# Practical Finite Elements (Linear Finite Element) (MFGE505) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Practical Finite Elements (Linear Finite Element) MFGE505 3 0 0 3 5
Pre-requisite Course(s)
MFGE 212, MFGE 301
Course Language English N/A Ph.D. Face To Face Lecture, Drill and Practice, Problem Solving. Asst. Prof. Dr. İzzet Özdemir This course aims to acquaint the students with theoretical and practical knowledge on reliable and robust finite element formulations for solid and structural mechanics. The students who succeeded in this course; Understanding the fundamentals of finite element method as a tool for solving linear solid and structural mechanics problems. Constructing the connection between the physical problem, mathematical model and approximate solution by means of the finite element method. Students are expected to enhance their mathematical and programming skills through applications and development of programs and subroutines. Students will have hands-on experience using commercial Finite Element Packages which are widely utilized by the Industry. Background and application of FE, direct approach, strong and weak forms, weight functions and Gauss quadrature, FE formulation for 1D problems, plane strain/stress and axisymmetric problems, displacement based FE formulation, isoparametric elements, performance of displacement based elements and volumetric locking; reduced selective integration.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Chapter 1: Introduction Background and use of finite element method in solid and structural mechanics, examples from linear and non-linear mechanics.
2 Chapter 2: Direct Approach Describing the behavior of a single bar (truss) element, assembly of the element equations, imposition of the boundary conditions and system solutions.
3 Chapter 2: Direct Approach Two dimensional truss systems. Geometric transformations, calculation of derived quantities. Thermal stresses.
4 Chapter 3: Strong and Weak Forms for One-dimensional Problems Strong and weak form for one-dimensional stress analysis, equivalence between strong and weak forms.
5 Chapter 4: Approximation of Trial solutions, Weight Functions and Gauss Quadrature in One-dimension Linear one-dimensional element, quadratic one-dimensional element, construction of shape functions in 1-dimension, Gauss quadrature.
6 Chapter 5: Finite Element Formulation for One-dimensional problems Element matrices for two-noded element, application to stress analysis and heat conduction problems, convergence by numerical experiments.
7 Chapter 6: Finite Element Formulation for Vector Field Problems - Linear Elasticity Kinematics, stress and traction, equilibrium, constitutive equation.
8 Chapter 6: Finite Element Formulation for Vector Field Problems - Linear Elasticity Dimensionally reduced problems (plane strain, plane stress, axisymmetric problems), strong and weak forms, finite element discretization for plane strain problems.
9 Chapter 6: Finite Element Formulation for Vector Field Problems - Linear Elasticity 3-noded triangular element, element equations, numerical integration in two dimensional space, boundary conditions, system solution and calculation of derived quantities, convergence study by numerical examples.
10 Chapter 7: Isoparametric Formulation Concept of isoparametric formulation, transformation between physical and parametric spaces.
11 Chapter 7: Isoparametric Formulation 4-noded plane strain element, element equations, convergence study by numerical tests and comparison of the results of 3-noded and 4-noded elements.
12 Chapter 8: Three-dimensional Elasto-statics Governing equations of linear elasticity in three dimensions.
13 Chapter 8: Three-dimensional Elasto-statics 8-noded hexahedral element, element equations and numerical integration in three dimension, imposition of boundary conditions and system solution.
14 Chapter 9: Performance of displacement based elements Performance of displacement based elements under certain deformation modes, e.g. bending dominated and volume preserving modes. Concept of volumetric locking and circumventing it by reduced integration.
15 Final Examination Period
16 Final Examination Period

### Sources

Course Book 1. Fish J., Belytschko T., A First Course in Finite Elements, John Wiley, 2007. 2. Bathe, K.J., Finite Element Procedures. Prentice Hall, 1996. 3. Zienkiewicz, O.C., Taylor, R.L., The Finite Element Method, Volume 1: The Basis, 6th Edition, Elsevier, 2005. 4. Zienkiewicz, O.C., Taylor, R.L., The Finite Element Method, Volume 2: Solid Mechanics, 6th Edition, Elsevier, 2005.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 6 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application 16 1 16
Special Course Internship
Field Work
Study Hours Out of Class 16 6 96
Presentation/Seminar Prepration
Project
Report
Homework Assignments 6 6 36
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 15 15