Mon, 1 May 00Schedule of deliverables Schedule of final deliverables
Syllabus Policy Unix matters Matlab matters Class project Schedule of deliverables Schedule of final deliverables
Properties of singular matrices: Null space, uniqueness of solution.
Bandwidth, reduction by renumbering dofs; substructuring analysis,
ordering of substructures.
Matrix transpose, reversal rule for the transpose of the product
of matrices, proof.
Algorithm for symmetric treatment of prescribed boundary conditions.
FINAL EXAM: Thu,
4 May 00, 12:30-2:30, 327 Aero.
Tips
for test takers.
Fri, 28 Apr 00
Wed, 26 Apr 00: Last day of class, course evaluation, teammate evaluation.
Project: Schedule
of final deliverables.
Lecture 35: 3-D Euler-Bernoulli Beam theory with shear correction.
Reading assignment: P[1968], Section 5.6, pp.70-82.
Wed, 26 Apr 00
Mon, 24 Apr 00: Project: Schedule
of final deliverables.
Lecture 34: 3-D Euler-Bernoulli Beam theory with shear correction.
Reading assignment: P[1968], Section 5.6, pp.70-82.
Fri, 21 Apr 00
WEEK 16 
Fri, 21 Apr 00: Project: Schedule of final deliverables.
Wed, 19 Apr 00: Project: Schedule of final deliverables.
Mon, 17 Apr 00: Project: Deliverable (See schedule of deliverables).
WEEK 15
Fri, 14 Apr 00: Project:
Deliverable (See schedule
of deliverables), removal of mechanisms in Stage 1 and Stage 3 of the
Saturn V rocket.
Lecture 33: Static substructuring analysis (cont'd): Data
structure (index arrays, assembly, coding, etc.)
Wed, 12 Apr 00: Project: Deliverable (See schedule of deliverables), eigenvalues and first three mode shapes for (i) the 3-D three-bay tower, for (ii) the Stage 2 and (iii) the Stage 3 of the Saturn V rocket.
Mon, 10 Apr 00: Project: Deliverable (See schedule of deliverables).
WEEK 14
Fri, 7 Apr 00:
Lecture 33: Static substructuring analysis (cont'd): Coding
aspects, index arrays.
Wed, 5 Apr 00:
Lecture 32: Brief introduction to structural dynamics:
Eigenvalue problems. Static substructuring analysis (cont'd):
Coding
aspects, index arrays.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Did you know: Stephen J. Gould, Harvard professor, and curator of the American Museum of Natural History in New York, will give a lecture titled "Questioning the Millennium: Why we can't predict the future" at the Center for the Performing Arts, 8pm, today (Wed, 5 Apr); it's free. Dr. Gould has written many award-winning and national best sellers books on evolutionary theory (see a review of some of his books). The best site that I found about Gould is in the Stanford Presidential Lectures: Stephen J. Gould. He is known to be a strong opponent to the creationists, and has won a major court battle in matters related to evolution versus creation. It is also interesting to note that creationists used Gould's theory of punctuated equilibrium to support creation theory. The punctuated equilibrium theory essentially says that "the history of evolution is concentrated in relatively rapid events of speciation rather than taking place gradually as slow, continuous transformations of established lineages".
Mon, 3 Apr 00: Project: Deliverable (See schedule of deliverables), discussion on the simple tests to validate the removal of all zero-energy modes in a substructures, index array to assemble substructure matrices.
Did you know: Student Government Elections: Tue, 4 Apr 00, and Wed, 5 Apr 00. I STRONGLY ENCOURAGE YOU TO VOTE. See the message from the Vice President of the Florida Engineering Society.
WEEK 13
Fri, 31 Mar 00: HW10 due.
Lecture 31: Static substructuring analysis (cont'd): Computational
algorithm (generation of FD relation for each substructure, assembly of
FD relation for whole structure and solution for boundary dofs for whole
structure, postprocessing).
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Did you know: What does TBIF stand for? TOO BAD IT'S FRIDAY! (so we need to wait till next Mon to continue the fun in class :-))
Wed, 29 Mar 00: HW8
due.
Lecture 30: Static substructuring analysis (cont'd): Summary
of complete theory, assembly process, postprocessing for element forces.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Mon, 27 Mar 00: Project:Deliverable (See schedule
of deliverables).
Lecture 29: Remark on the coding of the truss code: Post-processing
for element forces, index array.
WEEK 12
Fri, 24 Mar 00: HW8 due date extended
to Wed, 29 Mar 00.
Lecture 28: Static substructuring analysis (cont'd): Back
to the big picture, assembly of substructure matrices, boundary conditions,
submatrix extraction, solution for boundary dofs, post-processing for interior
displacements and element forces in each substructure.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Wed, 22 Mar 00:
Lecture 27: Static substructuring analysis (cont'd): Computation
of various partial solutions for Part alpha and Part beta; construction
of FD relation for a substructure with only boundary dofs.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Mon, 20 Mar 00: Project:
Deliverable (See schedule
of deliverables).
Lecture 26: Static substructuring analysis (cont'd): Additive
decomposition of displacements and forces in a substructure, superposition
of solution, etc.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Did you know: What does TGIM stand for? THANK GOD IT'S MONDAY (so we can have more fun in class). :-)
WEEK 11
Fri,
17 Mar 00: HW7b due.
Lecture 25: Static substructuring analysis: Additive
decomposition of displacements and forces in a substructure (alpha
part and beta part), superposition of solution.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
HW10:Please
download.
Wed, 15 Mar 00:
Lecture 24: Project: bracing, simple
model problem, zero-energy modes (rigid-body modes, mechanisms), eigenvalue
problem. Static substructuring analysis: Additive decomposition
of displacements and forces in a substructure, superposition of
solution, etc.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Mon, 13 Mar 00: HW6b
due. Project:
Deliverable (See schedule
of deliverables).
Lecture 23: Truss code: Computation of director cosines,
2-D, 3-D. Static substructuring analysis: The big picture(cont'd),
FD relation for each substructure treated as a "superelement", assembly
of substructure FD relations, solution for free boundary dofs.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
WEEK 10
WEEK 9: Spring break
Fri, 2 Mar 00: HW7a
due. HW6b extended to Mon,
13 Mar 00.
Lecture 22: Truss code on K&B[1997]: Weakness in
the post-processing for member forces; remedy: method taught in class.
Static
substructuring analysis (Cont'd): The big picture.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
HW8:Please
download.
Wed, 1 Mar 00:
Lecture 21: Zero-energy modes as eigenvectors corresponding
to zero eigenvalues, elimination of rigid-body modes, elimination of mechanisms
in substructures, submatrix extraction, eigenvalue problem.
Static substructuring analysis: Preliminary.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Have you heard: A friend sent the writing below to me; I thought
about sharing it with you.
LOOK FOR THE SPARK, IN PROFESSORS AND YOURSELF. There are two ways
to teach, two ways to learn.
SCENARIO 1: You walk into your Western Civilization I class and there are 200 students in the room. The professor stands rigid, hiding behind the podium. He reads his lectures like a robot, giving no weight to one thing or another. Just going through the motions.
SCENARIO 2: Same class, different professor. Animated, energetic, interested and interesting. He lectures about his topic but he also talks to you. He's passionate. He cares. You go to your section meeting with a different attitude, you can't wait to go and discuss ideas. This results in a much better experience.
Here's your job as a student: even if you're stuck with Scenario 1, turn it into Scenario 2. Throw yourself into the material, ask questions, try to stump the professor. Come at the material from a new and different angle. Maybe, just maybe, he'll catch your enthusiasm and that will flow back into his teaching. Even if that doesn't happen, you'll be a better student for the effort.
Mon, 28 Feb 00: Project:
Deliverable
(See schedule
of deliverables).
Lecture 20: Truss code (cont'd): Treatments of boundary
conditions, matrix partitioning (cont'd),
postprocessing for element forces.
Reading assignment: P[1968], Chap 9, Substructuring Analysis,
pp. 231-246; Section A.9, Matrix inversion, pp.420-422; Section A.11, Reversal
rule; Section A.23, Eigenvalues and eigenvectors, pp.440-442.
Have you heard: SUCCESS IS FOUNDED IN PERSISTENCE AND DETERMINATION.
"Nothing in the world can take the place of persistence. Talent
will not. Nothing is more common than unsuccessful men with talent. Genius
will not. Unrewarded genius is almost a proverb. Education will not. The
world is full of educated derelicts.
Persistence and determination alone are omnipotent. The slogan "press on" has solved and always will solve the problems of the human race." Calvin Coolidge (1872-1933), 30th U.S. President
WEEK 8
Friday, 25 Feb 00:
HW5
and HW6a due.
Lecture 19: Truss code (cont'd): Treatments of boundary
conditions, matrix partitioning, submatrix extraction.
Reading assignment: K&B[1997], Chap 7, pp.197-215; Chap
5, p.112; Chap.3, pp.51-56.
HW7a: Reproduce all Matlab examples
in Chap 1 of K&B[1997].
HW7b:Please
download.
Have you heard: ``Education is the progressive discovery of
our own ignorance.'' Will Durant.
(Contribution of Sean Gregg.)
Wed, 23 Feb 00:
Lecture 18: Trusses (cont'd): Matlab code to generate
the index array; algorithm to assemble element matrices into global matrix
using the index array.
Reading assignment: K&B[1997], Chap 7, pp.197-215; Chap
5, p.112; Chap.3, pp.51-56.
Mon, 21 Feb 00: Project: Deliverable (See schedule
of deliverables).
Lecture 17: Trusses (cont'd): Matlab codes for trusses
in K&B[1997]: index array for the mapping of local dof numbers to global
dof (equation) numbers for use in the assembly of the element matrices
into the global matrix.
Reading assignment: K&B[1997], Chap 7, pp.197-215; Chap
5, p.112; Chap.3, pp.51-56.
WEEK 7
Fri, 18 Feb 00:
HW4
due.
Lecture 16: Trusses: General 3-D truss assembly
by dof consideration. Matlab codes for trusses in K&B[1997]: General
parameters, nodal coordinates, element properties, element definition (nodal
connectivity), element matrices; Overview: assembly, boundary conditions,
solution, post-processing. We'll look at the detailed coding in the next
lecture.
HW6a: Reproduce
all examples in Matlab Primer.
HW6b:Please
download.
Wed, 16 Feb 00:
Lecture 15: Truss element with variable cross
section and material properties, FD relation (cont'd). Review of
truss element formulation and assembly of global stiffness matrix.
Reading assignment: K&B[1997], Chap 7, pp.197-215; Chap
5, p.112; Chap.3, pp.51-56.
Mon, 14 Feb 00: Project: Deliverable
(See schedule
of deliverables).
Lecture 14: Truss element with variable cross
section and material properties, FD relation (cont'd).
Did
you know: I learned from watching the PBSNews
Hour last Fri that Lincoln's birthday
was on Sat, 12 Feb. A commentator in the News Hour mentioned that
Lincoln, his life and work, was a subject that had been most written about:
17,000 volumes (search for recent books and related discussions at News
Hour). The second runner up was Jesus Christ. Lincoln was
an astute politician who, with his tremendous intellectual power coupled
with his knowledge of how to deal with people, could convert his political
adversaries into his stark supporters and admirers. Of course, Lincoln
was also famous for his communication skills. Whenever I visited the Lincoln
Memorial in Washington, DC, I often liked to reread his famous Gettysburg
Address (Library of Congress),
carved on marble in the Memorial.
WEEK 6
Fri , 11 Feb 00:
HW2
and HW3 due.
Lecture 13: Matlab: plotting example, submatrix
extraction coding (HW). Truss element: Variable cross section,
equation of equilibrium, FD relation by analytical integration of equation
of equilibrium.
HW5:Please
download.
Wed, 9 Feb 00:
Lecture 12: 1-D spring systems (cont'd): Matrix
partitioning (cont'd), static condensation, solution for "interior" dofs,
postprocessing for reaction forces. How to obtain the FD relation
for an elastic bar with variable cross section, numerical method by static
condensation.
Did you see: Amrit's
sketch of me lecturing in the course. (Don't do this too often. :-))
Mon, 7 Feb 00: Project: Deliverable (See schedule
of deliverables), Project co-leader designated: Jenny. E-maling
list feem-l@lists.ufl.edu,
how
to subscribe.
Lecture 11: 1-D spring systems (cont'd): Prescribed displacements,rearranging
(renumbering) dofs, matrix partitioning.
Did you know: My friend and former roommate during my first
undergraduate year in France now works for Alcatel Space Industries, a
French company specializing in telecommunication, and in particular in
designing and manufacturing communication satellites. He came to
Florida back in Dec 1999 to work on the launch review of Hispasat 1C, a
telecommunication satellite that Alcatel sold to the Spanish government.
Hispasat was later launched by an American rocket, the Atlas Centaur designed
by Lockheed-Martin. The successful launch is shown here
on 3 Feb 2000; notice the support points for the
rocket, provided by the tower structure on the right. See also an
article about the launch. (The photo and the article was provided to
me by my friend, Mr. Jean-Marc Raynaud of Alcatel.)
WEEK 5
Fri,
4 Feb 00: HW1 due.
Lecture 10: 1-D spring systems (cont'd):
Free-body
diagram (FBD) decomposition. Direct stiffness method, assembly by equilibrium
consideration, computer implementation of global stiffness assembly (by
dof consideration). Prescribed displacements. Solution by matrix partitioning,
introduction.
HW4:Please
download.
Wed, 2 Feb 00: E-mailing list
feem-l@lists.ufl.edu:
I
have created this e-mailing list for your coordination and discussion
on the class project, and on anything else related to the course.
I will write more instructions on how to use this mailing list.
Lecture 9: 1-D spring systems: properties
of element stiffness matrix, singularity, determinant test, null
space of a singular matrix, rigid-body motion, difference between zero-energy
mode and rigid-body mode. Global matrix matrix equation, assembly of global
stiffness matrix by dof consideration, properties (singularity) of global
stiffness matrix. Boundary conditions, partition of global matrix
equation, solution for unknown displacements, post-processing for reaction.
Reading assignment: K&B[1997], Chap 7, pp.197-205, on truss
structures. C[1995], Section 2.4, pp.25-26, on the singularity of the element
stiffness matrices and the global stiffness matrix.
Mon, 31 Jan 00: Project deliverable: Partition
the Saturn V rocket into substructures of comparable degree of complexity;
choice of global coordinate system; for each substructure, dimension,
weight, material properties, center of gravity. Each team takes up
to 2 min
to present their work. (Actually, it took more time than anticipated
for the first time the monday deliverable was done. In future, things
should run more efficiently.)
Lecture 8: Truss element (cont'd): stiffness matrix,
derivation by a quick method, limitations of the quick method. Particular
case: Spring systems, direct stiffness method, assembly process.
WEEK 4
Fri 28 Jan 00: HW1
due date extended to Fri, 4 Feb 00.
Lecture 7: Truss systems (cont'd): Review the big picture
of FEA. Mechanical interpretation of the stiffness coefficients
as member forces for unit displacement. Derivation of FD relation
in local coordinates from equilibrium of infinitesimal element.
HW3:Please
download.
Wed 26 Jan 00:
Lecture 6: Truss systems (cont'd): Local-to-global transformation
of FD relationship, transpose of the product of matrices (reversal rule),
symmetry of stiffness matrix (condition for symmetry of stiffness matrix
on global coord), role of the PVW (to be discussed in detail later).
Mon, 24 Jan 00: Team presentation of
proposed projects, and vote for class project: Each team will introduce
the team members, provide a team name,
take about 10 minto
advocate their project to the class, and provide me with a jpeg
graphics file of their proposed project
via e-mail. At the end of the presentation, each of you will give
your vote for a project to the project leader, who will forward to me the
ranking
of the projects by the number of votes.
I should receive this e-mail from the project leader by 3pm
of this day.
Proposed projects:
See Unix matters for a new nice web site on Unix and vi. The e-mailing list for the whole class can be obtained here. You may want to use this list to coordinate the class project. Communication is important for the success of the project.
WEEK 3
Fri, 21 Jan 00:
Team
structure: Class (project) leader and team leaders established.
Lecture 5: Truss systems (cont'd):
Detailed
derivation of the local-to-global transformation matrix lambda in terms
of the director cosines of the unit vector in the direction of the truss
element. Continued with the big picture of the FEM, transformation of the
FD relationship from local to global coordinates using the Principle of
Virtual Work (PVW).
Reading assignment: P[1968], pp.67-69, on transformation of
coordinate axes: Lambda matrix and PVW.
HW2:
Please download.
Did you know: That there is a person
who would die of hunger every 3.6 seconds, and that 3/4
of those are children under 5 years old? You can help to donate
food to these hungry people without
costing you a cent, just by clicking at the Hunger
Site of the UN World Food Program once
a day. To remind me to click at the Hunger Site every
day, I created the Hunger-Site
stickers (in MS Word doc format) for all computers in my office and
in my lab. You are welcomed to use these stickers for your computers.
(The best place to put a sticker is just below
the screen of your monitor.)
Wed, 19 Jan 00: To create the .forward
file in your grove Unix account, read the Unix
matters page.
Lecture 4: Truss systems (cont'd): Assembly operator.
Global force-displacement (FD) elationship: global matrices (stiffness,
displacement, force), dimensions. Element FD relationship: dimension of
element stiffness matrix (nst), number of global dofs per node (ndof),
number of element nodes (nen), element stiffness matrix in local coordinates
and in global coordinates. Transformation of dofs from local to global
coordinates.
Reading assignment: K&B[1997], Chap 1 on Matlab (do
use Matlab to reproduce the results while reading this chapter), and Chap
4 on 1-D spring systems.
Did you know:
I
read in a Saturday Gainesville Sun recently that some researchers have
ranked the 100 most influential speeches in US history, and that the
"I
have a dream" speech of Martin Luther King, Jr., was ranked number
one, far above the second runner up, based not only on its content, but
also on its masterful and emotional delivery, fittingly on the steps of
the Lincoln Memorial in Washington, D.C., in Aug 1963. One of the famous
lines in that speech: "I have a dream that my little four children will
one day live in a nation where they will not be judged by the color of
their skin, but by the content of their character."
Mon, 17 Jan 00: Martin Luther King, Jr. holiday. No class.
WEEK 2
Fri, 14 Jan 00:
Unix
accounts: distributed password cards; you can put your e-mail address
in the .forward (" dot forward") file in your Unix accounts
to have your e-mail forwarded. Note that the "dot" in front of "forward"
is important. Class leader, team leaders: To be elected by Fri,
21 Jan 00; recall that the presentation of the team's proposed projects
will take place on Mon, 24 Jan 00. We need the team structure put
in place so to have the project moving forward efficiently.
Lecture 3: Truss system (cont'd): The
big picture, going from a global truss structure to the truss elements
via FBD's. Numbering of nodes (local and global), degrees of freedom (dofs),
internal forces, and elements. Local and global coordinates. The
main steps in a finite element analysis (FEA). Force-displacement
(FD) relationship for a truss element in local coordinates.
Reading assignment: P[1968], Appendix
A, Matrix Algebra, Sections A1-A6, pp.409-418.
HW1:Please
download. HW sets are
numbered using the Week numbers. Thus, in Week 1, the
HW set is designatedby HW1.
Did
you know: The sinking
of the Sleipner A Offshore Platform in Aug 1991 in the North Sea cost
about $700 million, and was due to an error
in
the finite element analysis
of the platform structure (using NASTRAN).
Wed, 12 Jan 00: Organized class project:
Team presentations on Mon, 24 Jan 00; each team has up to12 min to convince
the class of their proposed project. Reference books: I will put
the reference books for this course on reserve in the library. Unix
accounts: Each of you will have a Unix account on the grove cluster.
I will send e-mail to the whole class using your Unix accounts. You
will also have access to a more powerful version of Matlab on the grove
cluster (because of more RAM memory available than on PCs). You can put
your preferred e-mail address in the .forward file in your grove account
to have your e-mail forwarded.
Lecture 2: Truss systems (cont'd):
Overview, FBDs, statically indeterminate systems, structural deformation
for additional equations, FEM.
Reading assignment: Matlab Primer(ps
, pdf
), cooperative
learning techniques.
You also have access to Matlab on the PCs in the Undergraduate Computing
Room 235 NEB (I need to check the room number); you should practice
using Matlab in parallel to your reading of the Matlab Primer
starting from today.
Did you know: "A classic is something that everyone wants to have read, but no one wants to read." Mark Twain. In this course, you will read the classic book of Przemieniecki [1968]. :-)
Mon, 10 Jan 00: Course organization, cooperative learning, video presentation of the use of FEM in industry, truss structures.
WEEK 1
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