ME586 VARIATIONAL PRINCIPLES IN ELASTICITY
| Course Code: | 5690586 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. HALUK DARENDELİLER |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of this course, the students will;
1. understand the solution of engineering problems through the use energy principles,
2. learn the first variation and Euler-Lagrange equations,
3. learn the variational notation,
4. learn first variation with several dependent variables,
5. learn to extremize functionals under several constraints and Lagrange multiplies,
6. learn kinematic and natural boundary conditions,
7. learn to extremize functionals with higher order derivatives,
8. learn to extremize functionals with more than one independent variable,
9. learn the virtual work principle and apply to structural mechanics,
10. learn the method of total potential energy and apply to structural mechanics,
11. learn the principle complementary virtual work and apply to structural mechanics,
12. learn the principal of total complementary energy and apply to structural mechanics,
13. learn the stationary principles, Reissner's Principle and apply to structural mechanics,
14. learn the Castigliono Theorems; First Castigliono Theorem, Second Castigliono Theorem and apply to structural mechanics.
Course Content
Cartesian tensors. Review of fundamental equations of elasticity. Basics of calculus of variations. First variation and Euler-Lagrange equations. Virtual work and complementary virtual work principles. Minimum potential energy, complementary energy, modified complementary energy and Hellinger-Reissner principles. Other derived principles. Application to bar, beam and plane stress problems. Introduction to finite element concepts. (S)
Course Learning Outcomes
1. Ability to solve the engineering problems in the form of functionals by the use of extremization.
2. Ability to obtain and solve the Euler-Lagrange Equations for engineering problems.
3. Ability to formulate engineering problems by using the variational notation.
4. Ability to extremize the functionals with several dependent variables.
5. Ability to extremize the functionals under constraint by Lagrange multipliers.
6. Ability to use kinematic and natural boundary conditions in the solution of extremization problems.
7. Ability to extremize the functionals with higher order derivatives.
8. Ability to extremize the functionals with more than one independent variable.
9. Ability to formulate and solve the structural mechanics problems by virtual work principle.
10. Ability to formulate and solve the structural mechanics problems by the method of total potential energy.
11. Ability to formulate and solve the structural mechanics problems by the principle of complementary virtual work.
12. Ability to formulate and solve the structural mechanics problems by the principle of total complementary energy.
13. Ability to formulate and apply stationary principles to the structural mechanics problems.
14.Ability to apply Castigliono Theorems structural mechanics problems.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Acquires the fundamental scientific knowledge required to analyze and solve advanced-level problems in the field of mechanical engineering. | ✔ | |||
| 2 | Gains the competence to utilize advanced engineering mathematics methods in the formulation, analysis, and solution of engineering problems. | ✔ | |||
| 3 | Conducts literature reviews using printed and online sources, analyzes the collected literature, and identifies the current state-of-the-art in the relevant scientific field. | ✔ | |||
| 4 | Demonstrates the ability to prepare and deliver a seminar on a technical subject. | ✔ | |||
| 5 | Develops the ability to conduct independent research on a specific topic and solve advanced engineering problems. | ✔ | |||
| 6 | Contributes to the national and/or international body of knowledge through original research. | ✔ | |||
| 7 | Gains the competence to effectively communicate the process and results of research conducted on a specific subject through scientifically structured written reports and oral presentations. | ✔ | |||
| 8 | Acquires the ability to publish research findings as articles in national and/or international scientific journals and/or present them as papers at conferences. | ✔ | |||
| 9 | Acts in accordance with universal principles of research and publication ethics. | ✔ | |||