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Information
| Code | MK0028 |
| Name | Finite Elements: An Introduction |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| 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 Goal / Objective
Obtaining numerical solutions to Differential Equation commonly encountered in Applied Mechanics via Finite Element Analysis.
Course Content
Mathematical prelimininaries about interpolation of functions. Weak form of second-order differential equations and their discretization into elements. Problems in Mechanics. Stability and dynamic problems. Basic examples of nonlinear equations
Course Precondition
none
Resources
Lecture Notes
Notes
Finite Element Book
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Solutions of Differential Equations by Finite Elements will be presented. |
| LO02 | Weak form of the equation and use of shape functions will be explained. |
| LO03 | One-dimensional, linear, eigenvalue, dynamic and nonlinear equations in Mechanics will be solved. |
| LO04 | Knowledge on the derivation of DE |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Understands and applies basic sciences, mathematics and engineering sciences at a high level. | 5 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | He/she has extensive and in-depth knowledge, including the latest developments in his/her field. | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | They reach the latest information in a field and have a high level of proficiency in the methods and skills necessary to comprehend and research them. | 5 |
| PLO04 | Yetkinlikler - Öğrenme Yetkinliği | They carry out a comprehensive study that brings innovation to science and technology, develops a new scientific method or technological product/process, or applies a known method to a new field. | 4 |
| PLO05 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Independently perceives, designs, implements and concludes an original research process; manages this process. | 5 |
| PLO06 | Yetkinlikler - Alana Özgü Yetkinlik | Contributes to the science and technology literature by publishing the outputs of its academic studies in respected academic environments. | 4 |
| PLO07 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Evaluates scientific, technological, social and cultural developments and conveys them to the society with the awareness of scientific impartiality and ethical responsibility. | 2 |
| PLO08 | Belirsiz | Performs critical analysis, synthesis and evaluation of ideas and developments in the field of expertise. | 4 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Communicates effectively, both verbally and in writing, with those working in the field of specialization and the wider scientific and social community, communicating and discussing at an advanced level of written, oral and visual communication using a foreign language at least at the C1 General Level of the European Language Portfolio. | 5 |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Carries out literature search |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Mathematical Preliminaries | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Interpolation of Functions | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Weighted Residual Method | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Examples in Thermodynamics | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | The anatomy of a Linear second-order equation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Constructing the Finite Element Structure | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Examples in Solid Mechanics | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Examples in Fluid Mechanics | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Fourth-order Problems | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Examples in Beam Analysis | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Time-Dependent Problems | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | System of Difeerential Equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Eigenvalue Problems | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Nonlinear Finite Elements | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | 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 | ||