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| INS7180 | Energy Methods in Elasticity | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of CIVIL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Volkan KAHYA | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Understand the meaning of variational principles in elasticity, using the variational methods for solutions of elasticity problems. and apply approximate solution methods for elasticity problems. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | understand the meaning of variational principles in elasticity. | | 1,3 | | PO - 2 : | determine the variational methods for solutions of elasticity problems. | | 1,3 | | PO - 3 : | apply approximate solution methods for elasticity problems. | | 1,3 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Extremum of functions. Conditional extremum. Extremum of functionals. Stress. Strain. Equations of elasticity. Principle of virtual work. Approximate solutions. Principle of complementary virtual work. Approximate solutions. Principle of minimum potential energy. Principle of minimum complementary energy. Castigliano's theorems. Approximate solutions. Rayleigh-Ritz method. Free vibrations of an elastic body. Approximate solutions. Torsion of bars. Elementary theory of beams. Streching and bending of a plate. Shells. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Extremum of functions. Conditional extremum. | | | Week 2 | Extremum of functionals. | | | Week 3 | Stress. Strain. Equations of elasticity. | | | Week 4 | Principle of virtual work. Approximate solutions. | | | Week 5 | Principle of complementary virtual work. Approximate solutions. | | | Week 6 | Principle of minimum potential energy | | | Week 7 | Principle of minimum complementary energy. Castigliano's theorems. | | | Week 8 | Approximate solutions. Rayleigh-Ritz method. | | | Week 9 | Mid-term exam | | | Week 10 | Free vibrations of an elastic body. | | | Week 11 | Buckling. | | | Week 12 | Approximate solutions. | | | Week 13 | Torsion of bars. Elementary theory of beams. | | | Week 14 | Streching and bending of a plate. | | | Week 15 | Shells. | | | Week 16 | End-of-term exam | | | |
| 1 | Washizu, K., 1982,Variational Methods in Elasticity and Plasticity, Pergamon Press. | | | 2 | Krashnov, M. L., Makarenko, G.I.,Kiselev, A. I., (English Translation: Yankovsky, George),1975,Problems and Exercises in the Calculus of Variations, Mir Publishers Moscov. | | | |
| 1 | Oden, J. T., Reddy, J. N., 1983, Variational Methods in Theoretical Mechanics, Springer-Verlag Berlin Heidelberg Newyork. | | | 2 | Reddy, J. N., 2002, Energy Methods and Variational Methods in Applied Mechanics. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 30 | | Homework/Assignment/Term-paper | 5
9
11
12 | | 2
2
2
2 | 20 | | End-of-term exam | 16 | | 3 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 7 | 14 | 98 | | Arasınav için hazırlık | 8 | 1 | 8 | | Arasınav | 2 | 1 | 2 | | Ödev | 8 | 4 | 32 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 3 | 1 | 3 | | Total work load | | | 200 |
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