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研究生:林儒禮
研究生(外文):Ru-Li Lin
論文名稱:異向性材料層域與壓延問題的理論解析
論文名稱(外文):The Theoretical Analysis of Anisotropic Multi-layered Medium and Punch Problem
指導教授:馬劍清
指導教授(外文):Chien-Ching Ma
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:219
中文關鍵詞:層域壓延薄層異向性格林函數應力函數映射法混合式邊界值問題
外文關鍵詞:Multi-layered mediumPunchThin-layerAnisotropicGreen''s functionStress functionImage methodMixed boundary value problems
相關次數:
  • 被引用被引用:12
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映射法是用簡單問題的基本解疊加出較複雜問題的解,這種方法所得的的解函數是具有物理意義的,二維異向性問題的映射性質經過一些學者的探討已經確定,然而二維等向性的映射性質則不是很清楚,本文將透過映射法原理確定具直線邊界之等向性材料的映射性質。
對於異向性複合層狀介質的反平面問題,由於材料係數以及幾何邊界的複雜性,使的這類的顯示解析解難以得到,本文則透過傅立葉轉換以及轉換域中的泰勒級數展開,得到這類問題的顯示解析解並表示成簡潔的形式,而處理的數學方法上,其實就是映射法原理的應用。
相較於反平面問題,異向性層域的平面問題更加複雜也較困難,本文也提出這個問題在傅立葉轉換域下的通解,雖然無法將顯示的解析解寫出,但這個結果足以直接使用在數值計算上。至於薄層問題,因為幾何邊界比較單純,所以可以獲得這個問題的顯式解析解,並可證明這個數學的處理方法其實就是映射法原理的應用。
至於異向性壓延問題方面,本文利用半平面表面位移與表面曳引力所建立的積分方程式,將半平面壓延問題的四種不同接觸面條件的混合型邊界值問題轉變為一般的邊界值問題而解決這類的問題。最後本文也希望結合這問題的解和薄層問題的格林函數,來探討薄層材料壓延問題的力學行為,由於問題本身的複雜性,使得目前只得到第一階的逼近解。最後則將本文的分析延伸到三維軸對稱問題,探討三維軸對稱下薄層問題的格林函數,經過分析可發現,三維軸對稱問題的格林函數,也可用映射法原理來解釋其隱含的意義,只是映射性質尚未清楚而已。
The method of image is a technique that uses superposition of known solution to solve another problems. The method had been used powerfully to deal two-dimensional elastic anisotropic bimaterials problem and the nature of image singularities were also discussed in detail. But for isotropic material, the degenerate case of anisotropic case, the image singularities are not simply forces and dislocations any more. The aim of this paper is to investigate the Green’s function of the half plane with straight boundary, and to discuss in detail the structure of image singularities on the image point.
It is hard to obtain the analytical solution for the anti plane problems of anisotropic multi-layered medium due to the material constants and boundary condition. With aid of the technique of Fourier transform and series expansion, the solutions can be derived in the study. The physical meanings of the solution can be regarded as the application of image method. The same method also used to obtain the solutions for the plane problem of anisotropic multi-layered medium.
By constructing the relation of surface displacement and traction for anisotropic half plane, it can transfer the punch problem, the mixed boundary value problem, into the boundary value problem. Combining the surface traction of half plane and the Green’s functions for anisotropic planar and axisymmetric problems, it can obtain the first order approximation for the punch problem of thin layer.
封面
目錄
誌謝
摘要
目錄
表目錄
圖目錄
符號說明
第一章 緒論
1-1 研究動機
1-2 論文回顧
1-3 本文研究方法與架構
第二章 基本理論
2-1 前言
2-2 異向性材料的材料常數
2-3 三維軸對稱問題
2-4 二維平面異向性材料-平面問題
2-5 二維平面異向性材料-反平面問題
第三章 二維等向性半平面奇異映射點的構造分析
3-1 前言
3-2 基本原理
3-3 半平面內承受垂直力的映射構造分析-自由邊界
3-4 半平面內承受垂直力的映射構造分析-固定邊界
3-5 半平面內承受水平力與差排的映射構造分析
3-6 矩陣形式表示的映射奇異量
3-7 結論
第四章 二維等向性雙異質材料奇異映射點的構造分析
4-1 前言
4-2 基本原理
4-3 雙異質材料內承受垂直力的映射構造分析
4-4 雙異質材料內承受其它載荷的映射構造分析
4-5 矩陣形式表示的映射奇異量
4-6 結論
第五章 異向性層狀介質內承受反平面載荷下的全場解析
5-1 前言
5-2 異向性問題轉換成等向性問題的座標轉換
5-3 半平面內承受集中力與差排作用的格林函數
5-4 無限長單層域受反平面剪力作用的格林函數
5-5 異向性層狀介質受剪力及差排作用的反平面問題
5-6 數值結果及討論
5-7 結論
第六章 二維平面異向性層域問題之力學解析
6-1 前言
6-2 轉換域下的通解與異向性全平面的格林函數
6-3 半平面內承受集中力與差排作用的格林函數
6-4 異向性半平面的映射法原理
6-5 平面異向性薄層問題的格林函數
6-6 異向性層狀介質受集中力及差排作用的平面問題
6-7 結論
第七章 二維異向性薄層的壓延問題之力學解析
7-1 前言
7-2 異向性半平面表面位移或曳引力的關係式
7-3 異向性半平面的壓延問題
7-4 薄層問題的表面格林函數及壓延問題的力學解析
7-5 結論
第八章 三維橫向等向性材料之薄層受壓延作用下的軸對稱問題
8-1 前言
8-2 漢克轉換與轉換域下的通解
8-3 半平面與薄層問題的格林函數
8-4 三維橫向等向性材料的壓延問題
第九章 結盟與未來研究方向
9-1 本文成果
9-2 未來研究方向
參考文獻
附錄
A 二維全平面等向性材料受各種載荷下的基本解
B 異向性反平面問題中各係數的循環公式
C 正交性全平面受集中力與差排作用下的格林函數
D 二維平面異向性薄層問題中各待定係數的解
E 二維異向性薄層問題表面格林函數各待定係數的解
F 三維軸對稱薄層問題各待定係數的解
Bahar, L. Y., 1972, “ Transfer Matrix Approach to Layered Systems,” ASCE Journal of the Engineering Mechanics Diversion, Vol. 98, pp. 1159-1172.
Barnett, D. M., and Lothe, J., 1974, “An Image Force Theorem for Dislocations in Bicrystals,” J. Phys., Vol. 4, pp. 1618-1635.
Bufler, H., 1971, “Theory of Elasticity of a Multilayered Medium,” Journal of Elasticity, Vol. 1, pp. 125-143.
Carvalho, J. L., and Curran, J. H., 1992, “Two-Dimensional Green’s Functions for Elastic Bi-materials,” ASME Journal of Applied Mechanics, Vol. 59, pp. 321-327.
Chiu, Y. T., and Wu, K. C., 1998, “Analysis for Elastic Strips under Concentrated Loads,” J. Appl. Mech., Vol. 65, pp. 626-634.
Choi, H. J., and Thangjithan, S., 1991, “Micro- and Macromechanical Stress and Failure Analyses of Laminated Composites,” Composites Science and Technology, Vol. 14, pp. 289-305.
Choi, H. J., and Thangjithan, S., 1991, “Stress Analysis of Multilayered Anisotropic Elastic Media,” ASME Journal of Applied of Mechanics, Vol. 58, pp. 382-387.
Dhaliwal, R. S., 1970, “Punch Problem for an Elastic Layer overlying an Elastic Fundamention”, Int. J. Engng Sci., Vol. 8, pp. 273-288.
Dundurs, J., and Hetenyi, M., 1965, “Transmission of Force Between Two Semi-infinite Solids,” ASME Journal of Applied Mechanics, Vol. 32, pp. 671-674.
Eshelby, J. D., Read, W. T., and Shockley W., 1953, “Anisotropic Elasticity with Applications to Dislocation Theory,” Acta Metallurgica, Vol. 1 pp. 251-259.
Fan C. W. and Hwu, C. B., 1996, “Punch Problems for an Anisotropic Elastic Half-Plane,” ASME Journal of Applied of Mechanics, Vol. 63, pp. 69-76.
Fan, H., and Keer, L. M., 1994, “Two-Dimensional Contact on an Anisotropic Elastic Half-Space,” ASME Journal of Applied of Mechanics, Vol. 61, pp. 250-255.
Gaydom, F. A., and Shepherd, W. M., 1964, “Generalized Plane Stress in a Semi-infinite Strip under Arbitrary End-load,” Proceedings of the Royal Society of London, Vol. A281, pp. 184-206.
Galin, L. A., 1953, Contact Problem in the Theory of Elasticity, Moscow. Translation by H. Moss. North Carolina State College.
Gladwell, G. M. L., 1980, Contact Problems in the Classical Theory of Elasticity, Sijthoff & Noordhoff, The Netherlands.
Green, A. E., and Zerna, W., 1954, Theoretical Elasiticity, Clarendon Press, Oxford, U.K.
Hasegawa, H., Lee, V. G., and Mura, T., 1992, “Green’s Function for Axisymmetric Problems of Dissimilar Elastic Solids,” ASME Journal of Applied Mechanics, Vol. 59, pp. 312-320.
Hills, D. A., Nowell, D., and Sackfield, A., 1993, Mechanics of Elastic Contacts, Butterworth-Heinemann.
Horgan, C. O., and Miller, K. L., 1994, “Antiplane Shear Deformations for Homogeneous and Inhomogeneous Anisotropic Linearly Elastic Solids,” ASME Journal of Applied Mechanics, Vol. 61, pp. 23-29.
Hwu, Chyanbin, and Yen, Wen J., 1991, “Green’s Functions of Two-Dimensional Anisotropic Plates Containing an Elliptic Hole,” Int. J. Solids Structures, Vol. 27, pp. 1705-1719
Huw, C. B., and Fan, C. W., 1998, “Solving the Punch Problems by Analogy with the Interface Crack Problems,” Int. J. Solids Structures, Vol. 35, pp. 3945-3960.
Jiang, Q., and Knowles, J. K., 1991, “A Class of Compressible Elastic Materials Capable of Sustaining Finite Anti-plane Shear,” Journal of Elasticity, Vol. 25, pp. 193-201.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, U.K.
Johnson, M. W., and Little, R. W., 1965, “The Semi-infinite Strip,” Quarterly of Applied Mathematics, Vol. 1, pp. 335-344.
Klintworth, J. W., and Stronge, W. J., 1990, “ Plane Punch Indentation of Anisotropic Elastic Half-Space,” ASME Journal of Applied of Mechanics, Vol. 57, pp. 84-90.
Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco, Calif.
Lin, W., and Keer, L. M., 1989, “Analysis of a Vertical Crack in a Multilayered Medium,” ASME Journal of Engineering for Industry, Vol. 56, pp. 63-69.
Love, A. E. H., 1927, Mathematical Theory of Elasticity, fourth edition, Cambridge.
Ma, C. C., 1992, “Antiplane Problems of Monoclinic Material,” ASCE Journal of Engineering Mechanics, Vol. 118, pp. 1765-1782.
Ma, C. C., 1996, “Relationship of Anisotropic and Isotropic Materials for Antiplane Problems,” AIAA Journal, Vol. 34, pp. 2453-2456.
Ma, C. C., and Hour, B. L., 1989, “Analysis of Dissimilar Anisotropic Wedges Subjected to Antiplane Shear Deformation,” Int. J. Solids and Structures, Vol. 25, pp. 1295-1309.
Ma, C. C., and Huang, K. C., 1996, “Exact Transient Solutions of Buried Dynamic Point Forces for Elastic Bimaterials,” Int. J. Solids and Structures, Vol. 33, pp. 4511-4529.
Melan E., 1932, “Der spannungszustand der durch eine einzelkraft in innern beanspruchten halbscheibe,” Z. Angew. Math. Mech. Vol. 12, pp. 343-346.
Mindlin, R. D., 1936, “Force at a Point in the Interior of a Semi-Infinite Solid,” Physics, Vol. 7, pp. 195-202.
Mindlin, R. D., and Cheng, D. H., 1950, “Nuclei of Strain in the Semi-Infinite Solid,” Journal of Applied Physics, Vol. 21, pp. 926-930.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticiy, Leydon, Noordhoff.
Phan-Thien, N., 1983, “On the Image System for the Kelvin-State,” Journal of Elasticity, Vol. 13, pp. 231-235.
Polignone, D. A., and Horgan, C. O., 1992, “Axisymmetric Finite Anti-plane Shear of Compressible Nonlinearly Elastic Circular Tubes,” Quarterly of Applied Mathematics, Vol. 50, pp. 323-341.
Qu, Jianmin, and Li, Qiangian, 1991, “Interfacial Dislocation and Its Application to Interface Crack in Anisotropic Bimaterials,” Journal of Elasticity, Vol. 26, pp. 167-195.
Retting, G., 1986, “Anti-plane Stress Analysis of a Cracked Rectangular Orthotropic Beam,” Engineering Fracture Mechanics, Vol. 23, pp. 441-454.
Sneddon I. N., 1950, Fourier Transforms, McGrwa-Hill book company, Inc. Printed in the United States of America.
Small, J. C., and Booker, J. R., 1984, “Finite Layer Analysis of Layered Elastic Materials Using a Flexibility Approach. Part 1-Strip Loadings,” International Journal for Numerical Methods in Engineering, Vol. 20, pp. 1025-1037.
Stroh, A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philosophical Magazine, Vol. 7, pp. 625-646.
Sundara Raja Iyengar, K. T., and Alwar, R. S., 1964, “Stresses in a Layered Half-Plane,”ASCE Journal of the Engineering Mechanics Division, August, pp. 79-96.
Suo, Z., 1990, “Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media,” Proc. Roy. Soc. London, Vol. A427, pp. 331-358.
Telles, J. C. F., and Brebbia, C. A., 1981, “Boundary Element Solution for Half-plane Problems,” Int. J. Solids and Structures, Vol. 17, pp. 1149-1158.
Ting, T. C. T., 1992, “Image Singularities of Green’s Functions for Anisotropic Elastic Half-Spaces and Bimaterials,” Q. J. Mech. Appl. Math., Vol. 45, pp. 119-139.
Ting, T. C. T., 1996, Anisotropic Elasticity : Theory and Applications, Oxford, New York, pp. 260-311.
Vijayakumar, S., and Cormack, D. E., 1987a, “Green’s Functions for the Biharmonic Equation : Bonded Elastic Media,” SIAM Journal of Applied Mathematics, Vol. 47, pp. 982-997.
Vijayakumar, S., and Cormack, D. E., 1987b, “Nuclei of Strain for Bi-material Elastic Media with Sliding Interface,” Journal of Elasticity, Vol. 17, pp. 285-290.
Wang, W., and Shi, M., X., 1998, “On the General Solutions of Transversely Isotropic Elasticity,” Int. J. Solids Structures, Vol. 35, pp. 3283-3297.
Willis, J.R., 1970, “Stress Field Produced by Dislocations in Anisotropic Media,” Philosophical Magazine, Vol. 21, pp. 931- 949.
Wu, K. C., and Chiu, Y. T., 1991, “Antiplane Shear Interface Cracks in Anisotropic Bimaterials,” ASME Journal of Applied Mechanics, Vol. 58, pp. 399-403.
Wu, K. C., and Chiu, Y. T., 1995, “The Elastic Fields of a Dislocation in an Anisotropic Strip,” Int. J. Solids Structure, Vol. 32, pp. 543-552.
Wu, K. C., and Chiu, Y. T., 1996, “Antiplane Shear Analysis of a Semi-infinite Multi-layered Monoclinic Strip,” Acta Mechanica, Vol. 117, Vol. 205-214.
Yang, W., and Ma, C. C., 1998, “Orthotrpic Transform for Planar Anisotropic Elasticity and Reduced Dependence of Elastic Constants,” Proc. Roy. Soc. London, Vol. A454, pp. 1843-1855.
Zwiers, R. I., Ting, T. C. T., and Spilker, R. L., 1982, “On the Logarithmic Singularity of Free Edge Stress in Laminated Composites under Uniform Extension,” ASME Journal of Applied Mechanics, Vol. 49, pp. 561-569.
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