Wed, 14 Mar 2001Wed, 2 May 01:Final exam, Turlington Building, Room L011, 5:30pm to 7:30pm Closed book, closed notes. One crib sheet of size 5.5" x 8.5" (half the regular letter-size paper, both sides) allowed.
EXAM WEEK
Wed, 25 Apr 01:
Lecture 41: Truss systems with nonlinear material behavior,
transformation from local coordinates to global coordinates, principle
of virtual work, nonlinear force-displacement in global coordinates, assembly
of equations of equilibrium by FBD's of nodes, solving system of nonlinear
equations by Newton's method, Taylor series expansion, Jacobian matrix,
iterative algorithm.
Reading assignment: G&W
(textbook), Chap 1, on solving nonlinear equations.
HW: pbs.2,13, pp.101, in G&W
(textbook).
Mon, 23 Apr 01:
Lecture 40: Remark on HW problems with inverse power method,
efficiency in coding, Matlab commands inv and "\", Gauss elimination and
its stages, organization of the code, multiple eigenvalues and corresponding
eigenvectors (for real symmetric matrices). Solving nonlinear
equation: Truss element with nonlinear material behavior, nonlinear
force-displacement relationship, solving nonlinear equation, bisection
method, Newton's method (derivation based on geometry, and based on Taylor
series expansion).
Reading assignment: G&W
(textbook), Chap 1, on solving nonlinear equations.
HW: pbs.2,13, pp.101, in G&W
(textbook).
WEEK 16
Fri, 20 Apr 01: HW12 due.
Class meets at
the Brain Institute, Room 100A, for
the BMES & MAE Competition.
Did you know: You may be interested in a talk on a new method of teaching the FEM at the undergraduate level (see abstract) at the 6th US National Congress on Computational Mechanics, Dearborn, MI, 1-4 Aug 2001.
Wed, 18 Apr 01:
Lecture 39: Integrating ODEs: Numerical methods for 1st-order
ODEs (both scalar and matrix equations): Euler method, local error, global
error, geometric interpretation; modified Euler method, geometric interpretation,
local error, chain rule, global error, connection to Taylor series method
of local order 3.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
Mon, 16 Apr 01:
Lecture 38: Integrating ODEs: 1st-order ODEs: Taylor
series method with local error of order 4, computation of third derivative
in general nonlinear (scalar) ODEs, chain rules; examples.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
WEEK 15
Fri, 13 Apr 01: HW11 due.
Lecture 37: Integrating ODEs: Numerical methods for 1st-order
ODEs (both scalar and matrix equations), Taylor series method, computation
of higher-order derivatives at time zero, scalar case; matrix case, equation
of motion of nonlinear SDOF system (remark on Newton's method and bisection
method for static case), Jacobian matrix, indicial notation, evaluating
second derivative at time zero.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
HW14: Do
Pbs. 5,7,9 on p.513, of G&W
(textbook).
Wed, 11 Apr 01: IPPD
final presentation, TODAY, 8am-1:30pm (see agenda here)
Lecture 36: 8
Integrating ODEs: Review of modal equations
in structural dynamics and orbital equations of motion of a point mass
in astrodynamics, similarities and differences (coupled equations). First-order
ODEs, Taylor series method, example of nonlinear dynamics of a SDOF system,
computation of first derivative at time zero, scalar case, matrix case.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
Mon, 9 Apr 01:
Lecture 35: Astrodynamics, structural dynamics, and integrating
ODEs: Example of nonlinear ODEs; equation for orbital
motion of a satellite in 3-D space in vector form, set of scalar second-order
ODEs, conversion to 1st-order ODEs. Integration of modal equations in structural
dynamics: Conversion of a 2nd-order ODE to a set of 1st-order ODEs.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
WEEK 14
Fri, 6 Apr 01: HW10 due.
Lecture 34: Structural dynamics (cont'd): Integration
of modal equations: Review of analytical method by superposing homogeneous
solution and particular solution for linear ODEs; Motivation for numerical
methods: Examples of nonlinear ODEs (orbital mechanics, zodiac sign libra,
the
Pink Floyd, Dark
Side of the Moon, librational motion, gravitational gradient, stable
motion of orbiting space shuttle, etc.); conversion of a 2nd-order ODE
to a set of 1st-order ODEs. Numerical method, finite difference method
for 2nd order ODEs, initial conditions.
Reading assignment: G&W
(textbook), Chap 6, pp.448-460, on numerical solution
of ODEs
.
HW13: Do
Pbs. 1,2,3,4, on p.513, of G&W
(textbook).
Did you know: Village boy, a numbers theorem in grade 5, SAT scores, MIT, professor at Johns Hopkins.
Wed, 4 Apr 01:
Lecture 33: Structural dynamics (cont'd):Review
on how to solve the coupled equations of motion using the eigenvalue problem.
Integration of modal equations: Analytical method (case of free vibration
with initial conditions), truncation.
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
Mon, 2 Apr 01: Penalty
for missing required HW reports.
Lecture 32: Structural dynamics (cont'd):Generalized
eigenvalue problem: Gram-Schmidt orthogonalization in general pseudo
code for inverse power method to search for all eigenpairs, derivation
of purification coefficients using orthogonality property of eigenvectors.
Integration of modal equations: Analytical (case of free vibration with
initial conditions), numerical (finite difference method for 2nd order
ODEs, initial conditions).
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
WEEK 13
Fri, 30 Mar 01: HW8
due. Penalty for missing required HW reports.
IPPD
1999-2000 project: Smart Composites for Comanche Helicopter; protypes.
Lecture 31: Structural dynamics (cont'd):Gram-Schmidt
orthogonalization in general pseudo code for inverse power method to search
for all eigenpairs of standard eigenvalue problems, derivation of purification
coefficients using orthogonality property of eigenvectors.
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
HW12: Develop
a matlab function to solve for all eigenpairs of a generalized eigenvalue
problem for structural dynamics as explained in class. Apply your matlab
function to the stiffness matrix and the mass matrix of the truss system
of Pb.2.1 (see HW10
). Compare your
results (eigenvalues and eigenvectors) with Matlab results.
Wed, 28 Mar 01:
Lecture 30: Structural dynamics (cont'd):Proof
orthogonality property of eigenvector, standard eigenvalue problem, generalized
eigenvalue problem; inverse power method with Gram-Schmidt orthogonalization
process to obtain all eigenpairs.
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
Mon, 26 Mar 01:
Lecture 29: Structural dynamics (cont'd):1-norm
and 2-norm of a vector, normalization (scaling) of eigenvector,
HW10
, pseudo-code for inverse power method with Gram-Schmidt orthogonalization
to obtain the second eigenpair.
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
WEEK 12
Fri, 23 Mar 01: HW7
due.
Lecture 28: Structural dynamics (cont'd):Re-emphasize
the importance of eigenvalue problem through a brief review, physical meaning
of a modal equation as a SDOF system (modal mass and modal stiffness),
Initial conditions for modal equations by mass orthogonality property of
eigenvectors (vibration modes), inverse power method for complete eigenvalue
problem, Gram-Schmidt orthogonalization process (to obtain the second eigenpair).
Reading assignment: G&W
(textbook), Sec 2.8, pp.155-158, on norms;
Sec 7.5, pp.541-546, on characteristic-value
(eigenvalue) problems; Sec 7.10, pp.568-579,
on theoretical matters related to the eigenvalue
problems.
HW11: Develop
a matlab function to solve for all eigenpairs of a real symmetric matrix
A
of
size nxn. Apply your matlab function to the stiffness matrix of the
truss system of Pb.2.1. Compare your results (eigenvalues and eigenvectors)
with Matlab results.
Wed, 21 Mar 01:
Lecture 27: Structural dynamics (cont'd):Single
degree-of-freedom (dof) system (SDOF), angular frequency, vibration period,
vibration frequency; Multiple dof system (MDOF), mass-orthogonality
property of eigenvectors, decoupling coupled equations of motion into n
uncoupled SDOF systems (modal equations), matrix form, initial conditions
for each modal equation.
Reading assignment: G&W
(textbook), Sec 7.5 on characteristic-value (eigenvalue) problems, pp.541-546.
Sec 7.10, pp.568-579.
Did you know: "I hear, I forget; I see, I remember; I do, I understand." (Oriental proverb.)
Mon, 19 Mar 01:
Lecture 26: Structural dynamics (cont'd):Two
methods of integrating the ordinary differential equations of motion: (1)
direct integration (finite difference method), (2) modal superposition
(eigenvalue problem). Free vibration problem, periodic solution, generalized
eigenvalue problem of free vibration, recall standard eigenvalue problems,
meaning of eigenvalues (relationship to vibration frequencies).
Reading assignment: G&W
(textbook), Sec 7.5 on characteristic-value (eigenvalue) problems, pp.541-546.
Sec 7.10, pp.568-579.
WEEK 11
Fri, 16 Mar 01:
Lecture 25: Structural dynamics (cont'd):Derivation
of equations of motion using lumped mass and equilibrium of the nodes (free-body
diagrams), prescribed boundary displacements as functions in time, reduced
equations of motion accounting for prescribed displacements, initial conditions,
motivation of eigenvalue problems.
Reading assignment: G&W
(textbook), Sec 7.5 on characteristic-value (eigenvalue) problems, pp.541-546.
HW10: Redo
HW7 and HW8, but using the normalization method in the book (using the
1-norm); compare your results with those in HW7 and in HW8. Apply
your codes of the inverse power method in HW10 and in HW8 to find the lowest
eigenpair of the truss structure in Pb. 2.1, assuming that the mass per
unit length of each bar is 100; compare the results (eigenvalues and eigenvectors).
Verify the mass orthogonality property of the eigenvectors (for this truss
problem) that are obtained using Matlab.
Did you know: On Fri, 29 Feb 01, we talked about Gauss and number theory; I also told the story about an interesting use of number theory.
Wed, 14 Mar 01:
Remark on coding in HW5,
Integrated
Product and Process Design (IPPD). Return midterm exam; discussion.
Lecture 24: Solving
Ax=b:
General case (nxn): Number of operations in Gauss elimination.
Remark on Gauss-Jordan method, number of operations. Structural dynamics:
Equations of motion of truss systems, mass lumping.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10. Sec 7.5 on characteristic-value (eigenvalue) problems,
pp.541-546.
Mon, 12 Mar 01:
Lecture 23: Solving Ax=b:
General
case (nxn): Recall number of operations in forward substutition
and back substitution. Number of operations in Gauss LU decomposition,
total number of operations in Gauss elimination.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
WEEK 10
WEEK 9
: Spring break week; no class.
Fri, 29
Feb 01: HW6 due.
Lecture 22: Solving
Ax=b:
General case (nxn): Gauss
at 7 years of age and the sum of integers from 1 to 100; proof of general
formula for summing intergers from 1 to n. Gauss elimination and LU decomposition,
number of operations in forward substitution, in backsubtitution (homework).
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
HW8:Please
download.
Wed, 28 Feb 01:Midterm exam, room 100 NEB, periods E2-E3 (8:20pm-10:10pm). There is no lecture today. There will be no make-up exam. Closed book, closed notes, one crib sheet of size 8 in x 5.5 in (half a letter-size paper, you can write on both sides). The use of calculators is restricted to simple operations on scalars (add, subtract, multiply, divide); matrix operations are not allowed.
Mon, 26 Feb 01:
Lecture 21: Solving
Ax=b:
General case (nxn): General LU decomposition, inverse of
lower triangular matrices, Gauss elimination and LU decomposition.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
WEEK 8
Fri, 23 Feb 01:HW6
due date extended.
HW4 and HW5
returned.
Remarks on methods of FEM, Matlab, comments from
students, Integrated Product and
Process Design (IPPD)
Lecture 20: Solving
Ax=b:
Gauss
elimination (cont'd): pseudo code (algorithm). General case
(nxn): General LU decomposition (lower triangular
matrices, product, inverse).
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
HW7:Please
download.
Wed, 21 Feb 01: Q&A on methods of FEM.
Lecture 19: Solving
Ax=b:
Gauss
elimination (cont'd): Determinant (Laplace expansion), general formula,
3x3 case, connection with vector triple product, volume, sign change due
to interchange of rows or columns, sign change in the general nxn case.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
Mon, 19 Feb 01:
Lecture 18: Solving
Ax=b:
Gauss
elimination (cont'd): Connection between general LU decompositions
(in class lecture and in G&W
book) and Gauss LU decomposition, pivoting, determinant (Laplace expansion),
2x2 case, sign change.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
WEEK 7
Fri, 16 Feb 01:HW4
due and HW5 due.
Lecture 17: Solving
Ax=b
(Cont'd): Further motivation for LU decomposition; repetitive solution
with many right-hand sides, computation of the inverse of a matrix; solving
the standard eigenvalue problem A x = lambda x by the power
method and inverse power method. Remark on the generalized eigenvalue problem
A
x = lambda B x , and its connection to structural dynamics.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
HW6:
Do Pbs. 27, 33 (use both Laplace expansion and LU decomposition), in G&W
(textbook), p.212. Develop the following
Matlab functions:
Follow
the pseudo code on p.129 to develop a function to do the LU decomposition
of a matrix, a function to do the forward reduction of the right-hand
side using the L matrix, and a
function to do the backsubstitution
using the U matrix to get the solution. Use these functions to solve Pb.34,
p.212 in
G&W
(textbook).
Did you know: The word "determinant" was first used by Gauss.
Wed, 14
Feb 01: The explosion of Ariane Flight 501
(firm
schedule).
Lecture 16: Solving
Ax=b:
Gauss
elimination: (3x3 case) Motivation, normalization of L in LU decomposition,
uniqueness, solution of
Ax=b, determinant.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
Did you know: The word "determinant" was first used by Gauss.
Wed, 14
Feb 01: The explosion of Ariane Flight 501
(firm
schedule).
Lecture 16: Solving
Ax=b:
Gauss
elimination: (3x3 case) Motivation, normalization of L in LU decomposition,
uniqueness, solution of
Ax=b, determinant.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
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.)
Better yet, since I am using Linux
,
I have set up my system to automatically display the Hunger
Site every morning at 8am, so that
I can ``donate'' food every morning before I start my day. If you are interested
in knowing how I did this setup, just ask me.
Mon, 12 Feb 01:
Lecture 15: Solving
Ax=b:
General LU decomposition (cont'd): (3x3 case) complete example and
verification, non-uniqueness, computation of determinant (also nxn case
for L and U).
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7, 2.10.
WEEK 6
Fri, 9 Feb 01: HW4
due date extended.
Remark: Lectures (first eye) + G&W
(textbook) (second eye) = depth of knowledge (stereoscopic view.)
Lecture 14: Solving
Ax=b:
General LU decomposition (cont'd): Example (3x3), how to invert lower
triangular matrices, matrix form of solution x, motivation (solving
for several loading cases).
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal matrices),
2.6, 2.7.
HW5:
Do Pb 11, p.210 in G&W
(textbook). Develop Matlab functions to solve HW2
(function to compute element stiffness matrices in global
coordinates, function to assemble element stiffness matrices
into the global stiffness matrix, function to extract stiffness
matrix with unknown degrees of freedom only, function to
extract element displacements from global displacement matrix, function
to compute the element forces in local coordinates from element disp in
global coordinates.) Test out your
Matlab functions with Pb. 2.1 and then Pb. 2.4
in HW2.
Wed, 7 Feb 01:
Lecture 13: Solving Ax=b:
Elimination method (cont'd): Triangulation (upper form), meaning,
matrix form, product of lower triangular matrices (3x3 case). LU
decomposition: Matrix inversion, inversion of a product of matrices.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3, 2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal
matrices).
Mon, 5 Feb 01: Remarks: Think
for yourself, model HW report (team Kapt), calculators with matrix
operations.
Lecture 12: Solution of Ax=b:
Diagonalization
(eigenvalue problem and characteristic polynomial); Triangulation: (upper,
lower), substitution (backward, forward), numerical example, matrix form.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3, 2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal
matrices).
WEEK 5
Fri, 2 Feb 01:HW2
due, and HW3 due (firm
due date for both HW2 and HW3).
Remark on team reorganization.
Lecture 11:
Truss systems (cont'd): Global stiffness
matrix, direct accouting for the boundary conditions (advantages, disadvantages);
properties of global stiffness matrix (symmetric, singular).
Numerical solution for general systems of
linear equations Ax=b: Elimination concept, motivation
(diagonal system, transformation of coordinates, eigenvalue problem, upper
triangular form, backsubstitution).
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3, 2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal
matrices).
HW4:Do
Pbs. 8, 9, 14, 16, in G&W,
pp.210-211.
Wed, 31 Jan 01:
Lecture 10: Discussions on HW2
problems; reorganization of course conduct.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3, 2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal
matrices).
Did you know: Success secret: Become an active learner
Mon, 29 Jan 01:
Lecture 9: Truss system (cont'd): Method
1: Justification of relation between applied forces and global
displacement relations. Back to Method 2: Model problem, matrix
form of relations between element-length increments and global displacement
dofs, relation between member forces and global displacement dofs, relation
between applied forces and global displacement dofs, stiffness matrix;
Pb. 86, p.217, in G&W,
application of Method 2.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3, 2.4, 2.5 (only pp. 145-147 on LU decomposition of tridiagonal
matrices); Problem 86, p.217.
WEEK 4
Fri, 26 Jan 01: HW2due
date extented.
Lecture 8: Truss system (cont'd): Interpretation
of member forces and deformed shape of truss model problem using
concepts learned in Statics (equilibrium of nodes, solution of statically-determinate
truss systems, small-deformation assumption, Taylor series expansion, retaining
leading terms), computation of reactions; Method 2 (to explain Pb.
86, p.217, in G&W):
Model problem, relation between member forces and element-length
increments, matrix form, stiffness matrix S, relation between element-length
increments and global displacement dofs.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3; Problem 86, p.217.
HW3:
Do Problems 1,2,3,4, 5, 6, p.210, in G&W
(textbook).
Did you know: ``Think for yourself, 'cause I won't be there with you.'' George Harrison (The Beatles), song Think for yourself (recorded on 8 Nov 1965).
Wed, 24 Jan 01:
Lecture 7: Truss system (cont'd): Force
matrix, application of boundary conditions, solution for nodal displacements,
member force computation.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3; Problem 86, p.217.
Mon, 22 Jan 01:
Lecture 6: Truss system (cont'd): Local
to global mapping,
assembly of element stiffness matrices into global
stiffness matrix.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3; Problem 86, p.217.
WEEK 3
Fri, 19 Jan 01: HW1
due. Remark on the policy for this course.
Lecture 5: Truss system (cont'd): Review
of matrix relations for trusses. Example of a
simple truss system (cont'd): Computation of element stiffness matrices,
matrix multiplication.
Reading assignment: G&W
(textbook), Chap 2, Problem 86, p.217.
HW2:Please
download.
Did you know: A friend just sent to me this Great Story; you may enjoy it.
Wed, 17 Jan 01: Remark on HW (posting,
downloading, and due dates).
Lecture 4: Truss system (cont'd): Principle
of virtual work:
Transformation of forces from global coordinates to
local coordinates; FD relation in global coordinates, stiffness matrix
in global coordinates. Example of a simple truss system; numbering of nodes,
elements, and global dofs.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3.
Mon, 15 Jan 01: Martin Luther King, Jr. holiday. No class.
WEEK 2
Fri, 12 Jan 01: Tour of course web page.
Lecture 3: Truss system (cont'd): Interpretation
of FD relation in local coordinates. Transformation of displacements
from local coordinates to global coordinates. Relation between member
forces in local coordinates and displacements in global coordinates; future
post-processing for member stresses. Principle of virtual work:
Brief
review.
Reading assignment: G&W
(textbook), Chap 2 on matrices and solving systems of equations; Sections
2.1, 2.2, 2.3.
HW1
Did
you know:
Around this time last year,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."
Wed, 10 Jan 01: Various remarks concerning
the course (team organization, grading, etc.)
Lecture 2: Truss systems (cont'd):
Overview, FBDs, statically indeterminate systems, structural deformation
for additional equations, FEM. Force-displacement (FD) relationship for
a truss element in local coordinates.
Reading assignment: Matlab
Primer by the late UF math professor K. Sigmon; Cooperative
learning techniques; G&W
(textbook), Chap 2 on matrices and solving systems of equations.
You should practice
using Matlab in parallel to your reading
of the Matlab Primer starting from today.
HW1:Please
download. Reproduce all examples
in the
Matlab
Primer. HW sets are numbered using the Week numbers.
Thus,
in Week 1, the HW set is designatedby HW1.
Mon, 8 Jan 01: Course organization, cooperative learning, video presentation of the use of FEM in industry, truss structures.
WEEK 1
MAE
Department home page.
