Information Package / Course Catalogue
Theory of Elasticity
Course Code: MCE520
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: English
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

This course is designed to give students derivation of field equations of linear elasticity theory , formulation and solution of typical problems of practicalinterest field. 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.

Course Content

Basic of Tensor Algebra and Transformation, Analysis of Stress, Analysis of Strain, Constituve Relations, Formulation of Problems in Elasticity, Two Dimensional Elasticity.

Name of Lecturer(s)
Learning Outcomes
1.Indicial notation and Cartesian tensor analysis
2.Analysis of stress and deformation
3.Basic field equations of linear elastic solids
4.Formulations and solution strategies of various boundary value problems
5.To obtain and discuss the results of elasticity problems and compare them with those of elementary level.
Recommended or Required Reading
1.Theory of Elasticity, by S.P. Timoshenko and J.N. Goodier, McGraw-Hill, Third Edition, 1970
2.R.W. Little, Elasticity, Prentice Hall, 1973
3.Elasticity in Engineering Mechanics, by A.P. Boresi and K.P. Chong, Wiley-Interscience, Second Edition, 2000
Weekly Detailed Course Contents
Week 1 - Theoretical
Definitions of scalars, vectors and tensors, Index notation , Vector transformation
Week 2 - Theoretical
Higher-order tensors ,The Kronecker delta, Tensor contraction, The alternating tensor, Gauss divergence theorem
Week 3 - Theoretical
Body and surface forces ,Traction vector and stress tensor ,Traction vector on an arbitrary plane , Equations of equilibrium
Week 4 - Theoretical
Stress transformation,Principal stresses and stress invariants,Mohr's circles
Week 5 - Theoretical
Displacement ,Strain and rotation tensors,Geometric construction of small deformation theory ,Strain transformation
Week 6 - Theoretical
Principal strains and strain invariants ,Strain compatibility
Week 7 - Theoretical
Generalized Hooke's law,Symmetry properties of the elasticity tensor, Planes of elastic symmetry
Week 8 - Theoretical
Monoclinic materials, Orthotropic materials
Week 9 - Theoretical
Tetragonal materials,Cubic materials,Isotropic materials,Lame's constants, Engineering constants of isotropic materials,Restrictions on elastic constants
Week 10 - Theoretical
Tetragonal materials,Cubic materials,Isotropic materials,Lame's constants, Engineering constants of isotropic materials,Restrictions on elastic constants
Week 11 - Theoretical
Review of field equations, Boundary conditions and fundamental problem classifications
Week 12 - Theoretical
Governing equations of elasticity, Displacement based formulation (Navier's equations)
Week 13 - Theoretical
Stress based formulation (Beltrami-Michell compatibility equations), Summary of three dimensional elasticity formulation
Week 14 - Theoretical
Principle of superposition
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Assignment4%15
Midterm Examination2%40
Final Examination1%40
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141356
Assignment40520
Midterm Examination220244
Final Examination127330
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
OÇ-1
5
4
5
4
5
4
5
4
5
4
5
4
5
OÇ-2
4
5
4
5
4
5
4
5
4
5
4
5
4
OÇ-3
5
4
5
4
5
4
5
4
5
5
4
5
4
OÇ-4
4
5
4
5
4
5
5
4
5
4
5
4
5
OÇ-5
5
4
5
4
5
4
5
4
5
4
5
5
4
Adnan Menderes University - Information Package / Course Catalogue
2026