Penn State University
Department of Mechanical and Nuclear Engineering
ME 461 – FINITE ELEMENT ANALYSIS
Prerequisites: E MCH 213, E MCH 210H or E MCH 210;CMPSC 200, CMPSC 201 or CMPSC 202
Text: T.Chandrupatla and A. Belegundu. Introduction to Finite Elements in Engineering, 4th Edition, Prendice Hall, 2001.
Time & Place: M W F 9:05 AM - 9:55 AM in 158 Willard Building
Instructor: Professor Reuben Kraft, 320 Leonhard Bldg., Tel: 814-867-4570, Email: reuben.kraft@psu.edu
Office Hours: Thursday 3:00 p.m. – 4:00 p.m. at 320 Leonhard Building or 341 Leonhard Building (my lab) (check both)
Teaching Assistant: Ziwen Fang, Email: zpf5016@psu.edu
Office location and hours: 341 Leonhard Bldg., Tuesday 9 AM – 10 AM or by appointment
Course Objectives: This is an introductory course in the Finite Element Method. The mathematical formulation of the method will be
presented and then applied to problems in elasticity and heat transfer. Projects will be assigned to demonstrate the finite element
method in simplified problems using C and realistic problems using the commercial code Abaqus. Upon completion of this course,
students should be able to:
1. Understand fundamentals of FE theory. This includes generalized Hooke’s law, Rayleigh−Ritz method with energy
functional, shape functions and derivation of FE matrices
2. Problem modeling, including concept of rigid body motion, symmetry, multipoint constraints
3. Hand−calculations on 1-D and 2-D problems
4. Understand code and use an in−house computer program
5. Do realistic linear FEA using a commercial code
6. Interpret results better through improved understanding of basic mechanics, and enhanced math and computer skills
Target Course Schedule:
Week Topic
1
Introduction, Elasticity Theory review
2
Elasticity Theory review, In-class computer work (HPC and Linux intro)
3
Potential Energy Theory, Rayleigh-Ritz Method, In-class Abaqus tutorial
4
Galerkin Theory Methods, 1D Elasticity Theory, In-class Abaqus tutorial (CAD to FEM)
5
Galerkin Theory Methods, 1D Elasticity Problems, Shape Function Theory
6
Exam 1, Truss Theory, In-class Abaqus Tutorial/Project Meetings
7
1D Elasticity Problems, Stiffness Matrices, Shape Functions
8
Isoparametric Formulation Theory, Two Dimensional Theory, In-class Abaqus tutorial (as needed)
9
Spring Break
10
Two-Dimensional Theory (constant strain triangle), Properties of Stiffness Matrix, 2D Example problem, In-class Abaqus
tutorial (as needed)
11
Heat Transfer modeling, 2D examples (isoparametric form)
12
Discussion of C-based FEM program, Numerical procedures to deal with stiffness matrix, FE Plotting
13
2D Quad Element Theory, Exam 2, Gauss-Legendre Quadrature Theory, In-class Abaqus tutorial (as needed)
14
Numerical Integration, Three-Dimensional FEA Formulation and Theory
15
Structural Dynamics Theory, Final Project Presentations, In-class Abaqus tutorial (as needed)
16
Final Project Presentations
Grading:
Midterm Exam (2)
Homework (10 total)
Attendance & Participation
Final Project Term Paper
Final Presentation
TOTAL
20% (10% each)
40% (4% each)
10% (Evaluated using quizzes and in-class Abaqus Screenshots)
20%
10%
100%
Course website: The course website is located on Angel. I will use the course website to post homework, solutions and all other
announcements.
Homework: Assignments are due in class. Papers must be stapled, not folded at the corner or paper clipped. Unstapled assignments
will not be accepted. No late homework will be accepted. For Abaqus/FE work use the Linux Lab
(http://www.mnelabs.mne.psu.edu/LinuxLab.html) or your personal computer with an ICS account (described below).
Examples of past projects are posted. They provide examples of what I am looking for in the quality of reports. These can be found at:
http://www.mne.psu.edu/compbio/teaching/me461/teaching-me461.html
Attendance and Lateness: Attendance is required unless excused by myself.
Make up Exams: No makeup exams are allowed. There will be two exceptions, (1) the student brings a medical certificate and (2) the
student appeals to the undergraduate program director, Dr. Eric Marsh, and Dr. Eric Marsh directly requests me to administer the
exam.
Grading Complaints or Concerns: Must be submitted in writing as a cover sheet to the assignment or test you are concerned with.
MUST BE TURNED-IN BY HAND (Emails will not be accepted because they get buried in my inbox too quick.)
Laptops: You will be required to bring a laptop on designated days to class for in-class tutorials and project work.
Abaqus Student Edition: http://academy.3ds.com/software/simulia/abaqus-student-edition/ (Can only handle meshes up to 1000
nodes.)
For class projects use the Institute for CyberScience. You can find out more information about ICS here:
http://ics.psu.edu/advanced-cyberinfrastructure/support/classroom-support/
To obtain an account follow the instructions here: Accounts on ICS: http://ics.psu.edu/advanced-cyberinfrastructure/accounts/
Click on the link next to “If you need to sign up for an account on a Lion-X system”
You will also need to download and install exceed on demand on your laptop.
Exceed on demand: http://ics.psu.edu/advanced-cyberinfrastructure/support/tutorials/exceed-ondemand/
Academic Integrity - http://www.engr.psu.edu/FacultyStaff/AcademicIntegrity/SyllabusStatement.aspx
The University defines academic integrity as the pursuit of scholarly activity in an open, honest and responsible manner. All
students should act with personal integrity, respect other students’ dignity, rights and property, and help create and maintain an
environment in which all can succeed through the fruits of their efforts (refer to Senate Policy 49-20). Dishonesty of any kind will not
be tolerated in this course. Dishonesty includes, but is not limited to, cheating, plagiarizing, fabricating information or citations,
facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person
or work previously used without informing the instructor, or tampering with the academic work of other students. Students who are
found to be dishonest will receive academic sanctions and will be reported to the University’s Office of Student Conduct for possible
further disciplinary sanctions (refer to Senate Policy G-9). You are encouraged to discuss the homework and design projects with your
peers. However, each individual is responsible for submitting his or her own unique assignment. It is essential to your success in ME
461 that you make a mature effort to understand the homework problems. Careful consideration of each problem, even if by trial and
error, develops your ability to solve real-world problems facing you upon graduation. Your colleagues may help you, but ultimately
the responsibility is your own.
Disability - http://equity.psu.edu/ods/faculty-handbook/syllabus-statement
Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an
office for students with disabilities. The Office for Disability Services (ODS) Web site provides contact information for every Penn
State campus: http://equity.psu.edu/ods/dcl. For further information, please visit the Office for Disability Services Web site:
http://equity.psu.edu/ods.
In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office
at the campus where you are officially enrolled, participate in an intake interview, and provide documentation:
http://equity.psu.edu/ods/doc-guidelines. If the documentation supports your request for reasonable accommodations, your campus’s
disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the
accommodations with them as early in your courses as possible. You must follow this process for every semester that you request
accommodations.