課程資訊

Theory of Plasticity

107-2

CIE7015

521 M1160

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1072CIE7015_plastic

(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 and 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.
(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 Plasticity 塑性的熱力學面向.
Thermodynamics 熱力學;
Thermodynamical restrictions on plastic behavior 塑性行為的熱力學限制;
Yield and dissipation 降伏與耗散.

To introduce the constitutive theories, mechanical behavior, experimental and analytical methods of elastoplasticity, and applications to materials, members, structures, geotechniques, and metal forming.

Office Hours

(1) Jirasek and Bazant, Inelastic Analysis of Structures, Wiley, 2002.
(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. (本校圖書

(4) Lubliner, Plasticity Theory, Macmillan, 1990.
(5) Kaliszky, Plasticity Theory and Engineering Applications, Elsevier,
Amsterdam, 1989.
(6) Martin, Plasticity, MIT Press, Cambridge, Mass., 1975. (台科大圖書館)
(7) Srinivasa and Srinivasa, Inelasticity of Materials: An Engineering Approach
and a Practical Guide, World Scientific, Singapore, 2009.
(8) Han and Reddy, Plasticity. Mathematical Theory and Numerical Analysis.
Springer-Verlag, Berlin, 1999.
(9) Brokowski, Analysis of Skeletal Structural Systems in the Elastic and
Elastic-Plastic Range, Elsevier, 1988.
(10) Nemat-Nasser, Plasticity, Cambridge University Press, 2004.
(11) Baker and Heyman, Plastic Design of Frames 1 Fundamentals, Cambridge
University Press, 1969.
(12) Heyman, Plastic Design of Frames 2 Applications, Cambridge University
Press, 1971.
(13) Horne, Plastic Theory of Structures, 2nd ed., Pergamon Press, Oxford,
1979.
(14) Mendelson, Plasticity: Theory and Application, Macmillan, 1968. (良宜出版

(15) Hill, The Mathematical Theory of Plasticity, Oxford University Press,
1950.
1959.
(17) Kachanov, Foundations of the Theory of Plasticity, North-Holland, 1971.
(18) Chakrabarty, Theory of Plasticity, 2nd ed., McGraw-Hill, 1998. (滄海書局)
3rd ed., Butterworth-Heinemann, 2006.
(19) Johnson and Mellor, Engineering Plasticity, Van Nostrand Reinhold, London,
1973.
(20) Cristescu, Dynamic Plasticity, North-Holland, 1967, 2nd ed., World
Scientific, 2007.
(21) Wong, Plastic analysis and design of steel structures, Elsevier,
Butterworth-Heinemann, Burlington, Mass., 2009. (本校圖書館有電子書)
(22) Hodge, Plastic Analysis of Strucrures, McGraw-Hill, New York, 1959.

(1).本課程備有講義，放在CEIBA網頁上，供選修同學下載，請同學務必精讀。

(2). 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.
(3). 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.
(4). 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.

(僅供參考)

 No. 項目 百分比 說明 1. 6次作業 33.4% 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。 2. 期中考與學末考 66.6% 期中考33.3%與學期考33.3%。考前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. Optional reports 20% 百分比占比0%~20%,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 reports[專題報告,筆記,或心得札記,或閱讀的論文或書籍等資料]。

 課程進度
 週次 日期 單元主題 第1週 2/22 Ch 1: Examples of Trusses and Beams Beyond Elasticity 第2週 2/23 Saturday (Sub. for 3/1) Ch 1: Examples of Trusses and Beams Beyond Elasticity; Ch 2: Evidences of Plastic Behavior 第3週 3/8 Ch 2: Evidences of Plastic Behavior; Appendix A: Tensor; Ch 3: Framework of MM, TS and TE 第4週 3/15 Ch 3: Framework of MM, TS and TE 第5週 3/22 Ch 4: Yield Conditions 第6週 3/29 Ch 4: Yield Conditions 第7週 (4/5) (holiday) 第8週 4/12 Ch 4: Yield Conditions; Ch 5: Models of Perfect Elastoplasticity 第9週 4/19 Midterm examination 期中考(Chs1+2+3+4) 第10週 4/26 Ch 5: Models of Perfect Elastoplasticity 第11週 5/3 Ch 5: Models of Perfect Elastoplasticity; Ch 6: Models of Hardening Elastoplasticity 第12週 5/10 Ch 6: Models of Hardening Elastoplasticity 第13週 5/17 Ch 7: Slip Line Theory; 第14週 5/24 Ch 7: Slip Line Theory; Ch 8: Limit Analysis (beams/trusses/frames) 第15週 5/31 Ch 8: Limit Analysis (beams/trusses/frames) 第16週 (6/7) (holiday) 第17週 6/14 Ch 8: Limit Analysis (beams/trusses/frames) 第18週 6/21 Final examination 期末考(Chs5+6+7+8)