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Information
| Code | MN0022 |
| Name | Finite Element Analysis in Engineering |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
This course will train you to analyse real world structural mechanics problems using the finite element method. You will be introduced to the mathematical basis of finite element analysis.
Course Content
Variational Notation. Galerkin formulations. Plane elasticity. Brief information about plates and shells. Isoparametric coordinates. Special value and time dependent problems. Programming techniques and introduction of existing package programs.
Course Precondition
None
Resources
Lecture Notes
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the basic concepts of finite element method. |
| LO02 | Learns some classical element shapes and shape functions. |
| LO03 | Gets information about the approach on one-dimensional, two-dimensional and three-dimensional reference elements. |
| LO04 | Students will have an idea about how the shape functions will be formed. |
| LO05 | The student will be able to learn how to implement shape functions. |
| LO06 | Students will be able to learn the integral formulations of engineering problems, discrete systems, continuous systems, linear equations, nonlinear equations, the method of weighted-residues, integral transformations and the weak integral form. |
| LO07 | Students will be informed about Variation calculus, variational notation, Euler differential equation and the discretization of integral forms. |
| LO08 | Students will be able to choose the weight function, collocation with sub-regions, Galerkin method, Galerkin method with partial integration, least squares method. |
| LO09 | The students who have taken this course will have knowledge about how to use the matrix notation in the finite element method and the transformation of the integral region. |
| LO10 | The student will be informed about how the element stiffness and mass matrices are calculated with finite elements. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Based on the qualifications gained during PhD studies, develops and deepens the current and advanced knowledge in the area by unique means of thinking and / or research at mastery level and comes up with original definitions which bring about novelty to the area. | 5 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Can effectively use the equipment used in the field. | |
| PLO03 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Selects experimental measurement methods of various physical quantities and uses instruments in accordance with their sensitivity limits. | 3 |
| PLO04 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets experimental and observational results. | |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Can draw conclusions from the information obtained during the preparation for the PhD qualifying exam. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Can interpret the information acquired about the field orally and in writing. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Uses mathematical methods related to the field of study. | 5 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have knowledge about the logic, design, conclusion and dissemination of results of scientific research. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Uses the theoretical and applied knowledge gained in the field of materials and nanotechnology at the level of expertise. | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains high-level skills in using research methods in studies related to materials science and nanotechnology. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Develops a scientific method that brings innovation to science. | |
| PLO12 | Yetkinlikler - Alana Özgü Yetkinlik | Makes critical analysis, synthesis and evaluation of new ideas related to the field. | 3 |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can carry out independent research on a specific topic related to materials and nanotechnology. | 4 |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Be able to lead in the execution of interdisciplinary studies. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Follows the developments in the her/his field of study and constantly renews herself/himself. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Calculate the predictions of the theories and compare them with the experimental results. | 5 |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Comprehends the interdisciplinary interaction that the field of study is related to. | |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | He/she shares his/her own ideas and suggestions regarding the problems in the field of study with groups in and outside the field by supporting them with quantitative and qualitative data. | 3 |
| PLO19 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can develop original solutions for problems in the field. | |
| PLO20 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can prepare a scientific article and publish scientific articles in international refereed journals. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction, Basic Concepts, General Parametric Approach, Objectives of Parametric Approach, Approach with Nodes, Approach with Finite Elements, Geometric Descriptions of Elements,Meshing. | Lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Some classical element shapes, shape functions, examples. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | One-dimensional, two-dimensional and three-dimensional reference elements, Approaches based on the reference elements, examples. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 4 | Formation of shape functions. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Applications of shape functions. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Integral formulations of engineering problems, discrete systems, continuous systems, linear equations, nonlinear equations, weighted-residual method, Integral transformations, Weak integral form | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Variation calculation, variational notation, Euler's differential equation, Discretization of integral forms. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Selection of weight function, Collocation with subregions, Galerkin method, Galerkin method with partial integration, least squares method. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Finite element method with matrix notation, transformation of integral region. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 11 | Calculation of element matrices, examples, element mass matrix, geometric transformation. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Dynamic loading, coding technique for sysytem rigidity and mass matrix calculations , system equation, boundary conditions. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 13 | numerical applications for Shape functions | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 14 | numerical applications for Galerkin method | Lecture notes | Öğretim Yöntemleri: Problem Çözme |
| 15 | numerical applications for Matrix notation | Lecture notes | Öğretim Yöntemleri: Problem Çözme |
| 16 | Review | Lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Final | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||