ENGR 690: FINITE ELEMENT ANALYSIS I
Patran/Abaqus FILES
Instructor: Dr. Chris Mullen
(http://www.olemiss.edu/~cvchris)
(Last Update: 11-4-02)
In class on Friday 8/31, an interactive session
was conducted in Room 213. During the session, the Matlab solution to a
simple 3-DOF eigenproblem, Example 11.1, Chopra, p.420, was discussed.
The first procedure for solving the system is the construction of the characteristic
polynomial or frequency equation. The file Cubic.m
was used to create the results file,Cubic.out,
which contains the normalized eigenvalues for the given cubic polynomial.
Use is made both of the Matlab function, root(a), and the exact analytical
procedure from the CRC Standard Math Tables reference .
The second procedure simply uses the Matlab function, eig(K,M), given the
mass and stiffness matrices. The file, Bldg3.m,
formulates the matrices given the data in Chopra and finds both the eigenfrequencies
and eigenmodes simultaneously. In addition, the program estimates k1 and
m1 directly from basic data about the building, such as column size, floor
plan, floor slab thickness, etc. The output file is, Bldg3.out.
In class on Tuesday 10/12, an interactive session
was conducted in Room 213. During the session, the Matlab solution to the
1-D wave equation under free vibration was demonstrated using the finite
element method.
The program Model1d.m and associated subroutines were modified to formulate
the mass matrices for a linear two-noded element using the procedure developed
in class. The resulting program,Mod1ddyn.m
,uses the Matlab function, eig(K,M), to find the eigenvalues and eigenmodes
for the case of c=1, H=1, and nel=4, corresponding to an idealized 4-DOF
problem such as a shear beam building. The output file is, Mod1dyn.out.