網(wǎng)格方法和數(shù)值流形方法以其新穎的計算思想和數(shù)值技術(shù)得到了力學與工程界的重視。無網(wǎng)格方法是近年來發(fā)展起來的一種新興的數(shù)值方法，因其具有不需要網(wǎng)格，只需要節(jié)點信息、前處理簡單、計算精度高等特點，已成為目前科學和工程計算方法的研究熱點之一；而數(shù)值流形方法通過引入數(shù)學與物理雙重網(wǎng)格和有限覆蓋技術(shù)解決了材料連續(xù)與非連續(xù)性的數(shù)學統(tǒng)一表述的問題，使得連續(xù)變形分析與非連續(xù)變形分析得到了統(tǒng)一，非常適合于各種非連續(xù)、大變形等問題的分析模擬。然而，在處理復雜非連續(xù)問題時（如多裂紋擴展問題），這兩種方法均有其各自的缺陷，例如無網(wǎng)格方法一般采用光線法（如可視、衍射準則）來處理域內(nèi)的不連續(xù)問題，這樣可能會由于插值點不足而導致試函數(shù)難以建立，產(chǎn)生數(shù)值解的不穩(wěn)定性等問題；數(shù)值流形方法在處理復雜非連續(xù)問題時，由于雙重網(wǎng)格的局限性，使得數(shù)值流形方法的覆蓋系統(tǒng)生成算法十分復雜，嚴重影響了它的應用。為了克服無網(wǎng)格方法和數(shù)值流形方法在處理復雜非連續(xù)問題時遇到的困難，本文提出和發(fā)展了一種基于單位分解法和有限覆蓋技術(shù)的、地下結(jié)構(gòu)破壞過程模擬分析的無網(wǎng)格流形MSIM（Meshless ShepardInterpolation Method,簡稱MSIM）新方法。在該方法中，插值函數(shù)除了不受域內(nèi)不連續(xù)面的影響外，還具有高階完備性、一致性，且可以在需要的節(jié)點處具備Kronecker-Delta屬性，能夠方便準確地施加各種邊界條件；克服了傳統(tǒng)無網(wǎng)格方法在處理不連續(xù)問題時由于采用光線法所遇到的困難及數(shù)值流形方法由于網(wǎng)格的存在使得覆蓋系統(tǒng)的生成異常復雜的問題。本文主要開展了以下工作： 1、基于單位分解和數(shù)值流形方法的有限覆蓋理論，建立和發(fā)展了基于MSIM插值的、用于地下結(jié)構(gòu)裂紋擴展和破壞過程分析的無網(wǎng)格流形MSIM方法，詳細地介紹和推導了相關(guān)公式，給出了無網(wǎng)格流形MSIM方法中的不連續(xù)問題處理方法和無網(wǎng)格流形MSIM方法數(shù)值實現(xiàn)的具體步驟； 2、在無網(wǎng)格流形MSIM方法中引入了J積分法、虛擬裂紋擴展法及虛擬裂紋閉合法等目前常用的幾種應力強度因子的計算方法，特別是把目前僅用于有限元計算的虛擬裂紋擴展法、虛擬裂紋閉合法引入到了無網(wǎng)格流形MSIM方法中，并對其相應的裂紋擴展準則選取和裂紋擴展步長的確定等進行了研究； 3、研究和發(fā)展了數(shù)學覆蓋被不連續(xù)面切割后的無網(wǎng)格流形MSIM方法物理覆蓋系統(tǒng)全自動生成理論與算法；基于Matlab平臺，給出了無網(wǎng)格流形覆蓋系統(tǒng)自動生成等無網(wǎng)格流形MSIM方法關(guān)鍵模塊的實施技術(shù)，并編制了可應用于地下結(jié)構(gòu)斷裂破壞分析的無網(wǎng)流形MSIM方法的計算程序； 4、利用具有解析解答的或參考解答的含裂紋試件算例，，對J積分法、虛擬裂紋擴展法及虛擬裂紋閉合法等各種方法的計算精度和穩(wěn)定性進行了對比分析研究，并在此基礎(chǔ)上對具有試驗或數(shù)值分析對照結(jié)果的各種裂紋擴展算例進行了裂紋擴展模擬分析研究，以驗證和測試本文所發(fā)展的地下結(jié)構(gòu)斷裂破壞分析的無網(wǎng)流形MSIM理論和方法的正確性和可靠性； 5、結(jié)合套拱加固的隧道襯砌破壞試驗，利用研制的無網(wǎng)格流形MSIM分析程序，對套拱加固后帶裂縫襯砌的具體破壞過程進行了分析研究，進一步對本文理論和方法的正確性、有效性進行了驗證。
[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.
【學位授予單位】：同濟大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU93
本文編號：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.
【學位授予單位】：同濟大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU93
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