課程大綱

課程資訊

課程名稱

彈性力學一
ELASTICITY (I)

開課學期

95-1

授課對象

應用力學研究所

授課教師

劉佩玲

課號

AM7050

課程識別碼

543EM5110

班次

學分

全/半年

半年

必/選修

必修

上課時間

星期一3,4(10:20~12:10)星期三2(9:10~10:00)

上課地點

應113

備註

本課程以英語授課。
限學號單號
總人數上限：60人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/951elasticityI

課程簡介影片

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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.

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, material symmetry,
relation between elastic constants and engineering constants for isotropic
materials.
4. formulation of elasticity problems in rectangular, cylindrical, and
spherical coordinate systems.
5. analysis problems with only on independent variables, such as a spherical
shell subjected to internal pressure.
6. 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.

課程要求

Students of the class are expected to do before-class preparations and all the
weekly assignments.

預期每週課後學習時數

Office Hours

每週三 14:00~16:00

指定閱讀

參考書目

1. Class notes
2. Boresi, A.P. and Chong, K.P. Elasticity in Engineering Mechanics, 2nd ed.
New York: Wiley, 1999.
3. Green, A.E. and Zerna, W. Theoretical Elasticity, 2nd ed. New York: Dover,
1992.
4. Landau, L.D. and Lifschitz, E.M. Theory of Elasticity, 3rd rev. enl. ed.
5. Love, A.E.H. A Treatise on the Mathematical Theory of Elasticity, 4th ed.
New York: Dover, 1944.
6. Muskhelishvili, N.I. Some Basic Problems of the Mathematical Theory of
Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion, and
Bending, 4th corr. and augmented. ed. Groningen: P.Noordhoff, 1963.
7. Sokolnikoff, I.S. Mathematical Theory of Elasticity, 2nd ed. New York:
McGraw-Hill, 1956.
8. Timoshenko, S. Theory of Elasticity, 3rd ed. New York: McGraw-Hill, 1970.
9. Timoshenko, S. and Gere, J.M. Theory of Elastic Stability, 2nd ed. New
York: McGraw-Hill, 1961.
10. Timoshenko, S. and Woinowsky-Krieger, S. Theory of Plates and Shells, 2nd
ed. New York: McGraw-Hill, 1959.
11. Weisstein, E.W. "Books about Elasticity."
http://www.ericweisstein.com/encyclopedias/books/Elasticity.html.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	mid-term exam	35%
2.	final exam	35%
3.	homework	30%

課程進度

週次	日期	單元主題
第0週		Class Notes
第1週	9/18, 9/20	Course introduction Chap.1 1. Kinematics of Deformation deformation gradient
第2週	9/25, 9/27	Chap.1 1. Kinematics of Deformation Cauchy-Green deformation tensor, Lagrange strain tensor
第3週	10/02, 10/04	Chap.1 1. Kinematics of Deformation principal strains, linear strains
第4週	10/09, 10/11	Chap.1 1. Kinematics of Deformation linear strains, compatibility conditions
第6週	10/23, 10/25	Chap.2 Stress Analysis principal stress, maximum shearing stress, Mohr's circle
第7週	10/30, 11/01	Chap.3 Constitutive Equations hyperelastic materials, generalized Hooke’s law, material symmetry
第8週	11/06,11/08	Chap.3 Constitutive Equations material symmetry, isotropic materials Chap.4 Formulation of Elasticity Problems boundary conditions
第9週	11/13, 11/15	Chap.4 Formulation of Elasticity Problems uniqueness of solutions, Navier-Cauchy equations, cylindrical & spherical coordinate systems
第10週	11/20,11/22	Chap.5 One-Variable Problems infinite cylindrical shell
第11週	11/27,11/29	Midterm Chap.5 One-Variable Problems spherical shell
第12週	12/04,12/06	Chap.5 One-Variable Problems spherical shell Chap.6 Two-Dimensional Problems basic equations, anti-plane strain problems
第13週	12/11,12/13	Chap.6 Two-Dimensional Problems plane strain problems, plane stress problems, generalized plane stress problems
第14週	12/18,12/20	Chap.6 Two-Dimensional Problems Airy stress function
第15週	12/25,12/27	Chap.6 Two-Dimensional Problems Airy stress function
第16週	1/03	Chap.7 Torsion of Prismatic Shafts
第17週	1/08,1/10	Chap.8 Bending of Beams