跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 馮詩維
Shi-Wei Feng
論文名稱： 橡膠材料有限大圓孔非對稱變形近似解的誤差分析
The rubber Materials of finite voids of asymmetric deformation of the approximate solution of the error analysis
指導教授： 李顯智
Xian-Zhi Lei
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
畢業學年度： 100
語文別： 中文
論文頁數： 110
中文關鍵詞： Hou-Abeyaratne filed (HAF) 、橡膠材料 、誤差
外文關鍵詞： error, Hou-Abeyaratne filed (HAF), Rubber
相關次數： 點閱：5  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 摘　　　要
    本文在探討不同橡膠材料模型中(包含Ogden、Beda、Mooney-Rivlin、neo-Hookean材料模型)有限大孔洞的非對稱變形。而橡膠材料在不少地方都有使用到，如土木工程的橋樑支承、機械工程的輪胎或皮帶等等都有使用到橡膠材料。本文將探討在Hou和Abeyaratne[21]的文章裡所提到的圓孔非圓對稱變形的近似解，此解使用橢圓變形公式來逼近圓孔的非對稱變形，本文則探討此近似解在各種橡膠材料模型下的誤差。
    關鍵字: 橡膠材料、Hou-Abeyaratne filed (HAF)、誤差

    Abstract
    This thesis investigates the asymmetrical deformation of finite voids in rubber materials described by different models includes Ogden,Beda, Mooney-Rivlin and neo-Hookean materials model. The use of rubber materials is extensive, such as bridge supports in civil engineering,tires and belts in mechanical engineering .This thesis analyzes the approximate solution proposed in [21] for asymmetrical deformation of a circular voide. This approximate solution was proposed by assuming that the circular void will be deformed into an elliptical one. This thesis compute the error of this approximate solution for materials modelled by those models mentioned above.
    Keywords: Rubber, Hou-Abeyaratne filed (HAF),error

    目　　　錄 摘　　　要 I Abstract II 誌　　　謝 III 目　　　錄 IV 圖目錄 V 符號表 X 第一章 緒論 1 第二章 基礎理論 6 2-1橡膠材料變形控制方程式的推導 6 2-2計算出壓力場的梯度 8 2-3誤差原理 9 第三章 Hou-Abeyaratne變形場 12 3-1 Hou-Abeyaratne變形場公式推導 12 3-2圓對稱與非圓對稱圓孔變形 16 3-3球體兩種會產生exact solution的變形形態: 21 第四章 誤差之比較 29 4-1 HAF yi=Aiψi(R)Xi的誤差 29 4-1-1四種真實材料之誤差比較 29 4-1-2主伸展應變λ1、λ2、λ3的比值大小不同之誤差比較 34 4-2 改良HAF yi=Aiψi(ρ)Xi的誤差 43 4-2-1四種真實材料之誤差比較 44 4-2-2主伸展應變λ1、λ2、λ3的比值大小不同之誤差比較 47 4-3小結 55 第五章 HAF之實用性 56 5-1 HAF yi=Aiψi(R)Xi的誤差 56 5-2 改良HAF yi=Aiψi(ρ)Xi的誤差 73 5-3 小結 89 第六章 結論與建議 91 6-1結論 91 6-2建議 92 參考文獻 93

    1. J.F. Kang and Y.Q. Jiang, Improvement of cracking-resistance and flexural behavior of cement-based materials by addition of rubber particles. J. Wuhan Univ. Tech.—Mater.Sci. Edition, 23(2008)579-583.
    2. G. Skripkiunas, et. al., Deformation properties of concrete with rubber waste additives.
    Mater. Sci.—Medziagotyra, 13(2007)219-223.
    3. M.K. Batayneh, et., al., Promoting the use of crumb rubber concrete in developing countries. Waste Management, 28(2008)2171-2176.
    4. L. Zheng, et. al., Strength, modulus of elasticity, and brittleness index of rubberized concrete. J. Mater. Civil Eng., ASCE, 20(2008)692-699.
    5.張惠文，砂土中減振模型樁之動態性質，國科會計劃(NSC96-2221-E008-059-MY3)。執行期間:九十八年八月至九十九年七月。
    6. T.J. Paulson, et. al., Shaking table study of base isolation for masonary buildings. J. Struct. Eng., 117(1991)3315-3336.
    7. A.D. Luca, et. al., Base isolation for retrofitting historic buildings: Evaluation of seismic performance through experimental investigation. Earthquake Eng. Struct. Dyn., 30(2001)1125-1145.
    8. B. Yoo and Y.H. Kim, Study on effects of damping in laminated rubber bearings on seismic responses for a 1/8 scale isolated test structure. Earthquake Eng. Struct. Dyn., 31(2002)1777-1792.
    9 Y.M. Wu and B. Samali, Shake table testing of a base isolated model. Eng. Struct., 24(2002)1203-1215.
    10. N. Lakshmanan, et. al., Experimental investigations on the seismic response of a base-isolated reinforced concrete frame model. J. Performance Constructed Facilities, ASCE, 22(2008)289-296.
    11. T.H. Kim, Y.J. Kim and H.M. Shin, Seismic performance assessment of reinforced concrete bridge piers supported by laminated rubber bearings. Struct Eng. Mech., 29(2008)259-278.
    12. M. Navarro, et. al., Biomaterials in orthopaedics. J. R. Soc. Interface, 5(2008)1137-1158.
    13. Y. Jung, et. al., Cartilaginous tissue formation using a mechano-active scaffold and dynamic compressive stimulation. J. Biomaterials Sci.—Polymer Edition, 19(2008)61-74.
    14. T. Hu and J.P. Desai, Characterization of soft-tissue material properties: Large deformation analysis. ‘Medical Simulation, Proceedings’ in Lecture Notes in Computer Science, 3078(2004)28-37.
    15. J.Z. Wu, et. al., Nonlinear and viscoelastic characteristics of skin under compression: experiment and analysis. Bio-Medical Mater. Eng., 13(2003)373-385.
    16. Z.Q. Liu and M.G. Scanlon, Modelling indentation of bread crumb by finite element analysis, Biosystems Eng., 85(2003)477-484.
    17. M. Zidi, Circular shearing and torsion of a compressible hyperelastic and prestressed tube. Int. J. Non-Linear Mech., 35 (2000) 201-209.
    18. M. Zidi, Torsion and axial shearing of a compressible hyperelastic tube. Mech. Res. Comm., 26 (1999) 245-252.
    19. M. Cheref, M. Zidi and C. Oddou, Analytical modelling of vascular prostheses mechanics. Intra and extracorporeal cardiovascular fluid dynamics. Comput. Mech. Pub., 1 (1998) 191-202.
    20. M. Zidi, Finite torsional and anti-plane shear of a compressible hyperelastic and transversely isotropic tube. Int. J. Engrg. Sci., 38 (2000) 1481-1496.
    21. H.S. Hou and R. Abeyaratne, Cavitation in elastic and elastic-plastic solids.. J. Mech. Phys. Solids, 40 (1992) 571-592
    22. M. Danielsson, D.M. Parks and M.C. Boyce, Constitutive modeling of porous hyperelastic material. Mech. Mater., 36(2004)347-358.
    23. J. Li, D. Mayau and F. Song, A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading. Int. J. Solids Struct., 44(2007)6080-6100.
    24. O. Lopez-Pamies and P. Ponte Castaneda, Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I—Analysis. J. Mech. Phys. Solids, 55(2007)1677-1701.
    25. O. Lopez-Pamies and P. Ponte Castaneda, Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II—Results. J. Mech. Phys. Solids, 55(2007)1702-1728.
    26. J. Li, D. Mayau and V. Lagarrigue, A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading. J. Mech. Phys. Solids, 56(2008)953-973.
    27. R.W. Ogden, On constitutive relations for elastic and plastic materials. Ph.D. Dissertation, Cambridge University, 1970.
    28. R.W. Ogden, Large deformation isotropic elasticity I: on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc.London, Series A, 326(1972)565-584.
    29. R.W. Ogden, ‘Elastic Deformations of rubberlike solids’ in Mechanics of Solids, The Rodney Hill 60th Anniversary Volume (Eds. H.G. Hopkins and M.J. Sewell). Pergamon Press, pp. 499-537, 1982.
    30. R.W. Ogden, “Non-Linear Elastic Deformations”. Ellis Horwood Limited, Chichester, England,1984.
    31. T. Beda, Modelling hyperelastic behavior of rubber: a novel invariant-based and a review of constitutive models. J. Polymer Sci.: Part B: Polymer phys., 45(2007)1713-1732.
    32. J.M. Hill, Some partial solutions of finite elasticity. Ph.D. thesis, University of Queensland (1972).
    33. J.M. Hill, On static similarity deformations for isotropic materials. Q. Appl. Math., 40(1982)287-291.
    34. H.C. Lei (李顯智) and J.A.Blume , Lie group and invariant solution of the plane-strain equation of motion of a neo-Hookean solid . Int. J. Non-linear Mech. , 31 (1996) 465-482 .
    35. H.C. Lei (李顯智) and M.J. Hung , Linearity of waves in some systems of non-linear elastodynamics . Int.J. Non-Linear Mech. ,32 (1997) 353-360 .
    36. H.C. Lei (李顯智)(2005), Sequentially linearizable initial-boundary value problems for a neo-Hookean cylinder, Journal of the Chinese Institute of Engineers,28(2005)763-769
    37. R.S. Rivlin and D.W. Saunders, Philos. Trans. R. Soc. London, Series A, 243(1951)251.
    38. R.S. Rivlin, In “Reology: Theory and Applications”. F.R. Eirich, Eds., Academic Press, New York, Vol. 1, 1956.
    39. A.E. Green and J.E. Adkins, Large Elastic Deformation and Nonlinear Continuum Mechanics. Clarendon Press, Oxford, 1970.
    40. L.R.G.. Treloar, The Physics of Rubber Elasticity, 3rd ed.. Oxford University Press, Oxford, 1975.
    41. T. Beda and Y. Chevalier, Hybrid continuum model for large elastic deformation of rubber . J. Appl. Phys. AIP, 94(2003)2701-2706
    42. T. Beda and Y. Chevalier, Non-linear approximation method by an approach in stages. Comput. Mech., 32(2003)177-184
    43. T. Beda, Reconciling the fundamental phenomenological expression of the strain energy of rubber with established experimental facts. J. Sci., Part B: Polym. Phys., 43(2005)125-134
    44. T. Beda, Optimizing the Ogden strain energy expression of rubber materials . J. Engrg. Mater. Technol. ASME, 127(2005)351-353.
    45. T. Beda, Combining Approach in Stages with Least Squares for fits of data in hyperelasticity . Comptes Rendus Mecanique, 334(2006)628-633

    QR CODE
    :::