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課程名稱 |
彈性力學一
ELASTICITY (I) |
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開課學期 |
96-2 |
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授課對象 |
工學院 應用力學研究所 |
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授課教師 |
劉佩玲 |
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課號 |
AM7050 |
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課程識別碼 |
543EM5110 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四2(9:10~10:00) |
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上課地點 |
應111應111 |
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備註 |
本課程以英語授課。本課程以英語授課。本課程以英語授課。本課程以英
總人數上限：98人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/962elas1 |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
When a body is subjected to external loads, internal stress is induced in the
body and the body deforms accordingly. If the body restores its original shape
as the external loads are removed, it is called an elastic body. On the other
hand, if the loading is so large such that permanent deformation takes place,
the response of the body is inelastic. Usually engineering materials are
designed to behave in the elastic range. The objective of the course is to
discuss methods that can be used to analyze the stress and deformation of
elasitic bodies under external loading. |
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課程目標 |
The students should acquire the following knowledge as the semester ends:
1. various measures to describe the deformation of a body, the physical meanings and the transformation of these measures, and compatibility condtions of strains.
2. relation between stress vector and stress tensor; equations of motion, principal stress, and maximum shearing stress.
3. hyperelastic materials and the generalized Hooke’s law, isotropic materials, and the relation between elastic constants and engineering constants.
4. formulation of elasticity problems in rectangular, cylindrical, and spherical coordinate systems, and the principle of virtual work.
5. analysis of problems with only on independent variables, such as a spherical shell subjected to internal pressure.
6. analysis of plane strain and plane stress problems, and the airy stress function.
7. analysis of torsion problems.
8. analysis of bending problems and the Timoshenko beam theory.
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課程要求 |
Students of the class are expected to do before-class preparations and all the
weekly assignments. |
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預期每週課後學習時數 |
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Office Hours |
每週三 14:00~16:00 |
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指定閱讀 |
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參考書目 |
1. Class notes.
2. Atkin, R.J. and Fox, N., `An Introduction to the
Theory of Elasticity,’ Longman, 1980.
Nice short book, but too limited as a reference.
3. Barber, J.R., `Elasticity,’ Kluwer Academic
Press, 2002, ISBN 1-4020-0966-6.
Great book – solves some really hard problems and comes
with useful.
MAPLE and mathematica scripts. Quite expensive – 86
Euros for the paperback.
4. Green, A.E. and Zerna, W., `Theoretical
Elasticity,’ O.U.P. 1968, reprinted by Dover 1992, ISBN 0-
486-67076-7.
A gold mine of information, but somewhat terse. The
notation makes the book very heavy going. Cheap – worth
getting for future reference!
5. Gurtin, M.E. `The Linear Theory of Elasticity,’
in Encyclopaedia of Physics, Vol. VI a/2, Springer, 1972.
A thorough exposition of the general theory of elasticity,
with a mathematical emphasis. Not a good source of
solutions to boundary value problems.
6. Landau, L.D. and Lifshitz, E.M., `Theory of
Elasticity,’ Pergammon, 1986, ISBN 0-08-033917.
A succinct summary of linear elasticity, from a physicist’
s perspective
7. Ting, T. T. C. Anisotropic Elasticity Theory and
Applications OUP, 1996, ISBN 0-19-507447-5.
If you need to get into anisotropic elasticity, this is
where to find it!
8. Timoshenko, S.P. and Goodier, J.N., `Theory of
Elasticity,’ McGraw-Hill, 1982, ISBN 0-07-085805-5.
A very popular book with engineers, well written and with
many useful solutions.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
mid-term exam |
35% |
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2. |
final exam |
35% |
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3. |
homework |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/19,2/21 |
Course introduction;
Chap.1 Kinematics of Deformation:
deformation gradient |
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第2週 |
2/26,2/28 |
Chap.1 Kinematics of Deformation:
Cauchy-Green deformation tensor, Lagrange strain tensor |
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第3週 |
3/04,3/06 |
Chap.1 Kinematics of Deformation: principal strains, linear strains, compatibility conditions |
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第5週 |
3/18,3/20 |
Chap.2 Stress Analysis:
principal stress, and maximum shearing stress. |
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第6週 |
3/25,3/27 |
Chap.3 Constitutive Equations:
hyperelastic materials, generalized Hooke’s law, isotropic materials |
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第7週 |
4/01,4/03 |
Chap.4 Formulation of Elasticity Problems:
boundary conditions, uniqueness of solutions |
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第8週 |
4/08,4/10 |
Chap.4 Formulation of Elasticity Problems:Navier-Cauchy equations |
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第9週 |
4/15,4/17 |
Midterm
Chap.5 One-Variable Problems: cylindrical shell |
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第10週 |
4/22,4/24 |
Chap.5 One-Variable Problems:
spherical shell |
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第11週 |
4/29,5/01 |
Chap.6 Two-Dimensional Problems
basic equations, anti-plane & plain strain problems |
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第12週 |
5/06,5/08 |
Chap.6 Two-Dimensional Problems
plane stress problems, generalized plane stress problems |
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第13週 |
5/13,5/15 |
Chap.6 Two-Dimensional Problems
Airy stress function |
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第14週 |
5/20,5/22 |
Chap.6 Two-Dimensional Problems
Airy stress function
Chap.7 Torsion of Prismatic Shafts: circular cross-section |
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第15週 |
5/27,5/29 |
Chap.7 Torsion of Prismatic Shafts:
non-circular cross-section |
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第16週 |
6/03,6/05 |
Chap.8 Bending of Beams:
pure bending, cantilever beam |
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第17週 |
6/10,6/12 |
Chap.8 Bending of Beams:
Timoshenko beam |
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