ECTS - Nonlinear Finite Element Method
Nonlinear Finite Element Method (MFGE576) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Nonlinear Finite Element Method | MFGE576 | 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 | The objective of this course is to introduce basic topics in nonlinear finite element analysis of metal forming operations. Sources of nonlinearities will be covered. Solution methods of nonlinear equation systems will be introduced. Based on these preliminary information one dimensional nonlinear problems will be used to deepen knowledge on the nonlinearities and their nature. Further lectures will cover two and three dimensional rigid plastic and large strain elasto-plastic behavior of metals and the necessary finite element concepts for the solution of metal forming processes. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Review of the linear FE-concepts, solution of nonlinear equations, one-dimensional nonlinear problems, two/there-dimensional rigid-plastic finite element solution, two/three-dimensional large-strain elasto-plastic FE-solutions. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Chapter 1: Introduction Linearity Assumption in Mechanics, Sources of Nonlinearity, Examples of Nonlinear Problems in Solid Mechanics | |
| 2 | Chapter 2: Review of Linear FEM-Concepts Common Procedure of FEA, Direct Approach (Example: Truss Solution), Types of Elements, Variational Approach, Example: Tapered Slab | |
| 3 | Chapter 3: Solution of Nonlinear Equations Incremental Solution Methods (Euler Method, Self-Correcting Euler Method), Iterative Solution Methods (Direct Iteration Method, Full Newton-Raphson Method) | |
| 4 | Chapter 3: Solution of Nonlinear Equations Iterative Solution Methods (Modified Newton-Raphson Method, Quasi-Newton Methods), Numerical Errors (Condition Number , Ill-Conditioned Set of Equations) | |
| 5 | Chapter 4: One-Dimensional Nonlinear Problems Material Nonlinearities: Small-Strain Elasto-Plasticity (Fundamentals , Finite Element Discretization, Incremental Newton-Raphson Solution, Initial Stiffness Solution) | |
| 6 | Chapter 4: One-Dimensional Nonlinear Problems Geometric Nonlinearities: Small-Strain Large-Displacements (Introduction, A Finite Strain Measure, Finite Element Discretization by Energy Method, An Example: Spring-Truss System) | |
| 7 | Chapter 5: Two/Three-Dimensional Rigid-Plastic Finite Element Solution One-Dimensional Observations on Theory of Plasticity (Idealized Observations, Idealized Stress-Strain Models, Microstructural Mechanisms of Plastic Deformation) | |
| 8 | Chapter 5: Two/Three-Dimensional Rigid-Plastic Finite Element Solution General Potential Theory of Plasticity (The Yield Condition, The Flow Rule-Drucker's Postulate, Work-Hardening Assumption, Extremum Principles of Plasticity) | |
| 9 | Chapter 5: Two/Three-Dimensional Rigid-Plastic Finite Element Solution Finite Element Solution: Problem Description, Finite Element Discretization | |
| 10 | Chapter 5: Two/Three-Dimensional Rigid-Plastic Finite Element Solution Finite Element Solution: Solution Procedure (Direct Iteration Solution, Newton-Raphson Solution, Element Selection and Integration Orders, Modelling Friction) | |
| 11 | Chapter 5: Two/Three-Dimensional Rigid-Plastic Finite Element Solution Finite Element Solution: Solution Procedure (Treatment of Rigid Regions, Contact-Algorithms, Remeshing-Algorithms, Application Codes) | |
| 12 | Chapter 6: Two/Three-Dimensional Large-Strain Elasto-Plastic FE-Solutions Static Implicit Methods: Governing Variational Statement | |
| 13 | Chapter 6: Two/Three-Dimensional Large-Strain Elasto-Plastic FE-Solutions Static Implicit Methods: Governing Variational Statement (Objective Stress Increment, Finite Strain Increment, Time Integration of the Constitutive Equation), Finite Element Equations | |
| 14 | Chapter 6: Two/Three-Dimensional Large-Strain Elasto-Plastic FE-Solutions Dynamic Explicit Methods (Mass-Spring-Damper System, Finite Element Equation of Motion, Computational Issues, Dynamic Relaxation) | |
| 15 | Final Examination Period | |
| 16 | Final Examination Period |
Sources
| Course Book | 1. Cook, R. D.; Malkus, D. S.; Plesha, M. E.: Concepts and Applications of Finite Element Anlaysis, New York: John Wiley & Sons, 1989 |
|---|---|
| Other Sources | 2. Malvern, L. E.: Introduction to Mechanics of a Continuous Media, Englewood Cliffs/New Jersey: Prentice-Hall, 1969 |
| 3. Kobayashi, S.; Oh, S.; Altan, T.: Metal Forming and the Finite-Element Method; New York: Oxford University Press, 1989. | |
| 4. Lubliner, J.: Plasticity Theory, New York: Macmillan, 1990 |
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 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | 16 | 2 | 32 |
| 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 | 179 | ||