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http://dx.doi.org/10.12989/sem.2020.76.6.799

Optimum design of shape and size of truss structures via a new approximation method  

Ahmadvand, Hosein (Department of Civil Engineering, University of Kurdistan)
Habibi, Alireza (Department of Civil Engineering, Shahed University)
Publication Information
Structural Engineering and Mechanics / v.76, no.6, 2020 , pp. 799-821 More about this Journal
Abstract
The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.
Keywords
consistent approximation; shape optimization; size optimization; truss structures;
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Times Cited By KSCI : 9  (Citation Analysis)
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1 Tejani, G. G., Pholdee, N., Bureerat, S., Prayogo, D., and Gandomi, A. H. (2019), "Structural optimization using multi-objective modified adaptive symbiotic organisms search", Expert Syst. Appl, 125, 425-441.   DOI
2 Tejani, G. G., Savsani, V. J., Bureerat, S., and Patel, V. K. (2018b), "Topology and Size Optimization of Trusses with Static and Dynamic Bounds by Modified Symbiotic Organisms Search", J. Comput. Civ. Eng, 32(2), 4017085.   DOI
3 Tejani, G. G., Savsani, V. J., Patel, V. K., and Bureerat, S. (2017), "Topology, shape, and size optimization of truss structures using modified teaching-learning based optimization", J. Comput. Civ. Eng, 2(4), 313-331.
4 Tejani, G. G., Savsani, V. J., Patel, V. K., and Mirjalili, S. (2018c), "Truss optimization with natural frequency bounds using improved symbiotic organisms search", Knowledge-Based Syst, 143, 162-178.   DOI
5 Mortazavi, A., Togan, V., and Nuhoglu, A. (2017b), "Weight minimization of truss structures with sizing and layout variables using integrated particle swarm optimizer", J. Civ. Eng. Manag, 23(8), 985-1001.   DOI
6 Muller, T. E., and Klashorst, E. (2017), "A quantitative comparison between size, shape, topology and simultaneous optimization for truss structures", Lat. Am. J. Solids Struct, 14(12), 2221-2242.   DOI
7 Najian Asl, R., Aslani, M., and Shariat Panahi, M. (2013), Sizing Optimization of Truss Structures Using A Hybridized Genetic Algorithm. NASA ADS.
8 Nguyena, X. H., and Lee, J. (2015), "Sizing, shape and topology optimization of trusses with energy approach", Struct. Eng. Mech, 56(1), 107-121.   DOI
9 Darvishi, P., and Shojaee, S. (2018), "Size and geometry optimization of truss structures using the combination of DNA computing algorithm and generalized convex approximation method", Int. J. Optim. Civ. Eng, 8(4), 625-656.
10 Dede, T., and Ayvaz, Y. (2015), "Combined size and shape optimization of structures with a new meta-heuristic algorithm", Appl. Soft Comput. J, 28, 250-258.   DOI
11 Degertekin, S. O., Lamberti, L., and Ugur, I. B. (2019), "Discrete sizing/layout/topology optimization of truss structures with an advanced Jaya algorithm", Appl. Soft Comput. J, 79, 363-390.   DOI
12 Ahrari, A., and Atai, A. A. (2013), "Fully stressed design evolution strategy for shape and size optimization of truss structures", Comput. Struct, 123, 58-67.   DOI
13 Ahrari, A., Atai, A. A., and Deb, K. (2015), "Simultaneous topology, shape and size optimization of truss structures by fully stressed design based on evolution strategy", Eng. Optim, 47(8), 1063-1084.   DOI
14 Felix, J. E. (1981), "Shape optimization of trusses subject to strength, displacement, and frequency constraints", Master's Thesis, Naval Postgraduate School.
15 Fleury, C. (1979), "A unified approach to structural weight minimization", Comput. Methods Appl. Mech. Eng, 20(1), 17-38.   DOI
16 Fleury, C. (1989), "CONLIN: An efficient dual optimizer based on convex approximation concepts", Struct. Optim, 1(2), 81-89.   DOI
17 Fleury, C., and Braibant, V. (1986), "Structural optimization: A new dual method using mixed variables", Int. J. Numer. Methods Eng, 23(3), 409-428.   DOI
18 Rahami, H., Kaveh, A., and Gholipour, Y. (2008), "Sizing, geometry and topology optimization of trusses via force method and genetic algorithm", Eng. Struct, 30(9), 2360-2369.   DOI
19 Ghoddosian, A., and Sheikhi Azqandi, M. (2011), "Using particle swarm optimization for minimization of moment peak in structure", Aust. J. Basic Appl. Sci, 5(8), 1428-1434.
20 Noii, N., Aghayan, I., Hahjirasouliha, I., and Kunt, M. M. (2016), "A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA", J. Civ. Eng. Manag, 23(2), 252-262.   DOI
21 Rajeev, S., and Krishnamoorthy, C. S. (1997), "Genetic algorithms-based methodologies for design optimization of trusses", J. Struct. Eng, 123(3), 350-358.   DOI
22 Schmit, L. A., and Farshi, B. (1974), "Some approximation concepts for structural synthesis", AIAA J, 12(5), 692-699.   DOI
23 Serpik, I. N., Alekseytsev, A. V., and Balabin, P. Y. (2017), "Mixed approaches to handle limitations and execute mutation in the genetic algorithm for truss size, shape and topology optimization", Period. Polytech. Civ. Eng, 61(3), 471-482.
24 Lamberti, L., and Pappalettere, C. (2004). "Improved sequential linear programming formulation for structural weight minimization." Comput. Methods Appl. Mech. Eng, 193(33-35), 3493-3521.   DOI
25 Shojaee, S., Arjomand, M., and Khatibinia, M. (2013), "A hybrid algorithm for sizing and layout optimization of truss structures combining discrete PSO and convex approximation", Int. J. Optim. Civ. Eng, 3(1), 57-83.
26 Lamberti, L. (2008), "An efficient simulated annealing algorithm for design optimization of truss structures", Comput. Struct, 86(19-20), 1936-1953.   DOI
27 Lamberti, L., and Pappalettere, C. (2003), "Move limits definition in structural optimization with sequential linear programming. Part II: Numerical examples", Comput. Struct, 81(4), 214-238.
28 Lee, K. S., and Geem, Z. W. (2004), "A new structural optimization method based on the harmony search algorithm", Comput. Struct, 82(9-10), 781-798.   DOI
29 Goncalves, M. S., Lopez, R. H., and Miguel, L. F. F. (2015), "Search group algorithm: a new metaheuristic method for the optimization of truss structures", Comput. Struct, 153, 165-184.   DOI
30 Gholizadeh, S., Barzegar, A., and Gheyratmand, C. (2011), "Shape optimization of structures by modified harmony search", Int. J. Optim. Civ. Eng, 3, 485-494.
31 Grygierek, K. (2016), "Optimization of trusses with self-adaptive approach in genetic algorithms", Archit. Civ. Eng. Environ. J, 9(4), 67-78.
32 Habibi, A. R. (2012), "New approximation method for structural optimization", J. Comput. Civ. Eng, 26(2), 236-247.   DOI
33 Hansen, S. R., and Vanderplaats, G. N. (1990). "Approximation method for configuration optimization of trusses." AIAA J, 28(1), 161-168.   DOI
34 Vanderplaats, G. N., Thomas, H. L., and Shyy, Y. K. (1991), "A review of approximation concepts for structural synthesis", Comput. Syst. Eng 2(1), 17-25.   DOI
35 Hosseini, S. S., Hamidi, S. A., Mansuri, M., and Ghoddosian, A. (2015), "Multi objective particle swarm optimization (MOPSO) for size and shape optimization of 2D truss structures", Period. Polytech. Civ. Eng, 59(1), 9-14.   DOI
36 Tejani, G. G., Savsani, V. J., Patel, V. K., and Savsani, P. V. (2018d), "Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics", J. Comput. Des. Eng, 5(2), 198-214.   DOI
37 Toklu, Y. C., Bekdas, G., and Temur, R. (2013), "Analysis of trusses by total potential optimization method coupled with harmony search", Struct. Eng. Mech, 45(2), 183-199.   DOI
38 Wang, D., Zhang, W. H., and Jiang, J. S. (2002a), "Truss shape optimization with multiple displacement constraints", Comput. Methods Appl. Mech. Eng, 191(33), 3597-3612.   DOI
39 Lee, K. S., Han, S. W., and Geem, Z. W. (2011), "Discrete size and discrete-continuous configuration optimization methods for truss structures using the harmony search algorithm", Int. J. Optim. Civ. Eng, 1(1), 107-126.
40 Lee, K. S., and Geem, Z. W. (2005), "A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice", Comput. Methods Appl. Mech. Eng, 194(36-38), 3902-3933.   DOI
41 Miguel, L. F. F., Lopez, R. H., and Miguel, L. F. F. (2013), "Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm", Adv Eng Softw, 56, 23-37.   DOI
42 Imai, K., and Schmit, L. A. (1981), "Configuration optimization of trusses", J. Struct. Div. ASCE, 107, 745-756.   DOI
43 Mortazavi, A., and Togan, V. (2016), "Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer", Struct. Multidiscip. Optim, 54(4), 715-736.   DOI
44 Mortazavi, A., Togan, V., and Nuhoglu, A. (2017a), "An integrated particle swarm optimizer for optimization of truss structures with discrete variables", Struct. Eng. Mech, 61(3), 359-370.   DOI
45 Hwang, S. F., and He, R. S. (2006), "A hybrid real-parameter genetic algorithm for function optimization", Adv. Eng. Informatics, 20(1), 7-21.   DOI
46 Kalatjari, V. R., and Talebpour, M. H. (2018), "Optimization of skeletal structures using improved genetic algorithm based on proposed sampling search space idea", Int. J. Optim. Civ. Eng, 8(3), 415-432.
47 Kaveh, A., and Ahmadi, B. (2014), "Sizing, geometry and topology optimization of trusses using force method and supervised charged system search", Struct. Eng. Mech, 50(3), 365-382.   DOI
48 Kaveh, A., and Mahdavi, V. (2015), "Colliding bodies optimization for size and topology optimization of truss structures", Struct. Eng. Mech, 53(5), 847-865.   DOI
49 Wang, L., and Grandhi, R. V. (1995), "Improved two-point function approximations for design optimization", AIAA J, 33(9), 1720-1727.   DOI
50 Wang, D., Zhang, W. H., and Jiang, J. S. (2002b), "Combined shape and sizing optimization of truss structures", Comput. Mech, 29(4-5), 307-312.   DOI
51 Wu, S. J., and Chow, P. T. (1995), "Integrated discrete and configuration optimization of trusses using genetic algorithms", Comput. Struct, 55(4), 695-702.   DOI
52 Xie, Y. M., and Steven, G. P. (1997), "Basic evolutionary structural optimization", Evol. Struct. Optim, 12-29.
53 Yang, J. P. (1996), "Development of genetic algorithm-based approach for structural optimization", Ph.D. Dissertation, Singapore: Nanyang Technology University.
54 Techasen, T., Wansasueb, K., Panagant, N., Pholdee, N., and Bureerat, S. (2018), "Multiobjective simultaneous topology, shape and sizing optimization of trusses using evolutionary optimizers", Proceedings of the IOP Conference Series: Materials Science and Engineering, 20-29.
55 Sonmez, M. (2011), "Artificial Bee Colony algorithm for optimization of truss structures", Appl. Soft Comput, 11(2), 2406-2418.   DOI
56 Svanberg, K. (1987), "The method of moving asymptotes-a new method for structural optimization", Int. J. Numer. Methods Eng, 24(2), 359-373.   DOI
57 Tang, W., Tong, L., and Gu, Y. (2005), "Improved genetic algorithm for design optimization of truss structures with sizing, shape and topology variables", Int. J. Numer. Methods Eng, 62(13), 1737-1762.   DOI
58 Kumar, S., Tejani, G. G., and Mirjalili, S. (2019), "Modified symbiotic organisms search for structural optimization", Eng. Comput, 35(4), 1269-1296.   DOI
59 Kaveh, A., and Talatahari, S. (2011), "An enhanced charged system search for configuration optimization using the concept of fields of forces", Struct. Multidiscip. Optim, 43(3), 339-351.   DOI
60 Kaveh, A., and Zolghadr, A. (2014), "A new PSRO algorithm for frequency constraint truss shape and size optimization Hybrid View project A new PSRO algorithm for frequency constraint truss shape and size optimization", Struct. Eng. Mech, 52(3), 445-468.   DOI
61 Kumar, S., Tejani, G. G., Pholdee, N., and Bureerat, S. (2020), "Multi-objective modified heat transfer search for truss optimization", Eng. Comput.
62 Kuritz, S. P., and Fleury, C. (1989), "Mixed variable structural optimization using convex linearization techniques", Eng. Optim, 15(1), 27-41.   DOI
63 Arora, J. S. (1989), Introduction to Optimum Design, McGraw-Hill, New York, USA.
64 Belegundu, A. D., and Arora, J. S. (1985), "A study of mathematical programmingmethods for structural optimization. Part II: Numerical results", Int. J. Numer. Methods Eng, 21(9), 1601-1623.   DOI
65 Cao, H., Qian, X., Chen, Z., and Zhu, H. (2017), "Enhanced particle swarm optimization for size and shape optimization of truss structures", Eng. Optim, 49(11), 1939-1956.   DOI
66 Cazacu, R., and Grama, L. (2014), "Steel truss optimization using genetic algorithms and FEA", Proceedings of the 7th International Conference Interdisciplinarity in Engineering (INTER-ENG 2013), 339-346.
67 Chu, D. N. (1997), "Evolutionary structural optimization method for systems with stiffness and displacement constraints", Ph.D. Dissertation, Department of Civil and Building Engineering, Victoria University of Technology, Melbourne, Australia.
68 Tejani, G. G., Pholdee, N., Bureerat, S., and Prayogo, D. (2018a), "Multiobjective adaptive symbiotic organisms search for truss optimization problems", Knowledge-Based Syst, 161, 398-414.   DOI