課程資訊
課程名稱
塑性力學
Theory of Plasticity 
開課學期
110-2 
授課對象
工學院  結構工程組  
授課教師
洪宏基 
課號
CIE7015 
課程識別碼
521 M1160 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期五2,3,4(9:10~12:10) 
上課地點
土研405 
備註
總人數上限:34人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1102CIE7015_ 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

(1). Examples of Trusses and Beams Beyond Elasticity彈性結構學所不知道的桁架與梁
Truss of three bars 三桿桁架之塑性行為,
Plastic hinges appear and disappear mysteriously? 神出鬼沒的塑鉸.
(2). Evidences of Plastic Behavior 塑性行為證據.
Experiments 塑性力學的材料與結構實驗證據;
State space, and path 狀態, 狀態空間, 路徑;
Path-dependent behavior 路徑相依的行為.
(3). Framework and Relationship of Mechanics of Materials, Theory of
Structures, and Theory of Elasticity 材料力學、結構學、彈性力學的關係與架構.
Kinematics, Constitution, and equilibrium 機動、組成、平衡;
Generalized stress and generalized strain 廣義應力、廣義應變;
State space, state versus path 狀態空間, 狀態 vs. 路徑.
Goal of the present course 本課程之目標.
(A). Indicial notation, Cartesian tensors, and Invariants 指標記法、張量、不變量.
(4). Yield Conditions and Yield Surfaces 降伏條件、降伏面.
Classical yield functions.
(5). Models of Perfect Elastoplasticity 完全彈塑性組成律.
Ingredient of elastoplastic models;
Plastic flow rules 塑流規則;
Associated plastic flow rules.
Switch of plasticity 塑性機制的開關;
Plastic multiplier 塑性乘子;
Prandtl-Reuss model;
Response to rectilinear paths;
Elastoplasticity with piecewise linear multiple yield surfaces.
(6). Models of Hardening Elastoplasticity 硬軟化彈塑性組成律.
Hardening and softening 硬化軟化;
kinematic hardening and isotropic harderning 走動硬化與等向硬化.
Models of bilinear and mixed hardening elastoplasticity;
Armstrong-Frederick rule;
Cam-clay models.
Thermodynamical restrictions on plastic behavior 塑性行為的熱力學限制;
Yield and dissipation 降伏與耗散.
(7). Slip Line Theory 滑移線理論.
(8). Limit Analysis 極限分析.
Limit states, collapse surface 崩塌面;
Upper and lower bound theorems, uniqueness theorem;
(Mechanism method, Methods via mathematical programming)
Direct method for trusses and frames.
(9). (Dynamic Plasticity: Wave and Vibration 塑性動力學─波動及振動)
(10). (Boundary Value Problems 彈塑性邊界值問題.)
(11). (Finite Element Method for Plasticity 有限元素法概述─計算塑性力學.)
(12). Thermodynamic Aspects of Elastoplasticity 彈塑性的熱力學面向.
Thermodynamics 熱力學.  

課程目標
To introduce the constitutive theories, mechanical behavior, experimental and analytical methods of elastoplasticity, and applications to materials, members, structures, geotechniques, and metal forming.
瞭解彈塑性材料之組成律理論、力學行為、實驗方法與分析方法,以及眾多之應用領域。 
課程要求
塑性力學原來是非常黑手的,意思是說它原來是由工程經驗累積出來的,所以它本來就是很實用的。很實用的學問要系統化,擴大適用範圍,並不容易。經過多年的發展,它的理路逐漸明朗,它實際上提供支撐廣大的應用實用工程領域的力學基礎。但是經過大學多門課的教育後,學生逐漸習慣於線性的思維、可逆性的思維、單相的思維,對於更接近真實的彈塑性行為,反而不習慣,難於掌握。因為真實的材料結構的行為是彈塑性的,而彈塑性卻是非線性的、不可逆性的、多相的。因此本門課要求同學要全神貫注,多思辨,要聽要問要討論,掌握思想的精髓,演繹整套學問所需要的理論工具,以及領悟它如何支撐廣大的應用實用工程領域,如何提供它們堅固的力學基礎。 
預期每週課後學習時數
 
Office Hours
每週五 12:10~12:30 備註: 歡迎面談, 每周五課間及課後20分鐘(或更長), 歡迎討論, 也可另約時間。主要 學生對象是碩博士班研究生,但是以往的經驗顯示,有些 大四同學修習本課,效果非常好,他們不但在課上表現很好,而且日後大都成為很 好的學者或領袖群倫的工程師。 
參考書目
(1) Lubliner, Plasticity Theory, Macmillan, 1990.
(2) Chen and Han, Plasticity for Structural Engineers, Springer-Verlag, 1988. (高立圖書)
(3) Wu, Continuum Mechanics and Plasticity, Chapman & Hall/CRC, 2005. (NTU Library Electronic)
(4) Jirasek and Bazant, Inelastic Analysis of Structures, Wiley, 2002.
(5) Freudenthal and Geiringer, The mathematical theories of the inelastic continuum, pp. 229-433, Elasticity and Plasticity, Vol. VI, Encyclopedia of Physics, Springer-Verlag, Berlin, 1958.
(6) Kaliszky, Plasticity Theory and Engineering Applications, Elsevier, Amsterdam, 1989.
(7) Martin, Plasticity, MIT Press, Cambridge, Mass., 1975. (NTUST Library)
(8) Srinivasa and Srinivasa, Inelasticity of Materials: An Engineering Approach and a Practical Guide, World Scientific, Singapore, 2009.
(9) Han and Reddy, Plasticity. Mathematical Theory and Numerical Analysis. Springer-Verlag, Berlin, 1999.
(10) Brokowski, Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range, Elsevier, 1988.
(11) Nemat-Nasser, Plasticity, Cambridge University Press, 2004.
(12) Horne, Plastic Theory of Structures, 2nd ed., Pergamon Press, Oxford, 1979.
(13) Baker and Heyman, Plastic Design of Frames 1 Fundamentals, Cambridge University Press, 1969.
(14) Heyman, Plastic Design of Frames 2 Applications, Cambridge University Press, 1971.
(15) Hodge, Plastic Analysis of Strucrures, McGraw-Hill, New York, 1959.
(16) Mendelson, Plasticity: Theory and Application, Macmillan, 1968. (良宜出版社)
(17) Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950.
(18) Prager, An Introduction to Plasticity, Addison-Wesley, Reading, Mass., 1959.
(19) Kachanov, Foundations of the Theory of Plasticity, North-Holland, 1971.
(20) Chakrabarty, Theory of Plasticity, 2nd ed., McGraw-Hill, 1998. (滄海書局) 3rd ed., Butterworth-Heinemann, 2006.
(21) Johnson and Mellor, Engineering Plasticity, Van Nostrand Reinhold, London, 1973.
(22) Wong, Plastic analysis and design of steel structures, Elsevier, Butterworth-Heinemann, Burlington, Mass., 2009. (NTU Library Electronic)
(23) Cristescu, Dynamic Plasticity, North-Holland, 1967, 2nd ed., World Scientific, 2007. 
指定閱讀
(1).Lecture Notes post on NTU COOL/CEIBA. Please download and study them carefully. 本課程備有講義,放在NTU COOL/CEIBA網頁上,供選修同學下載,請同學務必精讀。
(2). 23 Reference books, which you may either like to buy for collecting and building up your own personal library or to loan from the NTU Library.參考書目所列書籍,請同學就自己財力,價值觀,衡量選購,或到圖書館借閱。
(3)-(9) The following papers may be downloaded from NTU COOL/CEIBA or from the NTU Library electronic.
(3). Hong-Ki Hong and Chein-Shan Liu, On behavior of perfect elastoplasticity under rectilinear paths, International Journal of Solids and Structures, Vol. 35, Nos. 26-27, pp. 3539-3571. 1998.
(4). Chein-Shan Liu and Hong-Ki Hong, The Contraction Ratios of Perfect Elastoplasticity under Biaxial Controls, European Journal of Mechanics A/Solids, Vol.19, pp.827-848, 2000.
(5). Hong-Ki Hong and Chein-Shan Liu, Internal symmetry in the constitutive model of perfect elastoplasticity, International Journal of Non-Linear Mechanics, Vol.35, No. 3, pp. 447-466, 2000.
(6). Hong-Ki Hong and Chein-Shan Liu, Internal symmetry in bilinear elastoplasticity, International Journal of Non-Linear Mechanics, Vol. 34, No. 2, pp. 279-288, 1999.
(7). Li-Wei Liu and Hong-Ki Hong, A Description of Three-Dimensional Yield Surfaces by Cubic Polynomials, ASCE, Journal of Engineering Mechanics, Vol.143, Issue 11, 04017129, 2017.
(8). Shin-Jang Sung, Li-Wei Liu, Hong-Ki Hong, and Han-Chin Wu, Evolution of Yield Surface in the 2D and 3D Stress Spaces, International Journal of Solids and Structures, Vol.48, pp.1054-1069, 2011.
(9). Hong-Ki Hong, Li-Wei Liu, Ya-Po Shiao, and Shao-Fu Yan, Yield Surface Evolution and Elastoplastic Model with Cubic Distortional Yield Surface, ASCE, Journal of Engineering Mechanics, Vol.148, Issue 6, 04022027, 2022. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Optional report(s) 
0% 
占比0~10%或更多,屬於外加BONUS型.於期中考或期末考後一定期限內繳交.補期中考與期末考之不足;自己出題,自己答,其型式可以是 [專題報告,筆記,或心得札記,或閱讀的論文或書籍等資料]等等.都是optional,可交,可不交.若曾經花時間記筆記,或看過,找過其他(課程大綱所列之參考書以內或以外之)書本,報告,論文等資料,或整理心得札記,只要這些筆記,資料,心得札記等,可幫助老師了解學生所下功夫,或可顯示學生對塑性力學學理及其工程應用的了解程度者,或對正面評分有幫助者,則請交 Optional report(s)[專題報告,筆記,或心得札記,或閱讀的論文或書籍等資料]。  
2. 
Final Exam 
33% 
學期考33%。考前可能有作業及模擬題庫可參考。考試時間一般相當長,能夠發揮,請盡量寫,以便檢驗觀念思緒是否妥善建立,技術細節是否正確。 
3. 
Midterm exam. 
33% 
期中考33%。考前可能有作業及模擬題庫可參考。考試時間一般相當長,能夠發揮,請盡量寫,以便檢驗觀念思緒是否妥善建立,技術細節是否正確。 
4. 
Exercises (homeworks) 
34% 
寫作業主要是增進了解。寫作業可能會花很多時間,這是自我鍛鍊的好時機,請勿抄襲,但可在適當階段或時點前討論。  
 
課程進度
週次
日期
單元主題
第1週
2/18  Ch 1: Examples of Trusses and Beams Beyond Elasticity 
第2週
2/25  Ch 1: Examples of Trusses and Beams Beyond Elasticity;
Ch 2: Evidences of Plastic Behavior 
第3週
3/4  Ch 2: Evidences of Plastic Behavior;
Appendix A: Cartesian Tensor;
Ch 3: Framework of MM, TS, and TE 
第4週
3/11  Ch 3: Framework of MM, TS, and TE 
第5週
3/18  Ch 4: Yield Conditions 
第6週
3/25  Ch 4: Yield Conditions;
Ch 5: Models of Perfect Elastoplasticity 
第7週
4/1  Ch 5: Models of Perfect Elastoplasticity 
第8週
4/8  Midterm examination 期中考(Chs1+2+3+4+5) 
第9週
4/15  Ch 5: Models of Perfect Elastoplasticity;
Ch 6: Models of Hardening Elastoplasticity 
第10週
4/22  Ch 6: Models of Hardening Elastoplasticity 
第11週
4/29  Ch 6: Models of Hardening Elastoplasticity;
Ch 7: Slip Line Theory 
第12週
5/6  Ch 8: Limit Analysis (beams/trusses/frames) 
第13週
5/13  Ch 8: Limit Analysis (beams/trusses/frames) 
第14週
5/20  Ch 12: Thermodynamic Aspect of Elastoplasticity 
第15週
5/27  Ch 12: Thermodynamic Aspect of Elastoplasticity 
第16週
6/3  (vacation) 
第17週
6/10  Final examination 期末考(Chs5+6+7+8+12) 
第18週
6/17  optional report(s) due