ONE DIMENSIONAL FINITE ELEMENTS

AIM

Principles of developing one-dimensional displacement type finite elements. Solutions of static, dynamic and stability analysis of bars using displacement-type finite elements. Having the ability of using finite element programs

CONTENT

This course contains; Field equations of bars,Principles of energy, internal and external energy, strain energy,Potential and kinetic energy,Shape functions,Equation of motion,Equation of motion,Axial element,Torque element,Flexural element,Frame element,Moderately thick beam element,Analysis of free vibration,Stability analysis,Analysis of Forced vibration.

1. 1

   1. Using field equation of the bars/beams, constitutive equations, equation of motion, energy methods, shape functions and theory virtual work can derie finite element matrices. Can perform necessary mathematical calculations (method of variations, etc.) in order to derive the finite element matrixes

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

2. 2

   2. Can derive the mass, stiffness matrices and the load vectors of spring and axial elements. Can solve the problems by longhand matrix operations that are necessary for the finite element analysis.

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

3. 3

   3. Can derive mass and stiffness matrices and load vector for the torque element. Using finite element method, can solve torque problems by longhand calculations

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

4. 4

   4. Can derive the mass and stiffness matrices and load vectors of beam (frame) and deep beam elements. Using the finite element method, can solve the flexure problems by longhand calculations

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

5. 5

   5. Can run a finite element program, perform a static analysis and interpret the output . Can perform mesh refinement and convergence alanysis when it is necessary.

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

6. 6

   6. Can run a finite element program, perform a dynamic analysis and interpret the output

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

7. 7

   7. Can run a finite element program, perform a stability analysis and interpret the output

   Taught by: Discussion Method, Problem Solving Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Homework, Quiz

WEEKLY PLAN

1. WEEK 1

   Field equations of bars

2. WEEK 2

   Principles of energy, internal and external energy, strain energy

3. WEEK 3

   Potential and kinetic energy

4. WEEK 4

   Shape functions

5. WEEK 5

   Equation of motion

6. WEEK 6

   Equation of motion

7. WEEK 7

   Axial element

8. WEEK 8

   Torque element

9. WEEK 9

   Flexural element

10. WEEK 10

    Frame element

11. WEEK 11

    Moderately thick beam element

12. WEEK 12

    Analysis of free vibration

13. WEEK 13

    Stability analysis

14. WEEK 14

    Analysis of Forced vibration

ASSESSMENT

• Rate of Midterm Exam to Success50%
• Rate of Final Exam to Success50%

WORKLOAD

READING

• Mehmet H. Omurtag, Çubuk Sonlu Elemanlar, Birsen yayınevi, 2010 Mehmet H. Omurtag-Nihal Eratlı, Çözümlü Çubuk Sonlu Eleman Problemleri, Birsen yayınevi, 2010

TEACHING STAFF

• Prof.Dr. Mehmet Hakkı OMURTAGCOORDINATOR
• Prof.Dr. Mehmet Hakkı OMURTAG
• Assoc.Prof. Ümit Necmettin ARIBAŞ