 ELECTRIC-ELECTRONIC ENGINEERING (ENGLISH, NONTHESIS) Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

# Course Introduction and Application Information

 Course Code Course Name Semester Theoretical Practical Credit ECTS MCH5308 Finite Element Methods Spring 3 0 3 12
 This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

### Basic information

 Language of instruction: English Type of course: Departmental Elective Course Level: Mode of Delivery: Face to face Course Coordinator : Dr. Öğr. Üyesi ORHAN GÖKÇÖL Course Lecturer(s): Dr. Öğr. Üyesi ORHAN GÖKÇÖL Recommended Optional Program Components: N/A Course Objectives: Finite Element Method (FEM) is a numerical technique for solving differential equations that describe many engineering problems. The objective of the course is therefore to give students the mathematical background of FEM and make them able to develop FEM models and use the method to solve one, two and three-dimensional problems selected from structural mechanics, heat transfer and fluid mechanics by using FEM software.

### Learning Outcomes

 The students who have succeeded in this course; - Understand the need in engineering analysis and design for the Finite Element Method - Know mathematical foundations of FEM - Uses 1D, 2D and 3D elements in modeling - Know and use FEM software - Tie the understanding of mechanical engineering design concepts to use the Finite Element Method software correctly and efficiently - Use FEM to model and solve problems arising from structural mechanics, heat transfer and fluid mechanics Apply FEM to various problems from structural mechanics, heat transfer and fluid mechanics

### Course Content

 Mathematical Background; Introduction to Finite Elements; Integral Formulations and Variational Methods; Definitions of Truss, Beam, Membrane, Plate and Continuum Elements; Stiffness Matrix; Shape Functions; 1D (truss, beam), 2D (rectangular and quadratic) and 3D (tetrahedral, brick) finite elements, Direct Formulation and Basic Energy and Weighted Residual Formulation of Finite Elements; FEM Software Practices; Meshing Techniques; FEM Modeling and Solutions to Selected Problems from Structural Mechanics, Heat Transfer and Fluid Mechanics

### Weekly Detailed Course Contents

 Week Subject Related Preparation 1) Mathematical Background: Review of Partial Differential Equations 2) Mathematical Background (cont); Introduction to FEM; Examples Areas of Application; General Steps in Finite Element Analysis; Examples of Finite Element Modeling 3) Integral Formulations and Variational Methods 4) One Dimensional Problems - Truss and Beam 5) 2D Problems: Triangular, rectangular and quadratic elements 6) 2D Problem Examples: 2D Stress Analysis and Handling of Boundary Conditions 7) 2D Problems: Steady State Heat Transfer Analysis in One and Two Dimensions; Potential Flow Around a 2D Arbitrary Body; Two dimensional elasticity-Governing differential equations and FEM Solutions 8) 2D Problems (cont) 9) Numerical Integration -Newton Cotes Rules, Gauss-Legendre Rules, Multiple Integrals, Numerical Integration of Quadrilateral Elements 10) Midterm 11) Organisation of the Finite Element software, Data preparation and mesh generation through computer 12) Introduction to 3D Finite Elements Modeling 13) 3D Example: 3D elasticity-Governing differential equations, Four node tetrahedral element, Eight node hexahedral (brick) element,Twenty node isoparametric solid element, initial strains and thermal effects 14) Term Project Presentations

### Sources

 Course Notes / Textbooks: J. Reddy, "An Introduction to the Finite Element Method", McGraw-Hill Science/Engineering/Math; (3rd Ed.), 2005. ISBN:978-0072466850 References: I. ABACUS Manual II. Course web site

### Evaluation System

 Semester Requirements Number of Activities Level of Contribution Homework Assignments 4 % 20 Project 1 % 45 Midterms 1 % 15 Final 1 % 20 Total % 100 PERCENTAGE OF SEMESTER WORK % 35 PERCENTAGE OF FINAL WORK % 65 Total % 100