MEG 741 Energy and Variational Methods in
Mechanics
Fall Semester 2002
Professor: Brendan J. O'Toole, Ph.D.
Office: TBE B122
Phone: 895-3885
e-Mail: bj@me.unlv.edu
Days/Time/Room: TR /
4:00 PM - 5:15 PM / BHS 204
Text: “Mechanics
of Structures: Variational and Computational Methods”
Pilkey
&Wunderlich, CRC Press 1994, ISBN 0-8493-4435-2
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COURSE
DESCRIPTION & OBJECTIVE
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|
Class |
Dates |
Reading |
Lecture Topics |
HW |
|
1 2 |
T 8/27 R 8/29 |
1.1 - 1.2 |
Introduction:
Vectors, Matrices, Tensors Definitions, Strain-Displacement Equations |
|
|
3 4 |
T 9/3 R 9/5 |
1.3 – 1.4 1.5 – 1.6 |
Material Laws, Equilibrium Boundary Conditions & Governing Equations |
|
|
5 6 |
T 9/10 R 9/12 |
1.7 – 1.8 2.1 - 2.2 |
Beam Theory, Torsion Work & Energy, Classical Variational
Principles |
HW 1 |
|
7 8 |
T 9/17 R 9/19 |
2.3 2.4 |
Generalized Variational Principles Engineering Beam Theory |
|
|
9 10 |
T 9/24 R 9/26 |
2.5 App I |
Differential & Integral Forms of Gov.
Eqns. Fundamentals of Variational Calculus |
|
|
11 12 |
T 10/1 R 10/3 |
4.1 – 4.2 4.3 |
Fundamental Relations for a Beam Element Element Matrices |
HW 2 |
|
13 14 |
T 10/8 R 10/10 |
4.4 5.1 - 5.3 |
Stiffness Matrices Structural Systems, Displacement Method:
Virtual Work |
|
|
15 16 |
T 10/15 R 10/17 |
5.3 |
Displacement Method: Direct Derivation,
Stiffness Matrices Midterm
Exam: Chapters 1, 2, & 4 |
HW 3 |
|
17 18 |
T 10/22 R 10/24 |
5.3 6.1 |
Displacement
Method: Trusses & Frames Trial
Functions & Virtual Work |
|
|
19 20 |
T 10/29 R 10/31 |
6.1 6.2 |
Stiffness Matrix, Loading Vector,
Displacements & Stresses Convergence, Accuracy, h- and p- convergence |
HW 4 |
|
21 22 |
T 11/5 R 11/7 |
6.3 – 6.4 7.1 – 7.2 |
Numerical Integration, Isoparametric Elements Governing Differential Equations |
|
|
23 24 |
T 11/12 R 11/14 |
7.3 7.4 |
Residual Methods Variational Methods |
HW 5 |
|
25 26 |
T 11/19 R 11/21 |
7.5 11.1 – 11.2 |
Trial Function Methods Energy Criterion for Stability |
|
|
27 |
T 11/26 R 11/28 |
11.3 |
Variational Based Stability Analysis THANKSGIVING
(No Class) |
HW 6 |
|
28 29 |
T 12/3 R 12/5 |
10.1 – 10.2 10.3 |
Dynamic Response Free Vibration Analysis |
HW 7 |
2-Hour Final Exam Tuesday, December 10, 6:00 PM
HOMEWORK ASSIGNMENTS
This course provides an overview of the fundamentals used to solve many types of solid mechanics problems. The material presented in the course provides a solid background for other courses such as Finite Element Analysis for Structural Applications, Advanced Strength of Materials, Theory of Plates and Shells, or Computational Solid Mechanics. The objective of the course is to develop a better understanding of the fundamental theories behind most solid mechanics solution methods. The students should be able to apply the fundamental analysis techniques to solve a variety of different truss, beam, and plate mechanics problems.
My weekly schedule will be posted during the second week of the semester. Several hours will be set-aside as open office hours for questions regarding courses. I will generally be on campus between 8:00 AM and 5:30 PM. You are welcome to stop by at any time to ask questions. I will either help you right away or we will schedule another time to meet. The best way to get my attention is to send an e-mail or call requesting a meeting. Leave a few possible meeting times and I will respond as quickly as possible.
If you have a documented disability that
may require assistance, you will need to contact the Disability Resource Center
(DRC) for coordination in your academic accommodations. The DRC is located in
the Reynolds Student Services Complex room 137. Their phone number is 895-0866.
Your grade for the course will be based
on homework, midterm exam, final exam, and a research project. Homework will be
assigned periodically throughout the semester and a cumulative grade will be
recorded.
|
Mid-Term
Exam |
Homework |
Research Project |
Final Exam |
|
30 % |
25 % |
15 % |
30 % |