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課程名稱 |
彈性力學一
Elasticity (Ⅰ) |
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開課學期 |
110-1 |
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授課對象 |
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 |
02 |
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學分 |
3.0 |
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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 |
星期一3,4(10:20~12:10)星期三2(9:10~10:00) |
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上課地點 |
應113應113 |
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備註 |
本課程以英語授課。
限學號單號
總人數上限：98人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1101AM7050_02 |
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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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課程概述 |
Introduction
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.
Prerequisite courses
Mechanics of materials
Applied mathematics: differential equations, tensor, complex variables
Course outline：
1. Introduction (1 week)
2. Kinematics of Deformation (1.5 weeks)
3. Stress Analysis (2 weeks)
4. Constitutive Laws (1.5 week)
5. Formulation of Elasticity Problems (1.5 weeks)
6. One-Variable Problems (2 weeks)
7. Two-Dimensional Problems (3.5 weeks)
8. Torsion Problems (1.5 weeks)
9. Bending Problems (2 weeks)
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課程目標 |
Course objectives
The students should acquire the following knowledge as the semester ends:
1. linear strains 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
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 |
Requirements:
Students of the class are expected to do before-class preparations and all weekly assignments. |
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預期每週課後學習時數 |
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Office Hours |
每週四 10:00~12:00 |
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指定閱讀 |
Class notes |
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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. |
homework |
33% |
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2. |
mid-term exam |
33% |
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3. |
final exam |
34% |
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4. |
performance in class |
0% |
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週次 |
日期 |
單元主題 |
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第1週 |
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Introduction, Tensors |
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第2週 |
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Chap.1 Kinematics of Deformation: Linears Strain |
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第3週 |
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Chap.1 Kinematics of Deformation: linear strains, compatibility conditions |
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第4週 |
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Chap.2 Stress & Equilibrium: stress vector and stress tensor, Cauchy's equation of motion |
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第5週 |
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Chap.2 Stress Analysis: principal stress, and maximum shearing stress |
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第6週 |
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Chap.3 Constitutive Equations: hyperelastic materials, isotropic materials |
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第7週 |
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Chap.3 Constitutive Equations: isotropic materials
Chap.4 Formulation of Elasticity Problems: boundary conditions, uniqueness of solutions |
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第8週 |
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Chap.4 Formulation of Elasticity Problems: Navier-Cauchy equations, curvilinear coordinates |
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第9週 |
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Chap.5 One-Variable Problems |
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第10週 |
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Chap.5 One-Variable Problems
Chap.6 Two-Dimensional Problems: basic equations, anti-plane strain problems |
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第11週 |
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Chap.6 Two-Dimensional Problems: plane strain problems, plane stress problems |
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第12週 |
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Chap.6 Two-Dimensional Problems: Airy stress function |
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第13週 |
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Chap.6 Two-Dimensional Problems: Airy stress function |
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第14週 |
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Chap.7 Torsion of Prismatic Shafts |
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第15週 |
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Chap.7 Torsion of Prismatic Shafts |
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第16週 |
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Chap.8 Bending of Beams |
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第17週 |
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Chap.8 Bending of Beams |
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