ME 4180/5180 Finite Element Methods in Mechanical DesignTennessee Technological University

Fall 2004

How to Contact Me

Instructor: Chris Wilson Telephone: 931-372-3216Office: BN 311 (enter through 309) Office Hours: 9:00-12:00 noon MWF,Email: chriswilson@tntech.edu also by appointment

Class Times and Locations

Class Hours: 12:20-1:15 PM MWFClass Location: Brown 315 for lectures, Clement 313B for ANSYS mini-labs (see daily syllabus)

The Official Word on ME 4180/5180

The following course description is quoted from the Tennessee Technological University Undergraduate Catalog, July 2004.

ME 4180 (5180) Finite Element Methods in Mechanical Design Lec. 3 Credit 3.Prerequisites: ME 3050, ME 3710, ME 3720, and ME 4010. Fundamental concepts and Galerkin approximations; displacement-based formulation; one-dimensional elements and their applications in design of mechanical systems; isoparametric formulation; plane stress, plane strain, axisymmetric, and solid elements and their applications; modeling considerations and error analysis; introduction to ALGOR.

My Thoughts on ME 4180/5180

I have taught this course before using a different book (Logan’s A First Course in the Finite Element Method Using Algor) and different commercial software (Algor). The course was evenly populated with seniors and first-year graduate students. I have several observations about the course. First, there are some mathematical concepts in the course that are necessary and unavoidable. Certainly, linear algebra is a fundamental part of the finite element method. I will try to make the use of linear algebra as practical as possible. In some cases, we will use MATLAB or MAPLE as a linear algebra engine. However, you must understand and use some basic concepts on tests, so a total reliance on software tools is not advisable. Second, a proper mix of theory and application is necessary to really learn the finite element method. I have known many people who have taken one or more finite element courses at the university without learning anything practical. On the other hand, commercial finite element codes are very powerful tools that can be dangerously abused. An understanding of the theory and limitations built into the code may save you much pain and suffering later. To sum up my thoughts, finite element codes should not be treated as blackboxes.

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As far as the prerequisites listed in the university catalog, I think that ME 4010 is the most important. Based on my previous experience teaching the course, your need for ME 3050, ME 3710, and ME 3720 subjects is minimal. Frankly, I am working on a second course to offer in the coming spring semester that will deal with vibrations and heat transfer. I offered it two years ago at the 6000-level. Several undergraduate students took the course—some for undergraduate credit as a technical elective and some for graduate credit.

A final point to mention is the choice of commercial code to be used in the class. The university catalog mentions Algor; however, I plan to use a different code—ANSYS. The choice of codes is not really too important. Most of the commercial codes have the same basic features. ANSYS is more widely used in industry and I am more familiar with it. That is why I chose it.

What I’d Like to Do This Semester

Course Objective: The course objective is to introduce the finite element method in design. Key topics include matrix algebra, an overview of finite element analysis, displacement formulation for bars, beams, 2-D and 3-D continuum elements, and finite element modeling. We will use both some “home-grown” FORTRAN programs and a commercial finite element program, ANSYS, in the course.

Prerequisites: ME 3050 Vibrations, ME 3710 Heat Transfer, ME 3720 Fluid Mechanics, ME 4010 Machine Design. Please note that ME 4010 is the main prerequisite.

Course Weighting and Grade Scale:Homework, Quizzes, Etc. 25% A [90,100] D [60,70)Programming Project 15% B [80,90) F [0,60)Two Tests @ 20% 40% C [70,80)Final Exam 20%

• Homework problems will be assigned during the semester. Each homework set will be collected for grading. The solution of each problem will be logically organized and neatly presented. The solution will include a problem statement, all solution steps, pertinent equations, and supporting sketches and graphs. Numerical answers will be given with the proper significant figures. However, intermediate calculations will be made using the highest precision available to minimize computational round-off. Answers will be given with the proper units and will be boxed or double underlined. Only one side of a page will be used and each problem will start on a new page. An example homework problem is included.

• Each student will complete a special programming project. This is not a team effort!

• There are two tests and a final exam given during the semester. Tests may include both open and closed book portions. Many of the problems on exams will not be computational in nature. Be prepared for discussion questions, comparison questions, etc.

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Student Conduct: You are expected to uphold university standards of conduct. In particular, you should be aware that academic cheating or plagiarism may result in exclusion from the university or any lesser penalty.

Attendance Policy: Attendance is required—poor attendance may adversely affect your grade! No makeup tests will be given without prior consent of the instructor. No late homework will be taken. Borderline grades are determined using attendance and class participation.

Special Needs: Students with a disability requiring accommodations should contact the Office of Disability Services (ODS). An Accommodation Request (AR) should be completed as soon as possible, preferably by the end of the first week of the course. The ODS is located in the Roaden University Center, Room 112; phone 372-6119.

Equipment & Supplies: Bring your textbook and a calculator to each class meeting. You should have access to computer software such as a word processor, presentation software, and a spreadsheet (definitely), and a programming language (possibly) or math analysis package such as MAPLE or MATLAB.

Text: Cook, R.D., Malkus, D.S., and Plesha, M.E., and Witt, R.E., Concepts and Applications of Finite Element Analysis, 4rd Ed., Wiley, 2002.

We will cover most of Chapters 1-4, 6-10, and 14 of the text. The rest of the book has some great information, but we will not have time to cover all of it. Keep this book! It will be a useful reference for work or graduate school.

References:

Logan, D.L., A First Course in the Finite Element Method Using Algor, PWS, 1997.

Norton, R.L., Machine Design: An Integrated Approach, Prentice-Hall, 1996.

Juvinall, R.C., and Marshek, K.M., Fundamentals of Machine Component Design, 3rd Ed., Wiley, 2000.

Young, W.C., Roark’s Formulas for Stress and Strain, 6th Ed., McGraw-Hill, 1989.

Blake, A., Practical Stress Analysis in Engineering Design, 2nd Ed., Marcel Dekker, 1990.

Other references you should have include your statics and dynamics book, your vibrations book, and your mechanics of materials book, etc.

August 30, 2004

A Tentative Daily Syllabus:

Day Date Topic ReadingAssignment

HomeworkAssignment

1 Aug 30 Introduction & Matrix Algebra

Ch. 1

2 Sep 1 Matrix Algebra Appendix A3 3 1-D Elements Ch. 2

6 LABOR DAY4 8 Stiffness and Loads5 10 More Loads6 13 Solving Equations7 15 1-D Application8 17 FE Programming Handout9 20 FE Programming

10 22 ANSYS Introduction11 24 ANSYS Mini-Lab 112 27 Interpolation and Shape

FunctionsCh. 3

13 29 CST and LST Elements14 Oct 1 Q4 and Q8 Elements15 4 FE Programming Handout16 6 Solid Elements17 7 TEST 1 6:00-8:00 PM18 8 Element Modifications19 11 Even More Loads20 13 ANSYS 2-D21 15 ANSYS Mini-Lab 2

18 FALL BREAK22 20 Principle of SPE Ch. 423 22 Rayleigh-Ritz Method24 25 FE Form of R-R Method25 27 Convergence26 29 Axisymmetric Elements Ch. 1427 Nov 1 Axisymmetric Application28 3 ANSYS Mini-Lab 329 5 Gauss Quadrature Ch. 6

8 CDW out of town10 CDW out of town

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12 CDW out of town30 15 Isoparametric Elements31 17 Isoparametric Quads32 18 TEST 2 6:00-8:00 PM33 19 Isoparametric Application34 22 ANSYS Mini-Lab 435 24 Patch Test and More

26 THANKSGIVING36 29 Isoparametric Triangles Ch. 737 Dec 1 ANSYS 3-D38 3 ANSYS Mini-Lab 539 6 Coordinate

Transformations40 8 Dissimilar Elements41 10 Error Estimation Ch. 942 15 FINAL EXAM 3:30-5:30

August 30, 2004