1 EML 4507 FINITE ELEMENT ANALYSIS AND DESIGN Class time: MWF 4 th period Sect. 13G7 6 th period Sect 3258 Classroom: 303 MAE-A Instructors: Raphael T. Haftka, Nam-Ho Kim Haftka’s info: Office: 220 MAE-A Office hours: T 7 th period, W 8 th period, F 9 th period Phone: Also:

2 SYLLABUS Teaching Assistants –TBA Textbook: –Introduction to Finite Element Analysis and Design, by N. H. Kim and B. V. Sankar, Wiley, 2008 Required. Available in the University Bookstore

3 GRADES Homework –All HWs must be submitted before starting the due date class. Solution will be posted on Canvas. Lowest scored HW will be dropped in final grade calculation. No late homework will be accepted. Exams –Three or four, equal weight exams. Tentative schedule: Feb. 15 (Exam1), Mar. 25 (Exam2), Apr. 18 (Exam3). Optional comprehensive final on April 28 replaces lowest exam (or missed exam). –Quiz: There will be some pop-up quizzes for extra credit. Projects –Two projects in finite element analysis and design using Abaqus. Formal report is required. All projects should be submitted to Canvas.

4 GRADES Grading –Exams (51%), Projects (34%), Homework (15%) –Opportunities for extra credits will be posted on Canvas from time to time. Lectures –Lectures (PPT or PDF files) will be posted on Canvas and web page Rules –Since this is a large class, it would be difficult to accommodate individual excuses. Therefore, all the rules will be strictly kept AA-B+BB-C+CC-D+DD-E

5 Academic Honesty You have signed a statement of academic honesty You can discuss HWs and projects with classmates HWs: each problem must be solved by yourself Projects –All computer modeling simulation works should be done by yourself –Report must be written by yourself (no copy and past from other sources) –TA will check electronic version (model file & report) I will report all honor code violations to Student Conduct and Conflict Resolution Violation during exam: Fail the course Violation in submitted projects: Fail the course Violation during quiz: One letter grade down Violation in submitted HWs: One letter grade down

6 SOFTWARE We will use a commercial finite element analysis software called “Abaqus” for homework and projects Tutorials will be provided during the semester after hours when EDGE studio is available, so that they will be available on-line. Download software from edition/for-free/ edition/for-free/ –You will need an image file of your student ID. –You need to install the software in a week

7 COURSE SCHEDULE 0. Mathematical Preliminaries 1. Stress-Strain Analysis 2. Bar and Truss Finite Elements 4. Beam and Frame Elements 6. Finite Elements for Plane Solids 5. Finite Elements for Heat Transfer Problems 7. Finite Element Analysis Procedure and Modeling 8. Structural Design Using Finite Elements

8 TIPS FOR A Be patient and persistent –Read the text repeatedly until you understand it. –If you don’t understand it, ask a question until you get answered. Follow equations –Do not just read the equation. –You must follow equations by HAND, not EYE. Try to understand the meaning of equations –If you memorize an equation that you don’t understand, you can’t solve the problem. Math is a language. Follow the instructions carefully –Read carefully what is asked. If A is asked, then answer A not B. –Do not submit a blank answer. Explain to classmates as ultimate test of understanding

9 Rest of the lecture The rest of the lecture is not taken from the textbook, it is just an attempt to acquaint you with the concept and fields of applications of the finite element method. Look also at Wikipedia’s finite element entry.

10 INTRODUCTION TO FINITE ELEMENT METHOD What is the finite element method (FEM)? –A technique for obtaining approximate solutions to boundary value problems. –Partition of the domain into a set of simple shapes (element) –Approximate the solution using piecewise polynomials within the element F Fixed Structure Element u x Piecewise-Linear Approximation

11 How to discretize the domain? –Using simple shapes (element) –All elements are connected using “nodes”. –Solution at Element 1 is described using the values at Nodes 1, 2, 6, and 5 (Interpolation). –Elements 1 and 2 share the solution at Nodes 2 and 6. INTRODUCTION TO FEM cont Elements Nodes

12 INTRODUCTION TO FEM cont. Finite element analysis solves for nodal values. –All others can be calculated (or interpolated) from nodal solutions –Displacement within the element –Strain of the element u1u1 u2u2 L x N1N1 N2N2 Interpolation (Shape) Function

13 INTRODUCTION TO FEM cont. How to calculate nodal values? –Construct a huge simultaneous system of equations and solve for nodal values. –Different physical problems have different matrices and vectors.

14 EXAMPLE: FINITE ELEMENTS Plastic Wheel Cover Model –30,595 Nodes, 22,811 Elements –Matrix size is larger than 150,000  150,000. –MSC/PATRAN (Graphic user interface)

15 EXAMPLE: AUTOMOTIVE DOOR PANEL STAMPING

16 EXAMPLE: AIRBAG DEPLOYMENT

17 FORGING

18 EXAMPLE: VORTICITY

19 YouTube Videos Two vehicle impact NCAC FEA FEM – Downmilling – Rolling –