# COURSE UNIT TITLE

: THEORY OF ELASTICITY

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MEE 5083 THEORY OF ELASTICITY ELECTIVE 3 0 0 7

#### Offered By

Graduate School of Natural and Applied Sciences

#### Level of Course Unit

Second Cycle Programmes (Master's Degree)

#### Course Coordinator

ASSOCIATE PROFESSOR YUSUF ARMAN

#### Offered to

M.Sc. Metallurgical and Material Engineering
Mechanics
Mechanics
Metallurgical and Material Engineering

#### Course Objective

The aim of this course is to introduce the student to the analysis of linear elastic solids under mechanical and thermal loads. The primary intention is to provide for students the essential fundamental knowledge of the theory of elasticity together with a compilation of solutions of special problems that are important in engineering practice and design. The topics presented in this course will also provide the foundation for pursuing other solid mechanics courses such as theory of plates and shells, elastic stability, composite structures and fracture mechanics.

#### Learning Outcomes of the Course Unit

 1 Ability to define an elasticity problem 2 Ability to determine/explain the main concepts in elasticity such as plane stress, plain strain, equations of equilibrium, boundary conditions, compatibility equations and stress function 3 Ability to compare advantages and disadvantages of different solution strategies 4 Ability to select the best solution method to solve an elasticity problem 5 Ability to discuss the results of a solution and compare them with those of elementary level

Face -to- Face

None

None

#### Course Contents

 Week Subject Description 1 Introduction: Introduction, Stress, Components of stress, Components of strain, Hooke s Law, Index notation 2 Plane stress and plane strain: Plane stress, Plane strain, Stress at a point, Strain at a point, Differential equations of equilibrium, Boundary conditions, Compatibility equations, Stress function 3 Two-dimensional problems in rectangular coordinates: Solution by polynomials, End effects. Saint-Venant s Principle, Determination of displacements 4 Two-dimensional problems in rectangular coordinates: Bending of a beam by uniform load, Other cases of continuously loaded beams, Bending of a cantilever loaded at the end 5 Two-dimensional problems in polar coordinates: General equations in polar coordinates, Stress distribution symmetrical about an axis, Pure bending of curved bars, Strain components in polar coordinates 6 Two-dimensional problems in polar coordinates: Displacements for symmetrical stress distributions, Rotating disks, Bending of a curved bar by a force at the end, The effect of circular holes on stress distributions in plates 7 Two-dimensional problems in polar coordinates: Concentrated force at a point of a straight boundary, Any vertical loading of a straight boundary, Stresses in a circular disk, Other cases 8 1st Mid-Term Examination 9 Analysis of stress and strain in three dimensions: Introduction, Principal stresses, Determination of the principal stresses, Stress invariants, Determination of the maximum shearing stress, Strain at a point, Principal axes of strain, Rotation 10 Elementary problems of elasticity in three dimensions: Uniform stress, Stretching of a prismatic bar by its own weight, Twist of circular shafts of constant cross section, Pure bending of prismatical bars, Pure bending of plates 11 Torsion: Torsion of straight bars, Elliptic cross section, Membrane analogy, Torsion of a bar of narrow rectangular cross section 12 Torsion: Torsion of rectangular bars, Solution of torsional problems by energy method, Torsion of hollow shafts, Torsion of thin tubes 13 Bending of Bars: Bending of a cantilever, Stress function, Circular cross section, Elliptic cross section, Rectangular cross section 14 2 nd Mid-Term Examination

1. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity. McGraw-Hill, 3rd Edition, Singapore, 1984.
2. M.H. Sadd, Elasticity: Theory, Applications, and Numerics, Elsevier Academic Press, 2005.
3. A.C. Ugural, S. K. Fenster, Advanced Strength and Applied Elasticity, Prentice Hall, 2003.

#### Planned Learning Activities and Teaching Methods

Lecturing (theoretical)

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE 1 MIDTERM EXAM 1 2 MTE 2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + FCG * 0.5 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

None

To be announced.

Turkish

To be announced.

#### Contact Details for the Lecturer(s)

Dokuz Eylül University, Engineering Faculty, Department of Mechanical Engineering, Tınaztepe Campus, 35397, Buca / Izmir
Phone: + 90 232 3019242
E-mail: yusuf.arman@deu.edu.tr

To be announced.

None