EML 4507 FINITE ELEMENT ANALYSIS AND DESIGN Class

EML 4507 FINITE ELEMENT ANALYSIS AND DESIGN Class time: MWF 3 rd period Sect. 16 a 7 6 th period Sect 3258 Classroom: 101 Little Hall Instructor: Raphael T. Haftka Office: 220 MAE-A Office hours: MWF 9 th period Phone: 352 -392 -9595 E-mail: haftka@ufl. edu http: //www 2. mae. ufl. edu/haftka/ Also: http: //www 2. mae. ufl. edu/haftka/ugfe 1

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 2

GRADES • Quizzes – Almost every lecture will have an online quiz associated with it. The quiz can be taken as many times as you wish. You get full credit and a bonus if you do it in the window around the corresponding lecture and 90% in the ‘late’ version that will be posted after the original version expires. The highest grade is retained. – Will need your feedback on quizzes since they are new for me. • Homework – Homework will be mostly ABAQUS software plus hand calculations to verify or check on ABAQUS output. • Exams – Three in-term exams. Optional comprehensive final replaces lowest exam (or missed exam even if it is lower than that exam). – Exams will have only questions taken from the quizzes and quiz-like lecture questions. 3

GRADES • Grading – Exams (45%), Quizzes (40%), Homework (15%) A A- B+ B B- C+ C C- D+ D D- E 100 93. 3 89. 9 86. 6 83. 3 79. 9 76. 6 73. 3 69. 9 66. 6 63. 3 59. 9 93. 4 90 86. 7 83. 4 80 76. 7 73. 4 70 66. 7 63. 4 60 • Lectures – Lectures (PPT or PDF files) will be posted on Canvas and web page with solved Quiz-like questions. If you are familiar with material you can take the quiz before the lecture in order to decide whether you need to attend. • Rules – Since this is a large class, it would be difficult to accommodate individual excuses. Therefore, all the rules will be strictly kept 4

Academic Honesty • • You have signed a statement of academic honesty You can discuss HWs and quizzes with classmates HW and Quizzes: each problem must be solved by yourself I will report all honor code violations to Student Conduct and Conflict Resolution • Violation during exam: Fail the course • Violation in submitted HWs: One letter grade down • Very large discrepancy (>30%) between quiz grades and exam grades will lead to reduced quiz weight in grade calculation. 5

SOFTWARE • We will use a commercial finite element analysis software called “ABAQUS” for homework • Download software from http: //campus. 3 ds. com/simulia/freese • ABAQUS help from several TAs who are seasoned users. 6

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 7

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. 8

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 Structure Fi xe d u Piecewise-Linear Approximation Element x 9

INTRODUCTION TO FEM cont. • How to discretize the domain? – Using simple shapes (element) – All elements are connected using “nodes”. 5 6 1 1 7 2 2 8 3 3 Nodes Elements 4 – 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. 10

INTRODUCTION TO FEM cont. • Finite element analysis solves for nodal values. – All others can be calculated (or interpolated) from nodal solutions u 1 u 2 N 1 N 2 x L – Displacement within the element – Strain of the element Interpolation (Shape) Function 11

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. 12

EXAMPLE: FINITE ELEMENTS • Plastic Wheel Cover Model – 30, 595 Nodes, 22, 811 Elements – Matrix size is larger than 150, 000. – MSC/PATRAN (Graphic user interface) 13

EXAMPLE: AUTOMOTIVE DOOR PANEL STAMPING 14

EXAMPLE: AIRBAG DEPLOYMENT 15

FORGING 16

EXAMPLE: VORTICITY 17

You. Tube Videos • Two vehicle impact NCAC FEA FEM – http: //youtu. be/hrfc. ROMz 2 II • Downmilling – http: //youtu. be/p. YCOk. IVLA_c • Rolling – http: //youtu. be/E 1 d 4 WKkbtd. Y 18