ECTS - Practical Finite Elements (Linear Finite Element)
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 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Drill and Practice, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course aims to acquaint the students with theoretical and practical knowledge on reliable and robust finite element formulations for solid and structural mechanics. |
| Course Learning Outcomes |
The students who succeeded in this course;
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| Course Content | 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. |
|---|---|
| Other Sources | 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
| Requirements | Number | Percentage of Grade |
|---|---|---|
| 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 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir | X | ||||
| 2 | Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur. | X | ||||
| 3 | Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir | X | ||||
| 4 | Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir | X | ||||
| 5 | Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir. | X | ||||
| 6 | Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir | X | ||||
| 7 | Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir. | X | ||||
| 8 | Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur. | X | ||||
| 9 | Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir. | X | ||||
| 10 | Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir. | X | ||||
ECTS/Workload Table
| 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 |
| Total Workload | 163 | ||