COMPONENT-ORIENTED TESTING
Optimization of thin-wall structures using hybrid gravitational search and Nelder-Mead algorithm In literature, a lot of research works have been presented on crashworthiness in order to develop crash performance of vehicles and thin-wall structures. In this research, a new hybrid optimization algorithm based on gravitational search algorithm and Nelder-Mead algorithm is introduced to improve crash performance of vehicles during frontal impact. The results show that the hybrid approach is very effective to develop crash performance of the vehicle components and thin-wall structures.
Materials Testing downloaded from www.hanser-elibrary.com by Carl Hanser Verlag on January 11, 2016 For personal use only.
Ali Rıza Yıldız, Enes Kurtuluş, Emre Demirci, Betul Sultan Yıldız and Selçuk Karagöz, Bursa, Turkey Article Information Correspondence Address Ali Riza Yildiz Department of Mechanical Engineering Bursa Technical University, Bursa, Turkey E-mail:
[email protected] Keywords Thin-wall structures, crashworthiness, automotive, optimization algorithm
The design of new vehicles is effected by many competing criteria, such as safety, energy efficiency and lower cost. In the last thirty years, vehicle crashworthiness, lightweight design, energy economy and environmental protection are important issues which need to be solved urgently in the automotive industry. Weight reduction in vehicle industry is an important issue to carry out energy savings and oil economy [1-22]. To design vehicles lighter with a good rating in crashworthiness provides an automaker a strong opportunity for sales. Increased traffic intensity and growing concern of the public transportation have made vehicle safety one of the major research areas in automotive engineering. In vehicle safety, crash boxes have important tasks. Energy absorption capabilities of the thin-wall structures or crash boxes have been subject of different research works in the literature [1, 3, 20-22]. The thin-wall structures have been widely used in automotive industry. Optimization of the thinwall structures is an important issue. In the literature, different optimization techniques
are used in the designing of the thin-wall structures. In this paper, a new optimization technique is developed for optimum design of thin-wall structures used in automotive industry. This new method is called hybrid gravitational search algorithm and NelderMead algorithm (HGSANM).
Development of new thin-wall structures The thin-wall structures are used to convert the kinetic energy to plastic deformation. Main purpose of the thin-wall structures is to reduce the peak force to protect occupants from serious damages while subjected to impact load. In this work, firstly, an initial thin-wall structure was developed which is shown in Figure 1. The developed thin-wall structures geometry was imported into Hypermesh. Meshing of the components of the thin-wall structure was carried out using shell elements. In this research work, DP600 steel was used as material. Material model card selected was
σ (MPa)
391
700.89
777.6
814.86
845.42
856.51
859.26
861.7
ε
0
0.1
0.2
0.3
0.5
0.7
0.8
1
Table 1: True stress-strain values for DP600 steel
58 (2016) 1 © Carl Hanser Verlag, München Materials Testing
MAT/Law36 is in Radioss 12, known as Isotropic Elastic-Plastic Piecewise Linear. The material properties are given as: density = 7850 kg × m-3 elastisity modulus E = 210 GPa Poisson ratio PR = 0.3 shear stress SIGY = 391 MPa The true stress-strain values for the used material are given in Table 1. In this work, a rigid wall was modeled as 100 kg and moved at a speed of 15.6 m × s-1. The boundary conditions and other definitions are shown in Figure 2. The crash analysis of all designs was done using Radioss 12.
Hybrid gravitational search Nelder-Mead algorithm for optimum design Gravitational search algorithm (GSA) was proposed by Rashedi et al. [23] in 2009.
Figure 1: Initial design of the thin-wall structure
75
76
COMPONENT-ORIENTED TESTING
Table 2: Upper and lower limits of design variables
Figure 2: Rigid wall and spot welds
Design variables
Lower limit
Initial design
Upper limit
D1 (mm)
10
16
22
D2 (mm)
2
4
8
D3 (mm)
10
13
20
D4 (mm)
8
10.75
20
D5 (mm)
66.3
78
117
D6 (mm)
76
101.5
152
D7 (mm)
1
1.5
3
Materials Testing downloaded from www.hanser-elibrary.com by Carl Hanser Verlag on January 11, 2016 For personal use only.
Specific energy Peak force Weight absorption (kJ) (kN) (g) Table 3: Results of the crash analysis
Initial design
5.595
185.624
2003.29
Altair hyperworks [26]
8.765
117.320
1528.72
Optimum design with GSA
8.318
115.914
1524.13
Optimum design with HGSNM
7.615
109.514
1508.72
Figure 4: Design variables
Figure 3: General principle of GSA [23]
The algorithm is based on Newton’s law of universal gravitation, and directs the particles in search through simulated particleparticle interaction. The principle of GSA is shown in Figure 3. The local search mechanism of the GSA is weak [25]. In order to prevent disadvantage of the GSA, a new hybrid optimization algorithm based on gravitational search algorithm and Nelder-Mead algorithm (HGSNM) is proposed in this paper. In the proposed hybrid optimization algorithm, after a loop of the GSA algorithm was completed, Nelder-Mead algorithm was used to improve the population in the last run of the GSA. The process continued
Figure 5: Optimum design
until all iteration was completed. More explanations about GSA and Nelder-Mead algorithm can be found in [23, 24].
Optimization of the thin-wall structure using the HGSNM In this section, the optimum design of the thin-wall structure has been carried out. In the optimization study, seven design variables have been used as shown in Figure 4 and Table 2. Using lower and upper values of design variables and Latin hypercube approach, a doe table was obtained. From the mentioned table, equations for objective function and constraints were obtained using radial basis functions by meta-modeling technique. These equations were used in optimization loop. In optimization work, objective function is to maximize specific energy absorption of the thin-wall structure. Weight of the initial design and peak force values were chosen as constraints. Optimum design of the thin-wall structure is given in Figure 5.
Conclusions In this study, a new hybrid optimization algorithm based on gravitational search algorithm and Nelder-Mead algorithm is presented for optimization of thin-wall structures. In the optimization study, amounts of the energy absorption of the thin-wall structure were chosen as objective function. Maximum peak force and weight were considered as constraints. The crash parameters of the initial and optimum design are given in Table 3. As can be seen from Table 3, the proposed HGSNM algorithm has better performance as GSA. Additionally, mass and peak force of the initial design are reduced.
Acknowledgements The authors would like to express their sincere thanks and appreciation for the financial support by TÜBİTAK (The Scientific and Technological Research Council of Turkey) (Project number 114M029).
58 (2016) 1
COMPONENT-ORIENTED TESTING
Materials Testing downloaded from www.hanser-elibrary.com by Carl Hanser Verlag on January 11, 2016 For personal use only.
References 1 E. Demirci, A. R. Yildiz: Improving the vehicle crash safety with high performance energy absorbers, Engineer & the Machinery Magazine 56 (2015), No. 663, pp. 40-45 2 A. R. Yildiz, K. Solanki: Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach, International Journal of Advanced Manufacturing Technology 1 (2012), No. 4, pp. 367-376 DOI:10.1007/s00170-011-3496-y 3 M. Kiani, A. R. Yildiz: A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization, Archives of Computational Methods in Engineering (2015) DOI: 10.1007/s11831-015-9155-y 4 A. R. Yildiz: Comparison of evolutionary-based optimization algorithms for structural design optimization, Engineering Applications of Artificial Intelligence 28 (2013), No. 1, pp. 327-333 DOI:10.1016/j.engappai.2012.05.014 5 A. R. Yildiz: A new hybrid bee colony optimization approach for robust optimal design and manufacturing, Applied Soft Computing 13 (2013), pp. 2906-2912 DOI:10.1016/j.asoc.2012.04.013 6 A. R. Yildiz: A new hybrid particle swarm optimization approach for structural design optimization in automotive industry, Journal of Automobile Engineering 226 (2012), No. 10, pp. 1340-1351 DOI:10.1177/0954407012443636 7 I. Durgun, A. R. Yildiz: Structural design optimization of vehicle components using Cuckoo search algorithm, Materials Testing 54 (2012), No. 3, pp. 185-188 DOI:10.3139/120.110317 8 H. Gökdağ, A. R. Yildiz: Structural damage detection using modal parameters and particle swarm optimization, Materials Testing 54 (2012), No. 6, pp. 416-420 DOI:10.3139/120.110346 9 A. R. Yildiz, K. Saitou: Topology synthesis of multicomponent structural assemblies in continuum domains, ASME Journal of Mechanical Design 133 (2011), No. 1, pp. 1-9 DOI:10.1115/1.4003038 10 A. R. Yildiz: A novel particle swarm optimization approach for product design and manufacturing, International Journal of Advanced Manufacturing Technology 40 (2009), No. 5-6, pp. 617-628 DOI:10.1007/s00170-008-1453-1 11 A. R. Yildiz: A novel hybrid immune algorithm for global optimization in design and manufacturing, Robotics and Computer-Integrated Manufacturing 25 (2009), No. 2, pp. 261-270 DOI:10.1016/j.rcim.2007.08.002 12 A. R. Yildiz: A new design optimization framework based on immune algorithm and Taguchi method, Computers in Industry 60 (2009), No. 8, pp. 613-620 DOI:10.1016/j.compind.2009.05.016 13 A. R. Yildiz: An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry, Journal of Materials Processing Technology 50 (2009), No. 4, pp. 224-228 DOI:10.1016/j.jmatprotec.2008.06.028
58 (2016) 1
14 A. R. Yildiz: Hybrid immune-simulated annealing algorithm for optimal design and manufacturing, International Journal of Materials and Product Technology 34 (2009), No. 3, pp. 217-226 DOI:10.1504/IJMPT.2009.024655 15 N. Öztürk, A. R. Yıldız, N. Kaya, F. Öztürk: Neuro-genetic design optimization framework to support the integrated robust design optimization process in CE, Concurrent EngineeringResearch And Applications 14 (2006), No.1, pp. 5-16 DOI: 10.1177/1063293X06063314 16 A. R. Yildiz: Optimal structural design of vehicle components using topology design and optimization, Materials Testing 50 (2008), No. 4, pp. 224-228 DOI:10.3139/120.100880 17 A. R. Yildiz, N. Öztürk, N. Kaya, F. Öztürk: Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm, Structural and Multidisciplinary Optimization 34 (2007), No. 4, pp. 277-365 DOI:10.1007/s00158-006-0079-x 18 A. R. Yildiz, O. Alankuş, N. Kaya, F Öztürk: Optimal design of vehicle components using topology design and optimization, International Journal of Vehicle Design 34 (2004), No. 4, pp. 387-398 DOI:10.1504/IJVD.2004.004064 19 A. R. Yildiz, N. Öztürk, N. Kaya, F. Öztürk: Integrated optimal topology design and shape optimization using neural networks, Structural and Multidisciplinary Optimization 25 (2003), No. 4, pp. 251-260 DOI:10.1007/s00158-003-0300-0 20 A. Reyes, M. Langseth, O. S. Hopperstad: Square aluminum tubes subjected to oblique loading, International Journal of Impact Engineering 28 (2003), No. 10, pp. 1077-1106 DOI:10.1016/S0734-743X(03)00045-9
21 G. Nagel: Impact and Energy Absorption of Straight and Tapered Rectangular Tubes, PhD Thesis, The School of Civil Engineering, Queensland University, Queensland, Australia (2005) 22 A. A. A. Alghamdi: Collapsible impact energy absorbers: An overview, Thin-Walled Structures 39 (2001), pp. 189-213 DOI:10.1016/S0263-8231(00)00048-3 23 E. Rashedi, H. Nezamabadi-pour, S. Saryazdi: GSA: A gravitational search algorithm, Information Sciences 17 (2009), No. 9, pp. 2232-2248 DOI:10.1016/j.ins.2009.03.004 24 J. A. Nelder, R. Mead: A simplex method for function minimization, Computer Journal 7 (1965), No. 4, pp. 308-313 DOI:10.1093/comjnl/7.4.308 25 M. Khatibinia, S. Khosravi: A hybrid approach based on an improved gravitational search algorithm and orthogonal crossover for optimal shape design of concrete gravity dams, Applied Soft Computing 16 (2014), pp. 223-233 DOI:10.1016/j.asoc.2013.12.008
Bibliography DOI 10.3139/120.110823 Materials Testing 58 (2016) 1, pages 75-78 © Carl Hanser Verlag GmbH & Co. KG ISSN 0025-5300
The authors of this contribution Dr. Ali Riza Yildiz is Associate Professor in the Department of Mechanical Engineering, Bursa Technical University (BTU), Turkey. He is Vice Dean of Natural Science & Engineering Faculty of Bursa Technical University and he is also Director of the Multidisciplinary Product Design and
Abstract Optimierung von dünnwandigen Strukturen mittels eines neuen Algorithmus. In der Literatur wurden immense Forschungsarbeiten in Bezug auf das Crashverhalten gezeigt, um die Crashperformanz von Fahrzeugen und Crashboxen zu verbessern. In den diesem Beitrag zugrunde liegenden Forschungsarbeiten wurde ein neues Crashboxdesign entwickelt, das auf dem Gravitationssuch- und Nelder-Mead-Algorithmus basiert, um die Crashperformanz von Fahrzeugen beim Frontalaufprall zu verbessern. Hierfür wurden die maximale Spitzenkraft und der Betrag der Energieabsorption als objektive Funktionen gewählt. Die numerischen Studien beinhalten die Bestimmung der Energieabsorptionscharakteristika verschiedener Geometrien, wie zum Beispiel Trigger der Crashboxen. Die Untersuchungen zeigen, dass sich der Hybrid-Ansatz als sehr effektiv bei der Crashperformanzverbesserung von Automobilteilen und Crashboxen erweist.
77
Materials Testing downloaded from www.hanser-elibrary.com by Carl Hanser Verlag on January 11, 2016 For personal use only.
78
COMPONENT-ORIENTED TESTING
Optimization Laboratory (MPDOL) at BTU. He worked on ‘’Multi-component topology optimization of the structures’’ as Research Associate at University of Michigan, Ann Arbor, USA. Furthermore, he worked on a NSF and DOE funded research projects at Center for Advanced Vehicular Systems (CAVS), Mississippi State University, USA. In 2015, he is a winner of TÜBA-GEBİP Young Scientist Outstanding Achievement Award given by the Turkish Academy of Sciences (TÜBA). His research interests are vehicle design, vehicle crashworthiness, vehicle and pedestrian safety, crush box design and optimization, shape and topology optimization of vehicle components, meta-heuristic optimization techniques and sheet metal forming. Enes Kurtuluş received his Bachelor degree from the Department of Mechanical Engineering, Uludağ Üniversity, Turkey. He completed his MSc thesis on crash performance of vehicle compo-
nents. He is an R & D engineer in Yesilova Holding. Emre Demirci received his Bachelor and Master degree from the Department of Mechanical Engineering, Yildiz Technical University in İstanbul and Bursa Technical University, Turkey, respectively. He worked on optimum design of automobile crashboxes during his master studies. His master study was supported by the Ministry of Science, Industry and Technology of Turkey. He is currently a research assistant at Bursa Technical University. Betul Sultan Yildiz is a PhD student at Bursa Technical University, Turkey. Her research interests are optimum design of vehicle components and meta-heuristic optimization algorithms. Selçuk Karagöz received his Bachelor and Master degree from the Department of Mechanical Engineering, Uludağ Üniversity, Turkey. He is an expert on sheet metal forming and crash analysis. He is currently a lecturer at Bursa Technical University, Turkey.
58 (2016) 1
