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課程名稱 |
彈性力學一
Elasticity (Ⅰ) |
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開課學期 |
107-1 |
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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/1071AM7050_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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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 |
543 M5110 彈性力學一
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 (0.5 week)
2. Kinematics of Deformation (2.5 weeks)
3. Stress Analysis (2 weeks)
4. Constitutive Laws (1 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. 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 |
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 |
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參考書目 |
References
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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週次 |
日期 |
單元主題 |
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第1週 |
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Course 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, generalized Hooke’s law, isotropic materials |
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第7週 |
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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, cylindrical coordinates.
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第9週 |
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Chap.5 One-Variable Problems: cylindrical shell, spherical shell |
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第10週 |
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Chap.5 One-Variable Problems: spherical shell; |
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第11週 |
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Chap.6 Two-Dimensional Problems: basic equations, anti-plane strain problemsplane strain problems, plane stress problems |
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第12週 |
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Chap.6 Two-Dimensional Problems: generalized plane stress 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 Circular 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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第18週 |
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Final Exam |
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