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Information
| Code | İM504 |
| Name | Introduction to the Finite Element Methods |
| Term | 2022-2023 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. BEYTULLAH TEMEL |
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
No requirements
Resources
1) Finite Element Method, G. Dhatt and G. Touozot and E. Lefrançois, Wiley, 2012. 2) An Introduction to the Finite Element Method, J. N. Reddy. Mc-Graw Hill, 3. rd Edition (2006)
Notes
Mathematica Software
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. |
| LO11 | The student will be informed about how the system matrices are assembled with finite elements. |
| LO12 | Students will have information about how to calculated stiffness and mass matrices in solutions. |
| LO13 | Students will have information about how to use stiffness and mass matrices in solutions. |
| LO14 | Students will have information about how to use stiffness and mass matrices in solutions dynamic problems.. |
| LO15 | Students will have information about how to use stiffness and mass matrices in solution dynamic problems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have knowledge and understanding at advanced level providing required basis for original projects in the field of civil engineering based on qualifications gained at undergraduate level. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Gain required knowledge through scientific research in the field of engineering, evaluate, interpret and apply data. | 4 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Be aware of new and emerging applications,examine and learn where necessary. | |
| PLO04 | Yetkinlikler - Öğrenme Yetkinliği | Construct engineering problems, develop strategies to solve them, and apply innovative methods for solutions. | 3 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Design and implement analytical modeling and experimental research and solve complex situations encountered in this process. | |
| PLO06 | Yetkinlikler - Öğrenme Yetkinliği | Develop new and / or original ideas and methods; develop innovative solutions for the system, part, and process design. | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Have learning skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Be aware of innovative developments in the field of civil engineering, and analyse and learn them when needed. | 2 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | ransfer process and results of the projects in the field of civil engineering or on national and international platforms in written or oral form. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Have knowledge in current techniques and methods applied in civil engineering. | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Use computer software as well as information and communication technologies at the level required in the field of civil engineering. | 1 |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | Oversee social, scientific and ethical values in all professional platforms. |
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, Problem Çözme |
| 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, Örnek Olay, 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 |
| 8 | Mid-Term Exam | None | Öğretim Yöntemleri: Soru-Cevap |
| 9 | Selection of weight function, Collocation with subregions, Galerkin method, Galerkin method with partial integration, least squares method. | Lecture notes | Öğretim Yöntemleri: Anlatım, Benzetim, Örnek Olay, Problem Çözme |
| 10 | Finite element method with matrix notation, transformation of integral region. | Lecture notes | Öğretim Yöntemleri: Anlatım, Benzetim, 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 | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Numerical methods, numerical integration, solution of linear equations. | Lecture notes | Öğretim Yöntemleri: Anlatım, Örnek Olay, Problem Çözme |
| 15 | Dynamic problems, Newmark method, numerical examples. | Lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 16 | Term Exams | None | Öğretim Yöntemleri: Soru-Cevap |
| 17 | Term Exams | None | Ölçme Yöntemleri: Ödev |
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 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 20 | 20 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 20 | 20 |
| Total Workload (Hour) | 150 | ||
| Total Workload / 25 (h) | 6,00 | ||
| ECTS | 6 ECTS | ||