Application of parameterized analytical models

1
Application of parameterized analytical
models Dmitry Maslov Institute Giprostroymost
Saint-Petersburg, Saint-Petersburg, Russian
Federation
2
The structural design usually demands examination
of more than one analytical model for a limited
time period
The parameterization is a rational method for
improving design operations at structural
analysis. This technique effectively reduces the
time spent on creating and modifying models
3
A simple model of a plate meshed by n?n finite
elements has approximately 20 figures dependent
on parameter n
generate 1 joint list 1 0 0 0 repeat 10 times id
1 x 0.1 repeat 10 times id 11 y 0.1 status
support 1 to 11 type plane stress generate 1
element list 1 1 2 13 12 repeat 9 times id 1
from 1 to 1 to 1 to 1 repeat 9 times id 10 from
11 to 11 to 11 to 11 element properties 1 to 100
type 'PSR' thickness 0.1 loading 1 joint
loads 105 for y -1.0
Transition from one meshing to another requires
the creation of a new model
4
The parameterization allows modification by
changing only parameter n instead of altering
many numbers
var n10 generate 1 joint list 1 0 0 0 repeat
n times id 1 x 1/n repeat n times id n1
y 1/n status support 1 to n1 type plane
stress generate 1 element list 1 1 2 n3
n2 repeat n-1 times id 1 from 1 to 1 to 1 to
1 repeat n-1 times id n from n1 -
to n1 to n1 to n1 element
properties 1 to nn type 'PSR' thickness
0.1 loading 1 joint loads nnn/2 for y -1.0
Practical models may contain dozens of parameters
and hundreds of dependent numbers. Any
modifications take considerable time
5
Many errors may occur at altering a model
Most of them are not evident and cannot be
found. The engineer should make sure of the
model accuracy
6
The principal reasons for modifications of
analytical models
Improper results which demand more precise source
information
Changes of parameters whose exact values cannot
be determined at the beginning of analysis
Updating of a structure caused by revising the
design conditions
Consecutive analyses of various assembling stages
of a structure
7
The parameterization is replacement of numerical
constants by mathematical expressions
?
X 150.314
X nn/2Pi/s
It saves time and spares an engineer tedious
operations and possible errors because a smaller
range of figures has to be under control
8
Expressions Converter is a preprocessor for the
problem-oriented language that performs
parameterization of analytical models
?
?
?
It reads the text, carries out directives, and
calculates expressions
9
Each line starting with the sign is recognized
as a directive. These lines are removed at
creating the resulting text
format 6.3f var x 2 var y 3 var p
0 var r 5 JOINT COORDINATES for var i1 to 7
d 100i X xrcos(p) Y yrsin(p) p
2Pi/7 next
JOINT COORDINATES 101 X 7.000 Y 3.000 102 X
5.117 Y 6.909 103 X 0.887 Y 7.875 104 X
-2.505 Y 5.169 105 X -2.505 Y 0.831 106 X
0.887 Y -1.875 107 X 5.117 Y -0.909
?
In other lines all characters quoted by signs
are implied as a mathematical expression that is
replaced with its result Running the program
results in the creation of a text file containing
only GT STRUDL commands
10
The preprocessor directives compose a script
language featured with

• variables and arrays
• arithmetic, logical, comparison, and
  assignment operators
• standard and user-defined functions
• conditional and loop statements
• control and debugging directives

var array
- / and or xor not gt lt lt gt
ltgt - /
sin cos sqrt max rnd ... func ... endfunc
ifendif, switchendswitch, fornext,
whileloop, repeatuntil
format nobr ... assert debugout ...
It allows to parameterize any analytical model
11
The program can expand the GT STRUDL language
For generating the rigid bodies
TYPE RIGID SOLID RIGID BODY INCIDENCES for var i
0 to 3 'RB100i10' 101i10 TO
104i10 next
TYPE RIGID SOLID RIGID BODY INCIDENCES 'RB100'
101 TO 104 'RB110' 111 TO 114 'RB120' 121 TO
124 'RB130' 131 TO 134
For definition of member properties
var h0 1.0 var h1 0.6 var n 4 var dh
(h1-h0)/n var h h0 dh/2 var b 0.1 MEMBER
PROPERTIES for var i 0 to n-1 101i AX
bh IZ bh3/12 h dh next
MEMBER PROPERTIES 101 AX 0.095 IZ 0.00714 102
AX 0.085 IZ 0.00511 103 AX 0.075 IZ 0.00351 104
AX 0.065 IZ 0.00228
12
Preparation and debugging of a parameterized
model take more time than that of a
non-parameterized one
But the speed and ease of making changes quickly
compensate for the losses of time, particularly
for large analytical models
13
Combined bridge over the Oka River in Nizhny
Novgorod
8 span and a kilometer long superstructure
consists of main girders, deck orthotropic
plates, cross- and longitudinal beams
We examined many assembling stages with different
creeper cranes and positions of temporary piers
and locations of places where the orthotropic
plates had to be replaced with auxiliary elements
14
We made a model for the entire bridge, then we
deactivated elements and moved loads to create
the model for a stage
Before parameterization we spent over three hours
for the creation of every single model. After
parameterization it took us a minute to create a
new model
15
The cable-stayed bridge over the Neva River in
Saint-Petersburg
Many parameters were subject to change or they
had to be determined within analysis. We made
parameterized analytical model that sufficiently
simplified the problem and allowed completion of
analysis for the strictly scheduled time
16
The parameterized model proved useful to the
bridge construction analysis
We created a new analytical model for each stage
by modification of only two parameters numbers
of recently mounted block and last stressed
cable. The full analysis of 43 stages took less
than two weeks (without parameterization more
than a month)
17
Arch bridge over the Okhta River in
Saint-Petersburg
In the parameterized analytical model for the
examination of the bridge behavior in service we
wrote a subroutine that generated about 200
moving loads appropriate to influence lines, as
the Russian Codes require
18
Push launching of arch tie and deck beams
In the parameterized analytical model dependent
on only one parameter we automatically calculated
coordinates to all the joints, identifiers to the
supported ones, and initial gaps between supports
and structure in non-deformed situation. The
examination of 23 analytical models took only a
week
19
The Converter is not bound to GT STRUDL and may
be applied to any other software
func f(x) result exp(sin(x)cos(3x))exp(cos(
x)-sin(5x))cos(6x) 0.5sin(31x) endfunc va
r x0 var yf(x) PLINE while x lt
4Pi x,y yf(x0.01) loop br
For example, we use it to make AutoCAD drawings
20
Our experience shows that parameterization of
analytical models appreciably increases the
productivity of engineering work If we could use
the results of preceding analyses as input
parameters and perform postprocessing, we would
be able to expand the class of problems to be
solved in GT STRUDL (such as optimization
problems, special non-linear problems and many
problems demanding iteration procedures)
21
Thank you for your attention