ECONOMICS AND FINANCE
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MCH4205	Introduction to Finite Element Methods	Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Assoc. Prof. ARMAĞAN FATİH KARAMANLI
Recommended Optional Program Components:	None
Course Objectives:	The objective of this course is to equip the student with theoretical finite element methods background as well as practical experience. Matrix algebra, truss and beam element formulations, 1D, 2D and 3D element formulations and their analysis procedures will be shown within the theoretical content of that course. Hypermesh, Radioss Linear and Nastran software packages will be introduced.

Learning Outcomes

The students who have succeeded in this course;
I. Define the CAE methodologies and Finite Element Methods.
II. Explain the commrecial software packages and their application areas.
III. Describe the FEM philosophy and alternative methodologies.
IV. Describe basic geometric functions and meshing operations in Hyperworks, geometry clean-up, mesh editing and element quality check tools.
V. Apply linear 1D element formulations in solving the problems of different disciplines.
VI. Analyse one dimensional and two dimensional problems with 1D elements.
VII. Analyse the plane and space truss systems with Finite Element Methods.
VIII. Analyse the 2D and 3D systems under static loading by using Hypermesh software and with Radioss Linear and Nastran solvers.
IX. Explain 1D, 2D and 3D elastosatics, local and global shape functions.
X. Analyse the 2D and 3D systems in frequency domain, modal and frequency response analysis in Hyperworks.

Course Content

Methods in Computer Aided Engineering; Matrix Algebra Review, Introduction to Hypermesh; FEM Philosophy, Seven Steps of FEM.; Basic Functions in Hypermesh; Linear 1D Element Formulations with Spring Analogy and Assembly Process in 1D.; Hyperworks: Basic Geometric Functions in Hypermesh; 1D Elastostatic and Heat Transfer Problems, Applying Boundary Conditions with Direct and Elimination Methods.; Hyperworks: 1D and 2D Meshing in Hypermesh, Element Types for Different Solvers; Analysis of One-Dimensional Problems.; Hyperworks: 3D Meshing in Hypermesh, Element Types for Different Solvers Assembly Process in 2D for 1D elements. Hyperworks: Geometry Clean Up and Model Checking, Element Quality, Free Edge, Duplicate and Element Normal Checks, Mesh Editing Plane and Space Trusses, Material.;Hyperworks: Property and Component Definitions, Card Types for Different Solvers, Beam elements.
Hyperworks: Midsurface Generations, 2D Static Analysis - Preporcess in Hypermesh for Radioss Linear Solver, and Post Process in Hyperview; 1D Elastostatics, ID and IEN arrays.
Hyperworks: 3D Static Analysis - Preporcess in Hypermesh for Radioss Linear Solver, and Post Process in Hyperview, 3D Static Analysis in Nastran; Local and Global Shape Function Construction for 1D Linear Elements. Hyperworks: Modeling Tricks and Techniques for Assemblies - Point Welds, Welds, Brazing, Bolts; Local and Global Shape Function Construction for 1D Quadratic Elements. Hyperworks: Static Analysis for Assembled Structures 2D Elastostatics. Hyperworks: Introduction to NVH, Modal Analysis with Radioss Linear and Nastran; 2D Elastostatics cont'd, Introduction to 3D Elastostatics. Hyperworks: Frequency Response Analysis with Radioss Linear and Nastran

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Methods in Computer Aided Engineering
2)	Matrix Algebra Review, Introduction to Hypermesh
3)	FEM Philosophy, Seven Steps of FEM. Hyperworks: Basic Functions in Hypermesh
4)	Linear 1D Element Formulations with Spring Analogy and Assembly Process in 1D. Hyperworks: Basic Geometric Functions in Hypermesh
5)	1D Elastostatic and Heat Transfer Problems, Applying Boundary Conditions with Direct and Elimination Methods. Hyperworks: 1D and 2D Meshing in Hypermesh, Element Types for Different Solvers
6)	Analysis of One-Dimensional Problems. Hyperworks: 3D Meshing in Hypermesh, Element Types for Different Solvers
7)	Assembly Process in 2D for 1D elements. Hyperworks: Geometry Clean Up and Model Checking, Element Quality, Free Edge, Duplicate and Element Normal Checks, Mesh Editing
8)	Plane and Space Trusses, Material. Hyperworks: Property and Component Definitions, Card Types for Different Solvers
9)	Trusses cont'd, Beam elements. Hyperworks: Midsurface Generations, 2D Static Analysis -Preporcess in Hypermesh for Radioss Linear Solver, and Post Process in Hyperview
10)	1D Elastostatics, ID and IEN arrays. Hyperworks: 3D Static Analysis - Preporcess in Hypermesh for Radioss Linear Solver, and Post Process in Hyperview, 3D Static Analysis in Nastran
11)	Local and Global Shape Function Construction for 1D Linear Elements. Hyperworks: Modeling Tricks and Techniques for Assemblies - Point Welds, Welds, Brazing, Bolts
12)	Local and Global Shape Function Construction for 1D Quadratic Elements. Hyperworks: Static Analysis for Assembled Structures
13)	2D Elastostatics. Hyperworks: Introduction to NVH, Modal Analysis with Radioss Linear and Nastran
14)	2D Elastostatics cont'd, Introduction to 3D Elastostatics. Hyperworks: Frequency Response Analysis with Radioss Linear and Nastran

Sources

Course Notes / Textbooks:

Lecture Notes

References:

Saeed Moaveni, “Finite Element Analysis, Theory and Application with Ansys”, Pearson International Edition, 3rd Ed., ISBN-10: 0-13-241651-4, ISBN 13: 978-0-13-241651-1.

Robert D. Cook, David S. Malkus, Micheal E. Plesha, Robert J. Witt, “Concepts and Applications of Finite Element Analysis”, John Wiley & Sons, Inc., 4th Ed., ISBN 978-0-471-35605-9.

Klaus-Jurgen Bathe, “Finite Element Procedures”, Prentice Hall, ISBN 0-13-301458-4.

Zhangxin Chen, “Finite Element Methods and Their Applications”, Springer, ISBN 3-540-24078-0.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Attendance	14	% 0
Homework Assignments	5	% 10
Project	1	% 50
Total		% 60
PERCENTAGE OF SEMESTER WORK		% 10
PERCENTAGE OF FINAL WORK		% 50
Total		% 60

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	2	28
Laboratory	14	2	28
Study Hours Out of Class	14	4	56
Project	1	10	10
Homework Assignments	5	4	20
Total Workload			142

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Build up a body of knowledge in mathematics and statistics, to use them, to understand how the mechanism of economy –both at micro and macro levels – works.	3
2)	Understand the common as well as distinctive characters of the markets, industries, market regulations and policies.	2
3)	Develop an awareness of different approaches to the economic events and why and how those approaches have been formed through the Economic History and understand the differences among those approaches by noticing at what extent they could explain the economic events.	1
4)	Analyze the interventions of politics to the economics and vice versa.	3
5)	Apply the economic analysis to everyday economic problems and evaluate the policy proposals for those problems by comparing opposite approaches.	2
6)	Understand current and new economic events and how the new approaches to the economics are formed and evaluating.	2
7)	Develop the communicative skills in order to explain the specific economic issues/events written, spoken and graphical form.	3
8)	Know how to formulate the economics problems and issues and define the solutions in a well-formed written form, which includes the hypothesis, literature, methodology and results / empirical evidence.	2
9)	Demonstrate the quantitative and qualitative capabilities and provide evidence for the hypotheses and economic arguments.	2
10)	Understand the information and changes related to the economy by using a foreign language and communicate with colleagues.	3