ENERGY AND VARIATIONAL METHODS IN MECHANICS

MAK613

Course Code: MAK613
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Doctorate Of Science

Year of Study

Semester

ECTS

Name of Lecturer(s)

Professor Sami Karadeniz

Learning Outcomes

At the end of this course, the students;

An ability to apply knowledge of mathematics, science, and engineering.
An ability to identify, formulate, and solve engineering problems.
An ability to use the modern engineering techniques.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

None

Course Description

Mathematical preliminaries, Review of Elasticity problems. Axial loaded bars, beams and prismatic elements in torsion. Introduction to energy and variational principles, work and energy. Deformation, complementary deformation energy. Variational calculus,. Euler equation. Main and natural boundary conditions. Virtual work and energy principles. Minimum total potential energy principle. Virtual force and complementary potential energy principles. Stationary variational principles. Hellinger-Reissner and Reissner variational principles. Hamilton principle. Castigliano's First and Second Theorems. Ritz Method, weighted remainder methods. Kantorovich and Trefftz methods. Applications.

Course Contents

WEEK	TOPICS
1^st Week	Mathematical preliminaries
2^nd Week	Review of Elasticity problems
3^rd Week	Axial loaded bars, beams and prismatic elements in torsion
4^th Week	Introduction to energy and variational principles, work and energy
5^th Week	Deformation, complementary deformation energy
6^th Week	Variational calculus
7^th Week	Euler equation, Main and natural boundary conditions , Virtual work and energy principles
8^th Week	Minimum total potential energy principle, Virtual force and complementary potential energy principles
9^th Week	Stationary variational principles , Hellinger-Reissner and Reissner variational principles, Hamilton principle
10^th Week	Castigliano's First and Second Theorems
11^th Week	Ritz Method, weighted remainder methods
12^th Week	Kantorovich and Trefftz methods. Applications.
13^th Week	Applications
14^th Week	Final

Recommended or Required Reading

Energy principles and variational methods in applied mechanics,Second edition, J.N.Reddy
Energy and Variational Methods in Applied Mechanics, J. N. Reddy, 1984
Energy Methods in Applied Mechanics, H. L. Langhaar, 1962
Solid Mechanics: A Variational Approach, Clive L. Dym, Irving H. Shames, 1973 McGraw-Hill
Variational Methods in Elasticity and Plasticity, Washizu, K., 1982, 3rd edition, Pergamon Press, NewYork.
Methods of Applied Mathematics, F. B. Hildebrand, 2nd edition, 1965 Prentice-Hall, Inc.

Planned Learning Activities and Teaching Methods

Lecture
Presentation

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	35
Assignment	6	20
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	4	56
Preparation for Final exam	1	50	50
Course hours	14	3	42
Preparation for Midterm exam	1	30	30
Laboratory (including preparation)
Final exam	1	3	3
Homework	6	20	120
Total Work Load			304
Total Work Load / 30 (h)			10.13
ECTS Credit of the Course			10

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

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