

Course Information
Course Unit Title 
: 
Theory of Elasticity 
Course Unit Code 
: 
01MAK6114 
Type of Course Unit 
: 
Optional 
Level of Course Unit

: 
Second Cycle 
Year of Study

: 
Preb 
Semester

: 
255.Semester 
Number of ECTS Credits Allocated

: 
6,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 

Learning Outcomes of The Course Unit 
: 
Upon successful completion of this course, students will be able to
1. Use proficiently indicial notation and master manipulation of Cartesian vector and tensor equations. 2. Describe deformation of a body using various strain measures including deformation gradient, CauchyGreen deformation tensor, Lagragian strain tensor, infinitesimal strain tensor, principal strains; understand the meanings of these measures and the transformations among them; know what compatibility conditions the strains must satisfy. 3. Understand the definitions of stress vector and stress tensor and their relation，principal stresses and maximum shear stresses, and the stress equilibrium equations. 4. Understand generalized Hooke's law for linear elastic materials, material symmetries, and conversions of different material constants for linear isotopic elastic materials. 5. Write down the governing equations and boundary conditions in rectangular, cylindrical, or spherical coordinate system. 6. Analyze plane strain and plane stress problems with the method of Airy's stress function. 7. Understand the method of analysis for a cantilever beam subjected to an end load and Timoshenko beam theory. 8. Understand the method of analysis for a plate.

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Introduction; Vectors and tensors; Stress: stress tensor, transformation, differential equations of equilibrium, principal stresses and invariants; Strain: strain–displacement equations, transformation, relative displacement and rotation; Constitutive equations for linear elasticity; Plane stress and plane strain problems in linear elasticity; Airy stress functions; Bending of beams; Torsion of prismatic bars; Axisymmetric elements; Thermal elasticity; Summary of threedimensional linear elasticity

Languages of Instruction 
: 
Turkish

Course Goals 
: 

Course Aims 
: 
The objective of this course is to introduce the student to the analysis of linear elastic solids under mechanical and thermal loads. The material presented in this course will provide the foundation for pursuing other solid mechanics courses such as theory of plates and shells, elastic stability, composite structures and fracture mechanics.

WorkPlacement 

Not Available


Recommended or Required Reading
Textbook

: 
There is no assigned textbook for this course. Course notes will be distributed as required.

Additional Resources

: 
The following textbooks are recommended to provide useful background reading:
1. Advanced Strength and Applied Elasticity, Ansel C. Ugural and Saul K. Fenster, Fourth Edition, Prentice Hall, New Jersey, 2003.
2. Elasticity: Theory and Applications, Adel S. Saada, Second Edition, Krieger Publishing, Malabar, Florida, 1993
3. Theory of Elasticity, S. P. Timoshenko and J. N. Goodier, 3rd Edition, McGraw Hill Book Company, 1970, 1987.
4. Elastisite Teorisi, Çözüm Yöntemleri ve Bazı Matematiksel Teknikler, Prof. Dr. Sacit Tameroğlu, 1991
5. Elasticity in Engineering Mechanics, 2nd Edition, A. P. Boresi and K. P. Chong, John Wiley & Sons, 2000.
6. Classical and Computational Solid Mechanics, Y. C. Fung and P. Tong, World Scientific Publishing Co., Singapore, 2001
In addition to these supplemental textbooks, students will be provided selected research papers.

Material Sharing
Documents

: 

Assignments

: 

Exams

: 

Additional Material

: 


Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

Activity

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Time Of Studying Out Of Class

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Homeworks

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Presentation

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Visas

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Finals

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Workload Hour (30)

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Total Work Charge / Hour

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Course's ECTS Credit

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Assessment Methods and Criteria
Studies During Halfterm

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Visa

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Quiz

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Homework

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Attendance

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Application

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Lab

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Project

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Workshop

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Seminary

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Field study

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TOTAL

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The ratio of the term to success

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The ratio of final to success

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TOTAL

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Weekly Detailed Course Content
Week

Topics

1

Introduction: Strength of materials approach, elasticity approach



2

Basics of tensor algebra and transformation: Definitions of scalars, vectors and tensors, index notation, vector transformation, higherorder tensors, the Kronecker delta, tensor contraction, the alternating tensor



3

Analysis of stress: Body and surface forces, traction vector and stress tensor, traction vector on an arbitrary plane, equations of equilibrium, stress transformation, principal stresses and stress invariants, Mohr's circles



4

Analysis of strain: Displacement, strain and rotation tensors, geometric construction of small deformation theory, strain transformation, principal strains and strain invariants, dilatation, strain compatibility



5

Constitutive relations: Generalized Hooke's law, symmetry properties of the elasticity tensor, planes of elastic symmetry, monoclinic materials, orthotropic materials, isotropic materials, Lame's constants, engineering constants of isotropic materials



6

Formulation of problems in elasticity: Review of field equations, boundary conditions and fundamental problem classifications, governing equations of elasticity



7

Formulation of problems in elasticity: Displacement based formulation (Navier's equations)



8

Formulation of problems in elasticity: Stress based formulation (BeltramiMichell compatibility equations), principle of superposition



9

Two dimensional elasticity: Plane strain, generalized plane strain



10

Two dimensional elasticity: Plane stress, Airy stress function



11

Two dimensional elasticity: Twodimensional problem solution, Example: Long rectangular beam under uniform tension, Example: Bending of a cantilever beam by an end load



12

Two dimensional elasticity: Twodimensional problem solution, Example: Rotating rectangular beam, Stress function formulation with polar coordinates, Example: Effect of a circular hole in a strained plate



13

Thermoelasticity: Example: A plate with a temperature gradient through the thickness direction, example: Thermal stresses in a thin disk



14

Summary of three dimensional elasticity formulation



























































































