課程大綱

課程資訊

課程名稱

塑性力學
Theory of Plasticity

開課學期

103-2

授課對象

工學院結構工程組

授課教師

劉進賢

課號

CIE7015

課程識別碼

521 M1160

班次

學分

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

與劉立偉合開
總人數上限：34人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1032CIE7015_

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

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課程概述

1. Evidences of plastic behavior: examples of trusses, beams, and frame beyond elasticity and experiments.
2. Framework and relationship of structural mechanics
3. Yield conditions and yield surfaces.
4. Models of perfect elastoplasticity: plastic flow rules and switch of plasticity.
5. Models of hardening and softening elastoplasticity.
6. Limit analysis: collapse surface.
7. Slip line theory.
8. Recent advances in computational plasticity.
9. Dynamic plasticity: wave and vibration (optional).
10. Boundary value problems (optional).
11. Finite element method in elastoplastic theory (optional).
12. Thermodynamic aspects of plasticity (optional).

課程目標

One aim of this course is to introduce the constitutive theories, mechanical behavior of elastoplasticity, and applications to materials, members, structures, geotechniques, and metal forming.
A second aim is to discuss the experimental and analytical methods of elastoplasticity so that student is well informed about the theory of incremental analysis (time series analysis) useful in the study of elastoplastic problems.
The final aim is to discuss the theory of limit analysis in high-dimensional load space. This important topic has not been discussed in most plasticity book of engineering mechanics.
The benefits are for students to get familiar with experimental, theoretical, and computational fundamentals in plasticity, to be familiar with the formulation of incremental analysis, and to have a basic understanding of the high-dimensional limit analysis. These knowledge are essential in meeting the challenge posed by future engineering analyses and designs.
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

I will deliver lectures three times a week each for an hour. Students will be required to submit completed homework assignments. In addition, the students will be divided into groups and each group will be assigned a topic and carry out additional readings from journal articles. Students will take turn to present their findings. One midterm plus a final exam will be given.
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

每週一 13:30~16:30 備註： Li-Wei Liu (CERB 505)

指定閱讀

待補

參考書目

(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
有電子書)
(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) 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.
(14) Prager, An Introduction to Plasticity, Addison-Wesley, Reading, Mass., 1959.
(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)

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	期中考	25%
2.	期末考	25%
3.	報告	25%
4.	平時作業	25%

課程進度

週次	日期	單元主題
第2週	3/06	Review of elasticity and Preview of plasticity
第3週	3/13	Models of perfect elastoplasticity
第4週	3/20	Models of perfect elastoplasticity and bilinear elastoplasticity
第5週	3/27	Yield volume theory and smoothing stress-strain curve
第7週	4/10	Yield volume theory and smoothing stress-strain curve
第8週	4/17	Cam-Clay Models
第9週	4/24	Piecewise linear multi-yield-surfaces model of elastoplasticity/Shakedown analysis and Limit analysis
第10週	5/01	Midterm exam
第11週	5/08	Lie group SO(n) for plasticity
第12週	5/15	Generalized Hamiltonian
第13週	5/22	Lie-group differential algebraic equation (LGDAE)
第14週	5/29	LGDAE for models and elastoplastic oscillators
第15週	6/5	Plastic wave (I)
第16週	6/12	Plastic wave (II)
第18週	06/26	Final exam