FINITE ELEMENTS

AIM

One-, two- and three-dimensional displacement type finite elements are defined, Static, dynamic and stability analyses are performed using displacement type finite elements, performing engineering analysis using finite element programs

CONTENT

This course contains; Introduction to finite elements,General Concepts,Variational principles,Principles of energy,Small displacement theory,Moderately large displacement theory,Interpolation functions (length, area, and volume coordinates),Isoparametric shape functions (one, two and three dimensional),Generation of isoparametric finite element matrices,Stress analysis,Assemblage of finite element matrices,One dimensional and plate elements (plane stress and plane strain finite elements),Static analysis of plates (plane stress),Static analysis of plates (plane strain).

1. 1

   1. Necessary mathematical formation is achieved by introducing shape functions, vectorial form of equation of motion and virtual work theorem.

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

2. 2

   2. Derives mass and stiffness matrices and load vectors one dimensional finite elements. Solves problems by longhand calculations. Constructs the flowchart of finite element solution algorithm.

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

3. 3

   3. Knows the degrees of freedom of bar, plate and shell finite elements. Derives the plate stiffness matrices and mass matrices of finite elements using different shape functions.

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

4. 4

   4. Enters the necessary data to a finite element programs.

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

5. 5

   5. Performs the mesh refinement and the convergence analysis for a necessary engineering precision

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

6. 6

   6. Performs static analysis of bars and plates using some finite element program

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

7. 7

   7. Performs dynamic analysis of bars and plates using commercial finite element programs

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

8. 8

   8. Interprets the deflection, rotation and stress outputs of a one dimensional and/or plate finite element program

WEEKLY PLAN

1. WEEK 1

   Introduction to finite elements

2. WEEK 2

   General Concepts

3. WEEK 3

   Variational principles

4. WEEK 4

   Principles of energy

5. WEEK 5

   Small displacement theory

6. WEEK 6

   Moderately large displacement theory

7. WEEK 7

   Interpolation functions (length, area, and volume coordinates)

8. WEEK 8

   Isoparametric shape functions (one, two and three dimensional)

9. WEEK 9

   Generation of isoparametric finite element matrices

10. WEEK 10

    Stress analysis

11. WEEK 11

    Assemblage of finite element matrices

12. WEEK 12

    One dimensional and plate elements (plane stress and plane strain finite elements)

13. WEEK 13

    Static analysis of plates (plane stress)

14. WEEK 14

    Static analysis of plates (plane strain)

ASSESSMENT

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

WORKLOAD

READING

• Olek C Zienkiewicz, Robert L Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th Ed., Elsevier, 2013
• Klaus-Jürgen Bathe, Finite Element Procedures, 2nd Ed., Prentice Hall, Pearson Education, Inc, 2014

TEACHING STAFF

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