Genetic Algorithm Optimization
in Structural
Mechanics
S.I.Rodin
Department of Material Science and Mechanics
A genetic algorithm approach is
used in program FrameGA 3D to generate space structures and to
optimize space frames so as to minimize the weight or price of the structure. Island
ring topology is used to achieve solution. Island ring topology is used to
achieve solution.
Finite Element method is used with
finite deflections of hinges and stability analysis of the whole structure
(it’s important for tall compressed frames).
Program FrameGA 3D uses
several islands with parallel evolution and exchanging data from time to
time. Finite element method is used to calculate displacements and stresses
for any degree of freedom SS.
It uses Excel from MS Office 2000
for input data and output results.
It’s difficult to present
graphic results. Sure in the program it may rotate and move as you like, but
comprehensive solution hardly can be imagine looking at the screen.
It's possible to use anaglyphs to
represent results (See: About Anaglyphs). It gives Stereo view on ordinary
computer monitor. It's useful for engineering problems. You can see in this
case in front of or behind the screen real stereo image of the structure.
The saved results in Excel now may
be viewed with additional program View3D. As in main program:
isometric and anaglyph view with any rotations, scales, moves and also it's
possible to see displacements of the space frame.
On this page several examples of FrameGA
3D work are shown (corresponding Stereo view is at the bottom of this
page). All these examples and much more may be downloaded from Download Demo Page
and you may see them with program View3D demo form different
positions in Mono and Stereo view.
Most of the examples are symmetrical. But why to pay for
symmetry? (some asymmetrical examples).
On Download Demo Page
you may download FrameGA 3D demo and you may see how program works in
dynamics. There are instructions how to install.
All examples use program FrameGA
3D and View3D for Windows 98 / XP and all initial data are included in
corresponding EXE or Excel file. For Mono view tensile bars are blue,
compressed – red and zero bars are black.
In Excel files on ‘Help’ sheet there are basic principles for symmetry,
forces and coordinates.
Examples have limits on maximum cross section area and displacements.
There are possible two ways to create initial population:
- to use random position of hinges with random ties between them for every
member of first generation;
- to choose a standard shape with given ties and
optimize it by evolutionary algorithm, it’s faster but
less flexible.
Slenderness ratio limits are: compressed bars =
120, tensile bars = 200 and zero bars = 150.
Bars are made of steel with peak proportional stress 210MPa and yield stress
240MPa.
Demo Examples
All these examples have FrameGA 3D demo and
you may see them with program View3D demo form different positions in
Mono and Stereo view. Files for this demo may be downloaded from Download
Demo Page.
Fig. 1. Symmetrical frames (span = 30 m;
forces - each = 100 kN).
Fig. 2. Symmetrical frame
with self-weight (span = 40 m;
forces - each = 100 kN).
Fig. 3. Asymmetrical frame (span = 40 m, height = 100
m,
forces - each = 1000 kN).
Fig. 4.
Fig. 4. Cantilever (span = 45 m, force = 100 kN) with wind and
selfweight loading.
Fig. 5. Symmetrical frame with different
limits on maximum cross section area
(span = 40 m, height = 100 m; forces - each = 1000 kN)
for wave+current+wind loading (drag force – left, inertia force - right).
a.
b.
Fig. 6. Symmetrical frame (span = 20 m, height =
100 m; force = 100 kN).
a – wind loading; b – wind+selfweight loading
 
Fig. 7.
Frame with forbidden zone, one plate of symmetry
and optimal position of supports
(height = 45 m; force = 100 kN + wind loading).
Fig. 8. Snake - frame with forbidden zones, one plate of
symmetry
and optimal position of supports
(height = 45 m; force = 100 kN + wind loading).
Fig. 9.
Symmetrical frame with 2 forbidden zones and optimal
XZ-position of supports
(height = 8 m; forces - each = 100 kN).
Fig. 10. Frame with forbidden zone, one plate of symmetry
and optimal Z-position of supports
(span = 60 m; forces - each = 200 kN + wind loading).
 
Fig. 11. Plate frame (span = 6 x 24 m)
Fig. 12. Plate frame with forbidden zones (span = 6 x 24 m)
Fig. 13. Plate frame (span = 12 x 12 m)
Fig. 14. Plate frame (span = 12 x 12 m)
Fig. 15. Frame with forbidden zone (length = 50 m),
one plate of symmetry with airflow loading.
Fig. 16. Load combinations for symmetrical frame
(forces+wind+self-weight).
Fig. 17. Frame with forbidden zone, one plate
of symmetry
and optimal Z-position of supports
(span = 60 m; forces - each = 200 kN + wind loading + self-weight).
Bi-material – tensile bars are made of steel uniform rope.
Fig. 18. Frame with forbidden zone, one plate of
symmetry
and optimal Z-position of supports
(span = 60 m; forces - each = 200 kN + wind loading + self-weight).
Bi-material – tensile bars are made of steel uniform rope.
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Full functional copy of
program FrameGA 3D:
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uses Excel from MS Office 2000
for input data and output results, on which Worksheets all data are
presented - no learning how to operate;
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structure may have any number of
horizontal and vertical support ties at any position;
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structure may have any number of horizontal
and vertical loads;
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limits on maximum cross section area;
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limits on maximum horizontal and vertical displacements;
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slenderness ratio limits for compressed, tensile and zero bars;
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two ways of initial structures:
optimization of chosen shape with
given ties
or
random position of hinges with random ties between them for every member of first
generation;
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possible cross
sections may be defined:
as a table
or
as any form with given step of cross section area;
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implant
different types of symmetry (include round) for the solution, for any
type of symmetry cross section areas in the solution are also
symmetrical – so loads may be reversed;
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finite
deflections of hinges and stability analysis of the whole structure;
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has
Simple Mode – calculates frame without optimization;
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gives
Stereo anaglyph view with tuning color window - so one can tune colors
for it's individual glasses (if not standard - it's necessary to tune
three colors: left eye, right eye, background);
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the
saved results in Excel may be viewed with additional program View3D
and as in main program are possible isometric and anaglyph views
with any rotations, scales, moves and also it's possible to see
displacements of the space frame;
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has
Help file. |
Details by E-mail.
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By special request
it’s possible to add special features:
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special
loads - loads depending on the form and structure of frame and
its elements: self-weight, wind, wave etc.;
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| optimal
position – during optimization process optimal position of
desired loads and supports by desired directions is searched;
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| forbidden
zones - points of working space forbidden for bars and hinges;
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| load
combinations - multiple load cases.
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| Bi-material
– compressed and zero bars are made of material #1, tensile bars are
made of material #2 (yet it may be possible to divide bars by material
in different way: by position in the space for example). |
For
more details see Help3Ddemo.zip on
Download Demo Page. |
Demo Examples (Stereo View)
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