OPTIMIZATION OF PLANAR TRUSS STRUCTURE USING FIREFLY ALGORITHM MANIKANDAN .A 91710103025 MANIKANDAN .B 91710103026 MOHAMED ANSARI.S 91710103028 RAGAVAN.V 91710103040 THIRUNAVUKARASU.S 91710103055 Under the guidance of, MS. N. MUTHU ABINAYA.,ME, Assistant professor, Department of Civil Engineering Sethu Institute of Technology.

Content Introduction Optimization Objective of project Scope of project Review of literature Structural optimization 18 – bar truss structure Components of optimization objective function Constraints Variables Variables of choice Material property Allowable for 18-bar truss Range of design variables Results from firefly algorithm optimum layout conclusion

Introduction Traditional method – not satisfied. Nature inspried metaheuristic algorithms Firefly Algorithm (FA) Ability of metaheuristic algorithms

Optimization The act of obtaining the best result under the given circumstances. Design, construction and maintenance of engineering system involve decision making both at the managerial and technological level. Goals of such decision To minimize the effort required or To maximize the desired benefit.

Role of optimization in design Decision making Satisfactory decision under given circumstances Minimum weight design

Objective of the project Study the basic concept and functional behaviour Develop computer program for the optimization algorithm To obtain minimum weight of truss structure

Scope of the project Understand the need and origin of the optimization methods. Get a broader picture of the various applications of optimization methods used in engineering. Formulate optimization problem as mathematical programming problem.

Review of literature

S. Gholizadeh et al (2011) has described the shape optimization of truss structures tackled using an enhanced HS metaheuristic algorithm, in order to improve the computational performance of HS. The proposed meta-heuristic algorithm is termed as modified harmony search (MHS) algorithm. Both size and shape structural optimization problems were solved by the proposed algorithm and the results were compared to those of the other researchers. The numerical results indicate that using MHS not only better solutions can be found but also a significant reduction in computational effort may be achieved.

Xin - She Yang (2011)  The author intended to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications. The author had compared the proposed firefly algorithm with other meta-heuristic algorithms such as particle swarm optimization (PSO). Simulations and results indicate that the proposed firefly algorithm was superior to existing meta-heuristic algorithms. Finally author discussed its implications for further research.

S. Kazemzadeh Azad et al (2011) In this paper, optimum design of truss structures with both sizing and geometry design variables is carried out using the firefly algorithm. Additionally, to improve the efficiency of the algorithm, modifications in the movement stage of artificial fireflies are proposed and the general performance of the algorithm in 50 runs is reported . Numerical results indicate the efficiency of the proposed approach.

Structural optimization Three categories Sizing – cross – sectional areas Configuration – nodal co-ordinates Topology – nodal co-ordinates & connectivity

18 – bar truss structure

Components of optimization Objective function constraint variables optimization

Objective function The optimal design of truss optimization can be treated as Minimize f(x) So the objective function can be written as f(x)=∑ƿAl

Total design variables - 12 sizing variables – (A1,A2,A3,A4) - 4 geometry variables – (X3,Y3,X5,Y5,X7,Y7,X9,Y9) - 8 Total design variables - 12

Cross sectional area & geometry variable Variable of choice Design variables Discrete variables Continuous variables Cross sectional area & geometry variable Variable of choice

Optimization algorithm Constraints Optimization algorithm stress Set the constraint

Material property S. No Property Value 1 Material Aluminium 2 Young’s modulus 68947.6 Mpa 3 Density 2767.99 Kg/m3

Allowable for 18-bar truss S. No Allowable Value 1 Stress 137.895N/mm2 2 Range of design variables 1290.3 ≤ A ≤ 14032 mm2

Range of design variables S. No Design variable Lower limit (mm2) Upper limit 1 A1 (1,4,8,12,16) 7903.2 8871 2 A2 (2,6,10,14,18) 9838.7 12258 3 A3 (3,7,11,15) 2903.8 4032.3 4 A4 (5,9,13,17) 1290.3

Boundary limits for geometry variables S. No Design Variable Lower limit ‘mm’ Upper limit 1 X3 19685 31115 2 X5 13335 24765 3 X7 6985 18415 4 X9 635 12065 5 Y3 -5715 6223 6 Y5 7 Y7 8 Y9

Firefly algorithm The algorithm is formulated by assuming, All fireflies are unisexual Attractiveness is proportional to their brightness. If there are no firefly brighter than a given firefly, it will move randomly.

Mat lab implementation Check for constraints matlab program for 18 - bar truss.

Results from firefly algorithm S.NO SIZING VARIABLE INITIAL SOLUTION (mm2) FINAL SOLUTION (mm2) 1 A1 6451.5 8094 2 A2 9677.29 11560 3 A3 3225.78 3656 4 A4 4561.94 2200

Geometry variables using firefly algorithm S.NO GEOMETRY VARIABLE INITIAL SOLUTION (mm) FINAL SOLUTION 1 X3 25400 24562.5 2 X5 19050 15222.6 3 X7 12700 10811.3 4 X9 6350 5808 5 Y3 4897 6 Y5 3852 7 Y7 2389.3 8 Y9 1045 WEIGHT(kg) 13394 2053

Optimum layout of 18 – bar truss using firefly algorithm

Conclusions The effectiveness of the methods are demonstrated through a 18 - bar planar truss problem. The numerical results demonstrate the superiority of the various methods like firefly algorithm and particle swarm optimization. The results obtained by considering both the size and shape variable. Optimum solution obtained using firefly algorithm – From the optimum solution it is found that the firefly algorithm is more efficient

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