MCH5308 Finite Element MethodsBahçeşehir UniversityDegree Programs ELECTRIC-ELECTRONIC ENGINEERING (ENGLISH, NONTHESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
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 Fall 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


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
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 12 3 36
Study Hours Out of Class 14 4 56
Presentations / Seminar 1 6 6
Project 1 52 52
Homework Assignments 4 6 24
Midterms 1 8 8
Final 1 18 18
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution