Genetic Algorithm Optimization in Structural
Mechanics
S.I.Rodin
Department of Material Science and Mechanics
A genetic algorithm approach with island ring topology is
used for optimization of trusses so as to minimize the weight of the
structure.
Standard methods are used to determine cross
sections for compressed, tensile and zero steel bars with flexibility limits
(compressed bars = 120, tensile bars = 200 and zero bars = 150).
In all cases weight of the best truss is compared to
the weight of base steel standard model.
This solution is rather general - hinges are
scattered at random with 2 bars each to make structure geometrically stable.
Mutations are also applied to the position of hinges.
Loads are shown on the trusses and there may be any
number of load combinations - like it's in real construction design.
Two examples (Figure 1 and Figure 2) are shown
for a single load - a force is applied to one hinge.
Another example (Figure 3) is shown for a single load - forces
are applied to every hinge of lower chord.
On Figure 4 example is shown for a combination of 8 loads: a
force is applied in succession to every hinge of lower chord - moving load.
Figure 5 shows an example to get more optimal truss for chosen
shape with fixed number of hinges.
Figures 6,7 show shape dependence upon load value. Different
shapes of trusses for different values of force are due to influence of compressed bars
flexibility and flexibility limits for all bars.
Figure 7,8 shows possibility of implantation of one and two
forbidden areas for bars and hinges by modifying fitness function to get necessary
restrictions on shapes. It's important to point out - not by changing algorithm - but by
changing environment. It's like in living world - changing environment - changing
biological species (giraffe, whale, etc.).
Figure 9 shows plane structures upon different load values also
with implantation of forbidden area.
Figure 10 shows weight of steel plane structures for different
values of flexibility limits for bars. Normal flexibility limits are
taken as follows:
compressed bars = 120, tensile
bars = 200 and zero bars = 150.
Sure, not all best structures may be used - there is a possibility to choose
among either the best shown or the best in every island.