課程資訊

Theory of Plasticity

102-2

CIE7015

521 M1160

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1022CIE7015_

(1). Examples of Trusses and Beams Beyond Elasticity
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, 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
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
(5). Models of Perfect Elastoplasticity完全彈塑性組成律
Plastic flow rules 塑流規則
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-Softening Elastoplasticity硬軟化彈塑性組成律
Hardening and softening硬化軟化
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
Mechanism method
Methods via mathematical programming
Direct method
(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. (本校圖書館

(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) Brokowski, Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range, Elsevier, 1988.
(8) Nemat-Nasser, Plasticity, Cambridge University Press, 2004.
(9) Baker and Heyman, Plastic Design of Frames 1 Fundamentals, Cambridge University Press, 1969.
(10) Heyman, Plastic Design of Frames 2 Applications, Cambridge University Press, 1971.
(11) Horne, Plastic Theory of Structures, 2nd ed., Pergamon Press, Oxford, 1979.
(12) Mendelson, Plasticity: Theory and Application, Macmillan, 1968. (良宜出版社)
(13) Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950.
(15) Kachanov, Foundations of the Theory of Plasticity, North-Holland, 1971.
(16) Chakrabarty, Theory of Plasticity, 2nd ed., McGraw-Hill, 1998. (滄海書局)
3rd ed., Butterworth-Heinemann, 2006.
(17) Johnson and Mellor, Engineering Plasticity, Van Nostrand Reinhold, London, 1973.
(18) Cristescu, Dynamic Plasticity, North-Holland, 1967, 2nd ed., World Scientific, 2007.
(19) Wong, Plastic analysis and design of steel structures, Elsevier,
Butterworth-Heinemann, Burlington, Mass., 2009. (本校圖書館有電子書)

(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, Internal symmetry in bilinear elastoplasticity, International Journal of Non-Linear Mechanics, Vol.34(2), pp. 279-288, 1999.
(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(3), pp. 447-466, 2000.

(僅供參考)

 No. 項目 百分比 說明 1. 1. [專題報告]、[筆記，或心得札記，或閱讀的論文或書籍等資料] 10% [專題報告]一定要繳交。[筆記,或心得札記,或閱讀的論文或書籍等資料]則是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[筆記,或心得札記,或閱讀的論文或書籍等資料]。 2. 5次作業 30% 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。 3. 期中考與學期考 60% 期中考30%與學期考30%。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。

 課程進度
 週次 日期 單元主題 第1週 2/21 (1) Examples of Trusses and Beams Beyond Elasticity (2) Evidences of Plastic Behavior 第2週 2/28 (228 Memorial Day) 第3週 3/07 (1) Examples of Trusses and Beams Beyond Elasticity (2) Evidences of Plastic Behavior 第4週 3/14 (2) Evidences of Plastic Behavior (3) Framework and Relationship of Mechanics of Materials, Theory of Structures, and Theory of Elasticity 第5週 3/21 (3) Framework and Relationship of Mechanics of Materials, Theory of Structures, and Theory of Elasticity 第6週 3/28 (A) Indicial Notation, Cartesian Tensors, and Invariants (4) Yield Conditions and Yield Surfaces 第7週 4/04 (Spring Vacation) 第8週 4/11 (4) Yield Conditions and Yield Surfaces 第9週 4/18 (4) Yield Conditions and Yield Surfaces (5) Models of Perfect Elastoplasticity 第10週 4/25 (5) Models of Perfect Elastoplasticity 第11週 5/02 Midterm Examination 第12週 5/09 (5) Models of Perfect Elastoplasticity (6) Models of Hardening-Softening Elastoplasticity 第13週 5/16 (6) Models of Hardening-Softening Elastoplasticity 第14週 5/23 (6) Models of Hardening-Softening Elastoplasticity 第15週 5/30 (7) Slip Line Theory 第16週 6/06 (7) Slip Line Theory 第17週 6/13 (8) Limit Analysis