無元素分析之
無元素分析之積分權值調整法

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：39

、訪客IP：18.118.154.123

姓名

沈國瑞(Kou-Juei Shen) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

無元素分析之無元素分析之積分權值調整法
(A Weighting Adjustment Scheme of Gauss Integration in Element Free Method )

相關論文

★ 貼片補強構件之層間應力分析	★ 軌道不整檢測及識別方法
★ 混凝土結構分析之三維等效單軸組成材料模型	★ 卵形顆粒法向與切向接觸之等效線性彈簧值之推導與驗證
★ 以四面體離散化多面體系統之接觸分析與模擬	★ 軌道車輛三維動態脫軌係數之在線量測理論
★ 向量式DKMT厚殼元推導與模擬	★ 向量式預力混凝土二維剛架元之數值模擬與驗證
★ 向量式有限元應用於懸索橋非線性動力分析	★ 蛋形顆粒群之流固耦合分析
★ 複合版梁元素分析模型之橋梁動態識別法	★ 三維等效單軸應變與應力之材料組成模型
★ 人行吊橋的現有內力評估及動力分析	★ 薄殼結構非線性運動之向量式有限元分析法
★ 雷射掃描技術於鋼軌磨耗之檢測	★ 動態加載下的等效單軸應變與應力材料組成模型

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

摘要
無元素法( Element Free method，EFM)處理網格邊界與材料邊界不一致的不規則邊界問題，常以高斯積分點在材料邊界內外做為取捨標準，容易造成數值誤差。本論文提出積分權值調整觀念，由高斯積分的幾何意義著手，將積分網格中積分點與權的值拓展成積分面積的觀念，處理邊界網格積分時直接估算材料邊界內的高斯積分面積，使能量計算誤差降低，取代以往以高斯積分點點位座落於介質體內外為取捨的積分觀念。數值範例顯示積分權值調整觀念處理網格邊界與材料邊界不一致的邊界積分，不必細分網格也可以達到相當的分析精度，不論處理傾斜邊界或曲線邊界均呈現出穩定而且良好的分析結果。運用本法結合J積分計算版裂縫應力強度因子與運用完整高斯積分法情況所得相近。積分權值調整觀念使用於裂縫拓展分析中也相當便利，由彈性樑垂直邊裂縫拓展與版雙裂縫拓展分析顯示本法可以在處理移動性邊界問題時真正做到不必網格重建。此一新的積分法以簡單有效的權值調整觀念處理複雜的邊界網格積分問題，不僅符合無元素法的原創精神，也確保了無元素法能量積分的正確性。

摘要(英)

A Weighting Adjustment Scheme of Gauss Integration in Element Free Method
In this thesis, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Numerical examples illustrate that this proposed integration scheme for element-free methods does effectively improve the accuracy of solving solid mechanics problems, and is easy to handle the crack propagation problems of solids than it does in the finite element method.

關鍵字(中)

★ 無元素法
★ 元素釋放法
★ 高斯積分

關鍵字(英)

★ EFGM
★ element free

論文目次

目錄
摘要 I
A Weighting Adjustment Scheme of Gauss Integration in Element Free Method II
目錄 III
表目錄 VI
圖目錄 VII
第一章緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 論文內容 4
第二章文獻回顧 6
2.1無網格法的發展 6
2.2 斷裂損傷力學上的應用 10
2.3無元素法的邊界與介面處理 15
2.4 無元素法的積分處理 17
第三章無元素法之基本理論 19
3.1 移動式最小平方(MLS)內插法之應用 19
3.1.1 一致性(Consistency)檢驗 23
3.1.2 形狀函數(Shape Function)之性質 24
3.1.3 加權函數(Weight Function)之探討 26
3.2變分原理 28
3.3離散方程式 30
第四章無元素法的實行與積分改良 32
4.1無元素法的實行 32
4.2高斯積分的幾何新義 37
4.3不規則邊界處之積分處理 41
4.4 無元素法的積分改善 48
4.5權值調整法程式流程 51
第五章裂縫拓展分析的基礎 53
5.1 應力強度因子的求法 53
5.2 裂縫拓展的原則 59
5.3 無元素法於裂縫處的影響圓建構 64
5.3.1不連續邊界處的影響圓決定方法 64
5.3.2通視法定影響圓 66
5.3.3繞射法定影響圓 68
5.3.4透明法定影響圓 69
5.4 權值調整法在裂縫處之應用 70
第六章積分驗證與數值分析例 72
6.1積分驗證 72
6.1.1 一階多項式函數積分檢測 72
6.1.2 高階多項式函數積分檢驗 73
6.1.3指數函數積分檢驗 77
6.2一維微分方程數值例 80
6.2.1具一階線性解的一維微分方程問題 80
6.2.2 具較高階解的一維問題 91
6.3二維彈性介質數值例 96
6.3.1 拉桿 96
6.3.2 含圓孔之無限鈑 100
6.3.3 曲桿純彎曲 104
6.4 破壞力學數值例 105
6.4.1第一型應力強度因子分析 106
6.4.2複合型應力強度因子分析 108
6.4.3 含45度邊緣斜裂縫的版 110
6.4.4 樑三點彎曲試驗 112
6.4.5 含兩組圓孔與裂縫的版 116
第七章結論與建議 123
7.1 結論 123
7.2建議 125
參考文獻 127

參考文獻

參考文獻
Beissel, S., and T. Belytschko, ” Nodal Integration of the Element-Free Galerkin Method,” Computer Methods in Applied Mechanics and Engineering, Vol 139, pp. 47~74(1996).
Belytschko, T., Y. Y. Lu, and L. Gu, "Element﷓Free Galerkin Method," International Journal for Numerical Methods in Engineering, Vol. 37, pp. 229~256 (1994).
Belytschko T., Y. Y. Lu and L. Gu, “Crack Propagation by Element Free Galerkin Method.”, Engineering Fracture Mechanics, Vol.51, No.2, pp.295~315 (1995a).
Belytschko, T., D. Organ and Y. Krongauz,“Coupled finite element-element-free Galerkin method,”Computational Mechanics, Vol. 17, pp. 186~195 (1995b).
Belytschko, T., Y. Krongauz, D. Organ, and M. Fleming., "Meshless methods: An Overview and Recent Developments," Computer Methods in Applied Mechanics & Engineering, Vol. 139, pp. 3~47, (1996a).
Belytschko T., Y. Krongauz, M. Flemming, D. Organ and W. K. Liu, “ Smoothing and Accelerated Computations in the Element-free Galerkin Method," Journal of Computational and Applied Mechanics, Vol. 74, pp. 111~126 (1996b).
Belytschko, T., P. Krysl and Y. Krongauz, "A Three-dimension Explicit Element-free Galerkin Method", International Journal for Numerical Methods in Fluids, Vol. 24, pp. 1253~1270 (1997).
Belytschko T. and M. Flemming,“ Smoothing, enrichment and contact in the Element-free Galerkin Method., " Computers and Structures, Vol. 71, pp. 173~195 (1999).
Bobaru, Florin. and Subrata Mukherjee, “Shape Sensitivity Analysis and Shape Optimization in Planar Elasticity Using the Element-free Galerkin Method,” Computer Methods in Applied Mechanics & Engineering, Vol. 190, pp. 4319~4337, (2001).
Chen, J.S., C. Pan, C.T. Wu and W.K. Liu, "Reproducing Kernel Particle Methods for Large Deformation Analysis of non-linear structures.", Computer Methods in Applied Mechanics And Engineering. Vol. 139 pp. 195~227 (1996).
Chen, J.S., C. Pan and C.T. Wu, "Large Deformation Analysis of Rubber Based on a Reproducing Kernel Particle Method.", Computational Mechanics. Vol. 19 pp. 211~227 (1997).
Chen, J.S., C.T. Wu, S. Yoon and Y. You, "A Stablized Conforming Nodal Integration for Galerkin Mesh-free Methods.", International Journal for Numerical Methods in Engineering. Vol.50, pp.435~466, (2001)
Chu, Y.A. and B. Moran, “A Computational model for Nucleation of Solid-Solid Phase Transformations,” Modeling Simul. Mater. Sci. Engrg. Vol. 3, pp. 445~471 (1995).
Chung, H.-J. and T. Belytschko,“An error estimate in the EFG method,”Computational Mechanics, Vol. 21, pp. 91~100 (1998).
Cordes, L.W. and B. Moran, “Treatment of Material Discontinuity in the Element-Free Galerkin Method,” Computer Methods in Applied Mechanics & Engineering, Vol. 139, pp. 57~89 (1996).
Duarte C.A. and J.T. Oden, “Hp-clouds—a Meshless Method to Solve Boundary-value Problems,” Technical Report 95-05, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin, (1995).
Erdogan, F., and G.C. Sih, “On the Crack Extension in Plates under Plane Loading and Transverse Shear,” Journal of Basic Engineering, Vol. 85, pp. 519~527 (1963)
Fleming, M., Y. A. Chu, B. Moran and T. Belytschko,” Enriched Element-Free Galerkin Methods for Crack Tip Fields,” International Journal for Numerical Methods in Engineering, Vol. 40, pp. 1483~1504 (1997).
Gallagher, R.H., Finite Element Analysis Fundamentals, Plantis Company, (1975).
Gerald, C.F., Applied Numerical Analysis, Addison-Wesley Publishing Company, (1978).
Gu, Y.T. and G.R. Liu,"A Coupled Element Free Galerkin/boundary Element Method for Stress Analysis of Two-dimensional Solids.", Computer Methods in Applied Mechanics and Engineering.Vol. 190. pp.4405~4419, (2001).
Hardee E. and K.H. Chang, I. Grindeanu, S. Yoon, M. Kaneco, and J.S. Chen.,” A Structural Nonlinear Analysis Workspace (SWAN) besed on meshless methods,” Advances in Engineering Software. Vol 30. (1999) pp. 153~175.
Hegen, D., “Element-free Galerkin Methods in Combination with finite element approaches,” Computer Methods in Applied Mechanics & Engineering, Vol. 135, pp. 143~166 (1996).
Kaljevic, I. and S. Saigal, “An Improved Element Free Galerkin Formulation,” International Journal for Numerical Methods in Engineering, Vol. 40, pp. 2953~2974 (1997).
Krongauz, Y., and T. Belytschko, ”Enforcement of essential boundary conditions in meshless approximations using finite elements,” Computer Methods in Applied Mechanics and Engineering, Vol. 131, pp. 133~145 (1996).
Krysl, P. and T. Belytschko, "Analysis of Thin Plates by the Element﷓Free Galerkin Method," Computational Mechanics, Vol. 17, pp. 26~35 (1995).
Krysl, P. and T. Belytschko, "Analysis of Thin Shells by the Element﷓Free Galerkin Method," International Journal of Solids & Structures, Vol. 33, pp. 3057~3080 (1996).
Krysl, P. and T. Belytschko, ”ESFLIB: A Library to Compute The Element Free Galerkin Shape Functions,” Computer Methods in Applied Mechanics & Engineering, Vol. 190. pp.2181~2205 (2001).
Lancaster, P. and K. Salkauskas, "Surfaces Generated by Moving Least Squares Method,” Mathematics of Computation, Vol. 37, pp. 141~158(1981).
Lauterbach, B. and D. Gross, "Crack Growth in Brittle Solids under Compression.", Mechanics of Materials, Vol. 29, pp.81~92 (1998)
Li, C., R. Prikryl and E. Nordlund, "The Stress-strain Behavior of Rock Material Related to Fracture under Compression.", Engineering Geology, Vol. 49, pp.293~302, (1998).
Li, Shaofan., Dong Qian, Wing Kam Liu and Ted Belytschko, “ A Meshfree Contact-detection Algorithm,” Computer Methods in Applied Mechanics and Engineering, Vol.190, pp.3271~3292 (2001).
Lin, C.T., B. Amade, S. Ouyang and C. Haung., “Development of Fracturing Algorithms for Jointed Rock Masses with the Discontinuous Deformation Analysis,” Proceedings of ICADD-1 The First International Conference on Analysis of Discontinuous Deformation. 21-23 December 1995, Chungli, Taiwan , R.O.C.
Liu, W.K., S. Jun and Y.F. Zhang, “Reproducing kernel partical methods,” Int. J. Numer. Methods Engrg. Vol.20, pp. 1081~1106 (1995).
Lu, Y.Y., T. Belytschko and L. Gu,“A New Implementation of the Element Free Galerkin Method,” Computer Methods in Applied Mechanics & Engineering, Vol. 113, pp. 397~414 (1994).
Lucy, L.B., “A Numerical Approach to the Testing of the Fission Hypothesis,” The Astron. J. Vol.8, pp. 1013~1024 (1977).
Modaressi, H. and P. Aubert,“A Diffuse Element-Finite Element Technique for Transient Coupled Analysis,”International Journal for Numerical Methods in Engineering, Vol. 39, pp. 3809~3838 (1996).
Monaghan, J.J., ”Why partical methods work,” SIAM J. Sci. Stat. Comput. Vol.3, pp.422 (1982).
Monaghan, J. J., ”An Introduction to SPH,” Comput. Phys. Comm. Vol.48, pp.89~96 (1988).
Nayroles, B., G. Touzot and P. Villon," Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elememts, "Computational Mechanics, Vol. 10, pp. 307~318 (1992).
Oñate, E., S. Idelsohn, O. C. Zienkiewicz ,R. L. Taylor and C. Sacco, “ A Stabilized finite point method for analysis of fluid mechanics problems”, Computer Methods in Applied Mechanics & Engineering, Vol. 139, pp. 315~346 (1996).
Perrone, N. and R. Kao, “A General Finite Difference Method for Arbitrary Meshes,” Comput. Struct. Vol.5,pp. 45~58 (1975).
Rao, B.N. and S. Rahman, “A Coupled Meshless-Finite Element Method for Fracture Analysis of Cracks”, International Journal of Pressure Vessels and Piping, Vol. 78, pp.647~657 (2001).
Shah, S., Stuart Swartz and Chengsheng Ouyang., Fracture Mechanics of Concrete. John Wiley & Sons, Inc. (1995).
Sheng, J., C.-Y. Wang, and K.-J. Shen, “A Modified Gaussian Integration Scheme in Element-Free Method.”, Chinese Journal of Mechanics-Series A. Vol.18, No.1, pp. 17~27, (2002).
Shi, G.H. Manifold method. Proceeding of the first international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media, edited by M. Reza Salami and Don Banks, Berkeley California, USA, June 12-14, 1996, TSI Press: 1996: 52-204.
Swegle, J.W., D.L. Hicks and S.W. Attaway, “Smoothed Partical Hydrodynamics Stablity Analysis,” J. Comput. Phys. Vol. 116, pp.123~134 (1995).
Terry, T.G., Fatigue Crack Progration Modeling Using The Element Free Galerkin Method. Master of Science Thesis, Northwestern University, Evanston, IL. (1994).
Timoshenko, S., and J. Goodier, Theory of Elasticity, Third Edition. McGraw-Hill Book Company, (1970).
Wang, C.-Y., J. Sheng, and K.-J. Shen, “Calculation of Stress Intensity Factor of Crack Tip by Element-Free Method,.” Abstracts of the Sixth U.S. National Congress on Computational Mechanics, pp. 33, (2001).
Wu, C.T., J.S. Chen, L. Chi, F. Huck,"A Lagrangian Formulation for Analysis of Geotechnical Matericals.", ASCE Journal of Engineering Mechanics, Vol. 127, No. 5, pp. 440~449 (2001).
Xu, Y., B. Moran and T. Belytschko, "Uncoupled Characteristics of Three-dimensional Planar Cracks," Int. J. Engng Sci. Vol. 36, No.1, pp.33~48, (1998).
Xu, Yu. and S. Saigal, “ An Element Free Galerkin Analysis of Dynamic Growth of a Mode I Crack in Elastic-plastic Materials,” Computer Methods in Applied Mechanics and Engineering, Vol.154 (1998) pp.331~343.
Xu, Y. and S. Saigal, “ An Element Free Galerkin Formulation for Stable Crack Growth in an Elastic Solid,” International Journal of Solids and Structures , Vol.36 (1999) pp.1045~1079.
Zhu, T. and S. N. Atluri,“A Modified Collocation Method and a Penalty Formulation for Enforcing the Essential Boundary Conditions in the Element Free Galerkin Method,”Computational Mechanics, Vol. 21, pp. 211~222 (1998).
Zhu, T. and S. N. Atluri,“A Meshless Numerical Method Based on the Local Boundary Integral Equation (LBIE) to Solve Linear and Non-linear Boundary Value Problems,”Engineering Analysis with Boundary Elements, Vol. 23, pp. 357~389 (1999).
吳振瑞, 「元素釋放法之邊界處理」, 碩士論文, 國立中央大學土木工程研究所, 中壢 (1999).
吳伯壽, 「元素釋放法之層狀邊界處理」, 碩士論文, 國立中央大學土木工程研究所, 中壢 (2000).
陳俊民, 「波傳無元素法之層狀邊界處理」, 碩士論文, 國立中央大學土木工程研究所, 中壢 (2000).
張行, 「斷裂力學」, 宇航出版社, 北京(1990).
沈成康,「斷裂力學」,同濟大學出版社, 上海(1995).
林聰悟, 林佳慧, 「數值方法與程式」, 圖文技術公司, 台北市(1997).
何文欽, 「加權節點選配法之理論分析與數值模擬」, 碩士論文, 國立中央大學土木工程研究所, 中壢(1998).
盛若磐, 王仲宇, 陳銘鴻, 沈國瑞“加權節點選配法在不連續性問題之應用”, 第八屆大地工程學術研究論文集(1999).
盛若磐，王仲宇，吳振瑞，沈國瑞 “元素釋放法之邊界處理”,計算機在土木水利的應用研討會(1999).

指導教授

王仲宇(Chong-Yui Wang)

審核日期

2002-5-21

推文