1. Global topology optimization of truss structures Dmitrij Šešok Rimantas Belevičius Department of Engineering Mechanics. Vilnius Gediminas Technical University. 2007

2. Introduction The aim of this presentation is to propose a technology enabling to optimize the truss structures’ topology using genetic algorithms

3. Introduction Truss structures are widely used in engineering practice (bridges, towers, roof supporting structures, etc) The aim of topology optimization of truss systems is to find the best layout of connections between the given set of immovable nodes.

4. Problem formulation (merit function)

5. Problem formulation (constraints) Static equilibrium: Critical maximum stress: Local stability:

6. Software and hardware All numerical examples were solved using original software written in C++ Computer characteristics: processor AMD Athlon 1.09 GHz, 1 GB of RAM

7. Topology optimization by full search algorithm 5 nodes. 1024 possible connection variants. Global solution was found in < 1 sec

8. Topology optimization by full search algorithm 6 nodes. 32768 possible connection variants. Global solution was found in 6 sec

9. Topology optimization by full search algorithm 7 nodes. 2097152 possible combinations. Global solution was found in 406 sec (7 min)

10. Topology optimization by full search algorithm 8 nodes. 268435456 possible combinations. Global solution - in 59354 sec (17 h)

11. Simple Genetic Algorithm (SGA) Every generation includes: Initialization Selection Crossover Mutation

12. Topology optimization by SGA Global solution was not found. Best solution was found in 3 min 50 sec

13. Topology optimization by SGA We can improve solution by removing elements with stresses below threshold value

14. Modified Genetic Algorithm (MGA) Every generation includes: Initialization Selection Crossover Mutation Purification

15. Modified Genetic Algorithm (MGA) Purification of genotype is one additional phase of GA: the individual obtained after the selection, crossover and mutation is analyzed, and the values of genotype’s genes representing the elements with low stresses are reversed.

16. Topology optimization by MGA Global solution was found in 5 min 50 sec

17. Conclusions GA can be easily adapted to the topology optimization of truss structures GA yields a reasonable solution in a short time Purification of genotype enables to find a better solution