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研究生： 張竣堯
Chang, Chun-Yao
論文名稱： 三維線性彈性靜力學之介紹
An Introduction to Three-Dimensional Linear Elastostatics
指導教授： 林景隆
Lin, Ching-Lung
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2011
畢業學年度： 99
語文別： 英文
論文頁數： 26
中文關鍵詞： 線性彈性學 、彈性靜力學 、柯西應力張量 、虎克定律 、平衡方程式 、邊界值問題 、對稱性 、等方性 、納維爾方程式 、正負定性質 、橢圓性質
外文關鍵詞： linear elasticity, elastostatics, Cauchy stress tensor, equilibrium equations, boundary value problems, symmetries, isotropic, Navier equations, definiteness, ellipticity
相關次數： 點閱：67  下載：2 
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    • 在這篇論文中，我們將討論到主要平衡方程式，並介紹一些三維彈性靜力學的基本概念。

    In this thesis, we will discuss the governing equilibrium equations and introduce some basic concepts in three-dimensional elastostatics.

    摘要 I Abstract II 誌謝 III Contents IV Chapter 1 : Basic terms 1 1.1 Stress.........................1 1.1.1 Definition of stress.........1 1.1.2 Cauchy stress tensor.........2 1.2 Elastic modulus................4 1.3 Strain.........................5 1.4 Equilibrium equations..........7 Chapter 2 : Introduction to linear elastostatics 10 2.1 Governing equations....................10 2.2 Classical and weak solutions...........12 2.3 Isotropic cases and Navier equations...14 2.4 Imposed conditions on elasticities.....16 2.4.1 Definiteness properties..............16 2.4.2 Ellipticity properties...............20 Appendix : Some computations of the amounts of elasticities 25 Bibliography : 26

    [1] R.J. Knops and L.E. Payne , Uniqueness theorems in linear elasticity, Springer Tracts in Natural Philosophy, Volume 19. Springer-Verlag, Berlin (1971).
    [2] R.J. Knops , Uniqueness for the whole space in classical elasticity, J. London Math. Soc., 39, pp.708-712, (1964).
    [3] Phillip L. Gould , Introduction to Linear Elasticity (Second Edition), Springer-Verlag, Berlin (1994).
    [4] T.M. Atanackovic and A. Guran , Theory of Elasticity for Scientists and Engineers, Birkhäuser, Boston (2000).
    [5] J.R. Barber , Linear Elastostatics, in: Continuum Mechanics, Jose Merodio and Giuseppe Saccomandi eds., in EOLSS, Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford , UK (2008).
    [6] C.A. Felippa , Three-dimensional linear elastostatics, in: Advanced Finite Element Method, University of Colorado courses, Spring (2003).
    [7] H. Nagahama and R. Teisseyre , Micromorphic continuum and fractal fracturing in the lithosphere, Pure and Applied Geophysics, Volume 157. pp.559-574, (2000).
    [8] G. Fichera , Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics No.8, Springer-Verlag, Berlin (1965).
    [9] M. Hayes , On the displacement boundary-value problem in linear elastostatics, Quarterly journal of mechanics and applied mathematics, Volume 19. pp.151-155, (1966).
    [10] Z.J. Hwang , Linear algebra with application (Second Edition), Tingmao Publish Company, Taipei (2003).

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