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課程名稱 |
彈性力學一
Theory of Elasticity (Ⅰ) |
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開課學期 |
112-1 |
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授課對象 |
工學院 土木工程學系 |
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授課教師 |
劉立偉 |
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課號 |
CIE5005 |
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課程識別碼 |
521EU0100 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一2,3,4(9:10~12:10) |
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上課地點 |
新501 |
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備註 |
本課程以英語授課。
總人數上限：34人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
(A). Indicial notation and Cartesian tensors
(1). Kinematics
(2). Equilibrium
(3). Principle of virtual work and duality
(4). Constitution
(5). Summary of equations, various formulations of problems
(6-10). Problem solving
6). One-dimensional problems
7). Two-dimensional problems
8). Rods (Saint-Venant's problems of extension, bending, torsion, and flexure)
9). Plates
10). Three-dimensional problems |
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課程目標 |
To introduce the theory of elasticity (and coupled elasticity), including preliminaries on tensors and how to formulate and solve the various kinds of problems. The relations between the mechanics-of-materials approach and the theory-of-elasticity approach are clarified. |
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課程要求 |
(1) 6 exercises 34 percent,
(2) midterm exam 33 percent,
(3) final exam 33 percent.
(4) (optional 1 report; 10 percent bonus) |
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預期每週課後學習時數 |
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Office Hours |
備註： 3pm to 4pm of every Friday |
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指定閱讀 |
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參考書目 |
(1) I. S. Sokolnikoff, Mathematical Theory of Elasticity, New York: McGraw-
Hill, 1956.
(2) S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd edition, New
York: McGraw-Hill, 1970.
(3) Y. C. Fung, Foundations of Solid Mechanics, Englewood Cliffs, N.J.:
Prentice-Hall, 1965.
(4) J.R. Barber, Elasticity, Dordrecht: Springer, 2010. (本校圖書館有電子書)
(5) M. H. Sadd, Elasticity Theory, Applications, and Numerics, Amsterdam:
Elsevier, 2005.
(6) A. P. Boresi, K. P. Chong, and J. D. Lee, Elasticity in Engineering
Mechanics, Hoboken, N.J.: Wiley, 2011. (本校圖書館有電子書)
(7) M. E. Gurtin: The Linear Theory of Elasticity. Encyclopedia of Physics,
Mechanics of Solids II, VIa/2, pp. 1-295. Berlin: Springer, 1972.
(8) V. G. Rekach, Manual of the Theory of Elasticity, Moscow: Mir Publishers,
1979.
(9) H. Reismann and P. S. Pawlik, Elasticity, Theory and Applications, New
York: Wiley, 1980.
(10) J. J. Connor, Analysis of Structural Member Systems, Ronald Press, 1976.
(11) A. H. England, Complex Variable Methods in Elasticity, London: Wiley-
Interscience, 1971.
(12) A. E. Green and W. Zerna, Theoretical Elasticity, 2nd edition, Oxford:
Clarendon Press, 1968; New York: Dover, 1992.
(13) A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th
edition, Cambridge, UK: Cambridge University Press, 1927; New York: Dover,
1963.
(14) L. E. Malvern, Introduction to the Mechanics of a Continuous Medium,
Englewood Cliffs, N.J.: Prentice-Hall, 1969.
(15) R. W. Ogden, Non-linear Elastic Deformations, Chichester: Ellis Horwood,
1984; New York: Dover, 1997.
(16) J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of
Elasticity,
Englewood Cliffs, N.J.: Prentice-Hall, 1983; New York: Dover, 1994.
(17) L. D. Landau and E.M. Lifshitz, Theory of Elasticity, Oxford: Pergamon
Press, 1986.
(18) T. C. T. Ting, Anisotropic Elasticity: Theory and Applications, New York:
Oxford University Press, 1996. (本校圖書館有電子書)
(19) S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body,
San Francisco: Holden-Day, 1963.
(20) Weian Yao, Wanxie Zhong, and Chee Wah Lim, Symplectic Elasticity,
Singapore: World Scientific Publishing, 2009. (本校圖書館有電子書)
(21) N. I. Muskhelishvili: Some Basic Problems of the Mathematical Theory of
Elasticity. Groningen, The Netherlands: Noordhoff, 1963. |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
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Indicial notation and Cartesian tensors |
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Week 2 |
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Kinematics |
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Week 3 |
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Kinematics/Equilibrium |
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Week 4 |
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Equilibrium |
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Week 5 |
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Constitutions |
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Week 6 |
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Holiday |
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Week 7 |
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Summary of equations and various formulations |
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Week 8 |
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Midterm exam |
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Week 9 |
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One-dimensional problems/Two-dimensional problems |
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Week 10 |
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Two-dimensional problems |
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Week 11 |
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Two-dimensional problems/Rods (Saint-Venant's problems) |
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Week 12 |
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Rods (Saint-Venant's problems) |
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Week 13 |
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Plates |
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Week 14 |
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Plates/Three-dimensional problems |
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Week 15 |
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Three-dimensional problems |
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Week 16 |
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Final exam |
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