ME543 THEORY OF ELASTICITY
| Course Code: | 5690543 |
| 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. SERKAN DAĞ |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of this course, the students will be equipped to comprehend
1. tensor notation and operations
2. definition of strain, principal strains, and compatibility
3. definition of stress, traction vector, equilibrium equations, and principal stresses
4. constitutive relations of general elastic anisotropic and isotropic materials
5. general displacement - and stress - based formulations
6. displacement - and stress - based formulations and solution methods in 2D elasticity
7. advanced applications involving thermoelasticity, functionally graded materials, and contact mechanics
Course Content
Analysis of stress and strain. Constitutive equations. Plane problems of elasticity. Torsion and flexure of beams. Variational methods, theorems of minimum potential energy and complementary energy. Approximate solution by means of variational methods. Introduction to plate theory. (F)
Course Learning Outcomes
1. Ability to use and apply tensor notation
2. Ability to derive relations between strains and displacements
3. Ability to determine principal strains and their directions
4. Ability to derive the compatibility condition
5. Ability to define stress components in different coordinate systems
6. Ability to determine principal stresses and their directions
7. Ability to derive equilibrium equations in different coordinate systems
8. Ability to apply coordinate transformation for vector and tensor quantities
9. Ability to express the constitutive relations for generally anisotropic, monoclinic, orthotropic, cubic, and isotropic materials
10. Ability to derive the relations among engineering and Lame’s constants
11. Ability to derive the governing partial differential equations for a general 3D problem by following displacement - and stress - based formulations
12. Ability to derive plane stress and strain governing partial differential equations for displacement - and stress - based formulations
13. Ability to apply stress function and Fourier transform approaches to solve 2D problems
14. Ability to formulate and solve problems by utilizing polar coordinates
15. Ability to solve various thermal stress problems for beams and circular disks
16. Ability to solve basic problems involving functionally graded materials
17. Ability to formulate and solve basic contact mechanics problems by developing a singular integral equation based formulation
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. | ✔ | |||