H
DOCUMENTATION AND
USER INSTRUCTIONS OF
PROGRAM `TRAM'
Appendix H contains a brief documentation, user instructions and specimen input and output data le for program TRAM developed in Chapter
11.
H-1
H-2
H. Documentation and user instructions of program TRAM
H. Documentation and User Instructions of
Program TRAM
H.1 Program Documentation
H.1.1 Overview of the Program
This section describes program TRAM which performs the closed form transient as well as vibration and stability analysis of simply supported, Mindlin
plates as described in Chapter 11.
H.1.2 Main Routines
Program TRAM consists of a main segment and ten subroutines. The subroutines are now briey described:
1. MASTER is the main segment which controls the calling of all the other
subroutines.
2. FIMA handles the le management. This subroutine open and close the
necessary data les.
3. DATA reads in all the input data values.
4. OUTD prints out all of the input data values with appropriate annotations.
5. INIT zeroes all initial values apart from the input values.
6. COEF calculates the coeÆcients P11 ; P12 ; P13 ; etc.
7. EIGEN calculates eigenvalues, eigenvectors and buckling forces.
8. CONS calculates the qmn for a given loading function.
9. CONIN calculates the convolution integral for dierent pulsing functions.
10. SUMS sums the various Fourier series.
11. OUTP prints out the results for each time step in transient dynamic analysis.
12. OUTF prints out the results in vibration and buckling analysis.
H.2 Input instructions
H-3
H.2 Input Instructions
H.2.1 Glossary of Variable Names
Length of plate in the x; y directions respectively
Membrane force parameters in the x; y directions
respectively
amn1,bmn1,cmn1
The eigenvectors associated with the natural frequencies
bmx,bmy, bmxy
Mending moments Mx ; My ; Mxy
cx,cy,cxy
Curvatures
d11,d22,d12,d21,d66 Flexural rigidities D11 ; D22 ; D12 ; D21 ; D66
dp
Damping parameter
eta,etb
x; y coordinates of centroid of load
f0,f2
Blast load parameters
fx,fy
Membrane forces in the x; y directions respectively
fcr
Buckling forces values for each pair of m; n
g1
Shear modication factor
gfs
Elastic foundation modulus K
ip
= 1 for a sine pulse,
= 2 for a stepped pulse,
= 3 for a triangular pulse,
= 4 for a stepped triangular (nuclear blast) pulse,
= 5 for an exponential (blast) pulse
it
= 1 for non-symmetric loads and
= 2 for symmetric loads
iq
= 1 for uniform loads,
= 2 for concentrated loads,
= 3 for uniform patch loads and
= 4 for cosine patch loads
j
number of time steps in transient dynamic analysis
aa,bb
alfa,beta
kp
lpon
mpon
npon
num
numf
= 1 for vibration and buckling analysis only,
= 2 for transient dynamic analysis only and
= 3 for both analyses together
Maximum number of frequencies (buckling forces)
for each m; n is (20)
Maximum number of output points (140)
Number of output points
Number of Fourier terms
Number of frequencies (buckling forces) to be calculated for each m; n
H-4
H. Documentation and user instructions of program TRAM
p11,p12,p13, etc.
pi
pm
pz
qx,qy
qmn
CoeÆcients used to evaluate Amn ; Bmn ; Cmn ; !mn
and Fcr
Mass density per unit of area
Load intensity
Shear forces
The term qmn in the Fourier series representation
of the load
Shear rigidities S44 ; S55
Pulsing parameters
Time step length
Problem title
Dimensions of patch load
s44,s55
t1,t2,t3
tin
title
u,v
w,wux,wuy
wmn2
wmn
xcord,ycord
w; x ; y
2
!mn
!mn
X; Y coordiantes
of output points
H.2.2 Main Structure of Input Data
In the following section user instructions for preparing the input data are
presented.
Data set 1: Title of problem
| One record (20a4)
cols. variable name
1-80
title
description
Title of the problem
Data set 2: Plate dimensions
cols. variable name
| One record (2f10.5)
description
1-10
aa
side length parallel to x axis
11-20
bb
side length parallel to y axis
Data set 3: Flexural properties
cols. variable name
| One record (4f10.5)
description
1-10
d11
exural rigidity D11
11-20
d22
exural rigidity D22
21-30
d12
exural rigidity D12
31-40
d66
exural rigidity D66
H.2 Input instructions
Data set 4: Shear properties
cols. variable name
| One record (2f10.5)
description
1-10
s44
shear rigidity S44
11-20
s55
shear rigidity S55
Data set 5: Further plate parameters
cols. variable name
| One record (6f10.5)
description
1-10
pz
load intensity
11-20
gfs
foundation modulus
21-30
g1
shear modication factor
31-40
fx
membrane force in x direction
41-50
fy
membrane force in y direction
51-60
pm
mass density per unit of area
Data set 6: Control parameter
cols. variable name
1-5
kp
| One record (i5)
description
Type of analysis
= 1, vibration and buckling analysis only
= 2, transient dynamic analysis only
= 3, both analyses together
if kp = 1; next data set must be Data set 14.
Data set 7: Control data
| One record (2i5)
cols. variable name
description
1-5
num
number of Fourier terms
6-10
npon
number of output points
Data set 8: Sampling Points
cols. variable name
| npon records (i5,2f10.5)
description
1-5
jpon
point number
6-15
xcord(.)
x
coordinate
16-25
ycord(.)
x
coordinate
H-5
H-6
H. Documentation and user instructions of program TRAM
Data set 9: Loading type
| One record (2i5)
cols. variable name
description
16-20
iq
= 1, uniform loading
= 2, concentrated loading
= 3, uniform loading over rectangular
patch u v
= 4, cosine loading over rectangular
patch u v
21-25
it
= 1, non-symmetric loads
= 2, symmetric loads
Data set 10: Loading position
Omit this data set, if iq < 2
cols. variable name
| One record (2f10.5)
description
1-10
eta
x
coordinate of patch parallel to x axis
11-20
etb
x
coordinate of patch parallel to x axis
Data set 11: Load patch size
Omit this data set, if iq < 2
cols. variable name
| One record (2f10.5)
description
1-10
u
side length of patch parallel to x axes
11-20
v
side length of patch parallel to x axes
Data set 12: Pulsing function type
cols. variable name
| One record (i5, 6f10.5)
description
1-5
ip
=1, a sine pulse
=2, a stepped pulse
=3, a triangular pulse
=4, a stepped triangular pulse
=5, an exponential
6-15
f0
blast load parameter
16-25
f2
blast load parameter
26-35
dp
damping parameter
36-45
t1
pulsing parameter
46-55
t2
pulsing parameter
56-65
t3
pulsing parameter
H.3 Specimen input data le
Data set 13: Time step parameters
cols. variable name
1-5
j
6-15
tin
| One record (i5,f10.5)
description
number of time steps
time step length
Data set 14: Vibration analysis parameters
Omit this data set, if kp = 2
cols. variable name
H-7
| One record (i5,2f10.5)
description
1-5
numf
number of frequencies to be calculated
6-15
alfa
membrane force parameter in x direction
16-25
beta
membrane force parameter in y direction
If alfa = 0 and beta = 0 the buckling analysis is not considered.
H.3 Specimen Input Data File
In this section input and output data les are provided for a numerical example
presented in the text. This information will be of assistance to readers who
wish to run the program contained in the book on their own computer.
H.3.1 Free Vibration and Buckling Analysis of Square Plate
Problem denition: The example is concerned with free vibration and buckling
analyses of a thin square plate of thickness-to-span ratio h=a = 0:01. The
plate considered has the following properties: a = b = 1, D11 = D22 = 1:0,
D12 = 0:3, D66 = 0:35, S44 = S55 = 35000:0, = 0:3 and = 10:0.
A typical input and output les for T RAM is displaced in Table H.1 and
H.2.
H-8
H. Documentation and user instructions of program TRAM
Table H.1.
The input data le for square plate.
buckling forces for a thin square plate h/a=0.01
1.0
1.0
1.0
1.0
0.3
0.35
35000.0 35000.0
0.0
0.0
1.0
0.0
0.0
1
3 1.0
Table H.2.
data set
1
2
3
4
1.0
5
6
14
The output data le for square plate.
_______ ______ _______ _______
|
|_____/ |_____| | | |
|
|
\_ |
| | | |
Dynamic Analysis of Mindlin Plates
Closed Form Solution
Copyright (c) E. Hinton, J. Sienz and M. Ozakca
Swansea, 1988 - 2001
**** closed form solution ****
buckling forces for a thin square plate h/a=0.01
**************************************************
dimension of plate in x direction.(aa)= 0.10000E+01
dimension of plate in y direction.(bb)= 0.10000E+01
flexural rigidity....(d11)=
flexural rigidity....(d22)=
coupling rigidity....(d12)=
torsional rigidity...(d66)=
0.10000000E+01
0.10000000E+01
0.30000000E+00
0.35000000E+00
H.3 Specimen input data le
transverse shear rigidity.....(s44)= 0.35000000E+05
transverse shear rigidity.....(s55)= 0.35000000E+05
shear correction factor.........(g1)=
modulus for elastic foundation.(gfs)=
distributed loading.............(pz)=
membrane force in x direc.......(fx)=
membrane force in y direc.......(fy)=
mass density per unit area......(pm)=
0.10000000E+01
0.00000000E+00
0.00000000E+00
0.00000000E+00
0.00000000E+00
0.10000000E+01
control parameter...............(kp)=
1
numb. of freq. to be calculat.(numf)=
3
memb. force param. in x dir...(alfa)= 0.10000000E+01
memb. force param. in y dir...(beta)= 0.00000000E+00
**************************************************
table shows the computed values for the
frequencies and buckling forces for each
pair of modes
m
n
wmn
fcr
*********************************************
1
1
0.197336E+02 -0.394562E+02
1
2
0.493133E+02 -0.246393E+03
1
3
0.985572E+02 -0.984185E+03
2
1
0.493133E+02 -0.615982E+02
2
2
0.788679E+02 -0.157558E+03
2
3
0.128070E+03 -0.415468E+03
3
1
0.985572E+02 -0.109354E+03
3
2
0.128070E+03 -0.184652E+03
3
3
0.177204E+03 -0.353511E+03
H-9