I
DOCUMENTATION AND
USER INSTRUCTIONS OF
PROGRAM `VISOR'
Appendix I contains a brief documentation, user instructions and specimen input and output data le for program VISOR developed in Chapter
11.
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I. Documentation and user instructions of program VISOR
I. Documentation and User Instructions of
Program TRAM
I.1 Program Documentation
I.1.1 Overview of the Program
This section describes VISOR which is a program for the free vibration analysis
of solids of revolution and their sectors in order to make all of the subroutines
in VISOR modular in form a type of dynamic dimensioning has been used.
Dimensions are xed in the main routine and all necessary information is
transmitted between routines by the use of arguments. This approach has the
advantage that the maximum dimensions can be updated in a very simple
manner. Only the parameter statements in the main segment, which sets the
maximum dimension sizes, need modication.
I.1.2 Main Routines
Program VISOR consists of a master segment and four main 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. INSOR which reads in most of the input data,
4. STISOR which evaluates the stiness and mass matrices for solids of revolution and their sectors,
5. BERKEL which is an eigenvalue solver, and
6. OUTSOR which outputs the results.
Program VISOR is written in a modular form so that users can easily
implement their own modules for eigenvalue solution and for output. Thus,
BERKEL and OUTSOR are not compulsory routines in the program. They are
routines which illustrate the implementation of the eigenvalue solver, described
and coded by Bathe [1], which employs a subspace iteration method with
Strum sequence checks. Next the function of the main segment and major
subroutines will be described.
Main segment: which controls the calling of the major routines is now described.
I.1 Program documentation
I-3
1. Initialise variables in data statements.
2. Call INSOR to read in most of the data.
3. Loop over each harmonic.
3.1 Call STISOR to evaluate K and M.
3.2 Call BERKEL to nd eigenvalues.
3.3 Call OUTSOR to print the results.
Subroutine INSOR: The main function of INSOR is to read most of the input
data. The basic structure of INSOR is of the following form.
1.
2.
3.
4.
5.
6.
7.
Read and write problem title.
Read and write control data.
Read and write element connections and property set numbers.
Initialise array coord.
Read and write nodal coordinates.
Read and write xity conditions.
Read and write element properties.
Subroutine STISOR: The main function of STISOR is to evaluate stiness and
mass matrices for SOR elements and SOR sectors. Subroutine STISOR has the
following structure.
1. Rewind les 1 and 7 ready for writing K and M.
2. Set up Gauss sampling data.
3. Loop over each element.
3.1 Put nodal coordinates in local array.
3.2 Set up element D matrix.
3.3 Extract element density and included angle.
3.4 Initialise K and M arrays.
3.5 Evaluate stiness and mass matrix.
3.6 Make K and M symmetric.
3.7 Write K and M to les 1 and 7 respectively.
Subroutine BERKEL: is the interface routine for the eigenvalue solver. It prepares all necessary data for subspace iteration coded in subroutine SSPACE.
BERKEL call subroutine COLHT to calculate column heights and subroutine ADDRES to calculate addresses of diagonal elements in a banded matrix
whose column heights are known. From les 1 and 7 BERKEL reads and writes
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I. Documentation and user instructions of program VISOR
in vector form strip stiness and mass matrices, then calls ADDBAN to assemble the upper triangular part of those strip matrices into the compacted
global matrices.
BERKEL reads two indicators for subspace iteration as input data:
ifss | indicator for Strum sequence check and
ifpr | indicator for printing during iteration.
Note: The subroutines COLHT, ADDRES , ADDBAN and SSPACE are
fully described and listed in reference [1].
To match subroutine BERKEL with subroutine OUTSOR it is necessary
to make some modications in SSPACE and they are:
Input DATA statement | data iout1/4/
Substitute iout with iout1 in the following lines: spce0269 and spce0292
Subroutine OUTSOR: simply prints out eigenvalues, modes and error norms
after reading from le 4. If printing during iteration is required (ifpr=1) then
corresponding results are stored in le 3.
I.2 Input Instructions
I.2.1 Glossary of Variable Names
alpha
coord(mpoin,2)
dense
estif(27,27)
emass(27,27)
ifpre(mvfix,ndofn)
iharm
lnods(melem,9)
matno(melem)
melem
mevab
mmats
mpoin
mvfix
ndofn
nevab
nelem
included angle for nite prism analysis
r- and y- coordinates of nodes
density
element stiness matrix for a given harmonic
element mass matrix
xity code matrix,
0 = free,
1 = xed
counter for harmonic terms
element nodal connectivities
material set numbers for each element
maximum number of elements
= 27, maximum number of element variables
maximum number of material sets
maximum number of nodal points
maximum number of restrained nodes
= 3, number of degrees of freedom per node
= 27, number of degrees of freedom per element
number of element
I.2 Input instructions
nharm
nmats
nmode
nnode
nofix(mvfix)
npoin
ntype
poiss
props(mmats)
young
number of harmonic terms to be used
number of dierent material properties
number of eigenvalues required
= 9, number of nodes per element
nodes with at least one prescribed variable
number of nodes
indicator for analysis type
= 0, for axisymmetry
= 1, for asymmetry
= 2, for prism
Poisson's ratio
properties for each material set.
Young's modulus
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I. Documentation and user instructions of program VISOR
I.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
cols.
variable name
1-80
title
| One record (20a4)
description
Title of the problem
Data set 2: Problem parameters
| One record (9i5)
cols.
variable name
description
1-5
npoin
number of nodes
6-10
nelem
number of elements
11-15
nvfix
number of prescribed nodes
16-20
ntype
analysis type indicator
= 0 for axisymmetric analysis
= 1 for asymmetric analysis
= 2 for nite prism analysis
21-25
nmats
number of dierent materials
26-30
nprop
number of material properties (3 or 4)
31-35
ngaus
number of Gauss points (3)
36-40
nharm
number of harmonics
41-45
nmode
number of eigenmodes per harmonic
Data set 3: Nodal connections
cols.
variable name
1-5
numel
6-10
matno(numel)
| nelem records (11i5)
description
element number
material number for the element
11-15 lnods(numel,1)
global number of node 1.
..
..
..
..
..
.
51-55 lnods(numel,9) global number of node 9
I.2 Input instructions
Data set 4: Nodal Coordinates
cols.
variable name
1-10
ipoin
6-15
I-7
| npoin records (i5,2f10.5)
description
number of node
coord(ipoin,1) r- coordinate of node
16-25 coord(ipoin,2) y- coordinate of node
Data set 5: Fixed Values
cols.
variable name
1-5
nofix(ivfix)
| nvfix records (i5,2x,3i1)
description
number of xed node
8
ifpre(ivfix,1) indicator for constraint in
u
9
ifpre(ivfix,2) indicator for constraint in
v
10
ifpre(ivfix,3) indicator for constraint in
w
indicator = 1 constrained, = 0 free
Note: nvfix= 0 implies that for the prism analysis, the sector is simply
supported at both ends. Also a constraint in a degree of freedom implies
that the displacement associated with that degree of freedom is zero
along the nodal line between the sector boundary planes. Other nonzero constraints are not allowed in this program
Data set 6: Material properties data
One record for each dierent material. Total of nmats records (i5,5f10.5)
cols.
variable name
1-5
numat
description
Material set number
6-15 props(numat, 1) Elastic modulus E
16-25 props(numat, 2) Poisson's ratio 26-35 props(numat, 3) Material density 36-45 props(numat,4)
included angle in prism analysis
Data set 7: Sturm sequence indicators
| One record (2i5)
cols.
variable name
description
1-5
ifss
indicator for Sturm sequence check
= 0, no check
= 1, check applied
6-10
ifpr
indicator for printing during iteration
= 0, no printing
= 1, printing
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I. Documentation and user instructions of program VISOR
I.3 Specimen Input Data File
In this section input data le are provided for some of numerical examples
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.
I.3.1 Simply Supported Circular Plate
Problem denition: In the rst example, the axisymmetric and asymmetric
modes of vibration of a simply supported circular plate of thickness-to-radius
ratio of h=a = 0:1 (shown in Figure I.1) are evaluated using VISOR. The
frequency parameters 2n;s = !ns a2 (h=D)1=2 for nodal diameters n = 0; 1; 2; 3
and concentric circles s = 0; 1; 2; 3 are obtained from VISOR using 5 SOR
elements. Note that is the mass density per unit volume and D is the exural
rigidity of the plate expressed as D = Eh3 =12(1 2 ) where E is the elastic
modulus and is Poisson's ratio.
y; v
h
B
C
D
A
r; u
a
Simply supported circular plate: h=a = 0:1; boundary conditions A
C (u = w = 0); B (w = 0); C (u = v = w = 0); D(w = 0).
Fig. I.1.
!
A typical input le for V ISOR is displaced in Table I.1.
Table I.1.
The input data le for simply supported circular plate.
simply supported circular plate 33
5 13
1
1
3
3
1
1
1
2
3
6
9
2
1
7
8
9 12 15
3
1 13 14 15 18 21
4
1 19 20 21 24 27
5
1 25 26 27 30 33
1
0.0
0.1
2
0.0
0.05
3
0.0
0.0
asymmetric
3
3
8
7
14 13
20 19
26 25
32 31
data set
- h/a = 0.1
1
2
4
5
3
10 11
16 17
22 23
28 29
4
I.3 Specimen input data le
4
5
6
7
9
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
2
5
8
11
14
17
20
23
26
29
31
32
33
1
1
101
101
101
101
101
101
101
101
101
101
001
111
001
1
0.1
0.1
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.4
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.8
0.9
0.9
0.9
1.0
1.0
1.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
0.1
0.05
0.0
1.0
0.3
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5
1.0
6
7
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I. Documentation and user instructions of program VISOR
1
1
1
1
1
1
1
1
I.3.2 Simply Supported Square Plate
Problem denition: This example demonstrates the use of VISOR for the nite
prism analysis of a sector of a solid revolution with simple support conditions
on the radial plane boundaries. By using a very large average radius R and
the special choice of included angle so that R = a it is possible to simulate
quite accurately the behaviour of structures with rectangular planforms.
Simple supports
(
Simple
supports
v = w = 0)
(
Simple
supports
v = w = 0)
(
u = w = 0)
R
Fig. I.2.
Simply supported square plate analysed using a curved nite prism method:
a = R = 1:0; = 0:0001; R = 10; 000:0.
To illustrate this artice, the square simply supported plate shown in Figure
I.2 is analysed using VISOR. An radius average of R = 10; 000:0 is assumed
and an included angle of = 0:0001 is used to represent a plate of span
a = R = 1:0. By specifying NTYPE = 2 in the input for VISOR, the nite
prism approach is adopted.
A typical input le for V ISOR is displaced in Table I.2.
Table I.2.
The input data le for simply supported square plate.
square plate by finite prism method h/a = 0.1
33
5 15
2
1
4
3
3
3
1
1
1
2
3
6
9
8
7
4
2
1
7
8
9 12 15 14 13 10
data set
1
2
5
3
11
References
3
4
5
1
3
7
9
13
15
19
21
25
27
31
33
1
2
3
5
8
11
14
17
20
23
26
29
31
32
33
1
1
1
1
1
1
1
1
1
13
19
25
999.5
999.5
999.7
999.7
999.9
999.9
1000.1
1000.1
1000.3
1000.3
1000.5
1000.5
001
111
001
101
101
101
101
101
101
101
101
101
001
111
001
10920.0
1
1
1
1
1
14
20
26
15
21
27
0.1
0.0
0.1
0.0
0.1
0.0
0.1
0.0
0.1
0.0
0.1
0.0
0.3
18
24
30
21
27
33
20
26
32
19
25
31
16
22
28
17
23
29
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4
5
10.0 0.001
6
7
References
[1] Bathe, K.J., Finite element procedures in engineering analysis, Prentice{Hall,
Englewood Clis, New Jersey, 1982.