NONLINEAR THEORY OF ELASTICITY

MAK522

Course Code: MAK522
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Master's Degree With Thesis

Year of Study

Semester

ECTS

Name of Lecturer(s)

Professor Sami Karadeniz

Learning Outcomes

At the end of this course, the students;

To learn approximation techniques to solve nonlinear systems.
Students should be able to derive and analyze the boundary value problems for a variety of simple deformations involving homogeneous, isotropic materials.
An ability to identify, formulate, and solve engineering problems.
Gaining presentation skill.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Strain geometry, Stresses, Balance of an element in continuum media, Strain Energy, Boundary conditions, Constitutive equations, Expression of elastic problems types of stresses, Elastic stability, Deformation of elastic materials.

Course Contents

WEEK	TOPICS
1^st Week	Introduction
2^nd Week	Tensors, the divergence theorem, material time derivatives
3^rd Week	Principles of linear and angular momentum, the stress tensor
4^th Week	Piola-Kirchhoff tensors
5^th Week	Cauchy stress, principal stresses, stress invariants
6^th Week	Constitutive equations, material symmetry
7^th Week	Hyper-elasticity and hypo-elasticity
8^th Week	Midterm
9^th Week	Incompressibility, forms of the strain-energy function.
10^th Week	Homogeneous deformations, inverse methods
11^th Week	Simple shear, pure homogeneous deformations
12^th Week	Non-homogeneous deformations
13^th Week	Simple torsion
14^th Week	Extension and Torsion

Recommended or Required Reading

o P. Chadwick, Continuum Mechanics, Dover Publications, 1999.
o R. W. Ogden, Non-linear Elastic Deformations, Dover Publications, 1997.
o G. A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineers, John Wiley and Sons, 2000.
o M. E. Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981.

Planned Learning Activities and Teaching Methods

Presentation
Lecture
Questions/Answers
Problem Solving

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	35
Assignment	3	15
Presentation of Case Study	1	5
Total(%)		55
Contribution of In-term Studies to Overall Grade(%)		55
Contribution of Final Examination to Overall Grade(%)		45
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	3	3
Preparation for Quiz
Individual or group work	14	5	70
Preparation for Final exam	1	50	50
Course hours	14	3	42
Preparation for Midterm exam	1	40	40
Laboratory (including preparation)
Final exam	1	3	3
Homework	3	25	75
Presentation (including preperation)	1	20	20
Total Work Load			303
Total Work Load / 30 (h)			10.1
ECTS Credit of the Course			10

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4
K1	X
K2
K3		X
K4
K5	X	X	X
K6
K7				X
K8
K9
K10
K11