Isogeometric Topology Optimization of Continuum Structures using an Evolutionary Algorithm

Document Type : Research Paper


Department of Civil Engineering, CVR College of Engineering, Hyderabad, India


Topology optimization has been an interesting area of research in recent years.  The main focus of this paper is to use an evolutionary swarm intelligence algorithm to perform Isogeometric Topology optimization of continuum structures.  A two-dimensional plate is analyzed statically and the nodal displacements are calculated.  The nodal displacements using Isogeometric analysis are found to be in good agreement with the nodal displacements acquired by standard finite element analysis.  The sizing optimization of the beam is then performed.  In order to determine the stress at each point in the beam a formulation is presented.  The optimal cross-section dimensions by performing Isogeometric analysis are acquired and verified with the cross-section dimensions achieved by hiring bending stress and shear stress criteria, as well.  The topology optimization of a two-dimensional simply supported plate continuum and a problem on three-dimensional continuum are optimized and presented.  The results show that the minimum weight which is found by applying Isogeometric topology optimization gives better results compared to the traditional finite element analysis. 


Main Subjects

[1] Archana, B., Chandrasekhar, K.N.V., (2017). “A Study on Parameters of Firefly Algorithm for Topology Optimisation of Continuum Structures – II”, i-manager’s Journal on Structural Engineering 6(1), 16-27.
[2] Clough, R.W., Penzien J. (2010), Dynamics of Structures, Computers and Structures, 2nd edition, 2010.
[3] Gondegaon S, Voruganti H. “Static Structural and Modal Analysis Using Isogeometric Analysis”, Journal of Theoretical and Applied Mechanics (JTAM), Sofia. 2016; 46(4): 36–75p.
[4] Gondegaon, S., Ahmada, R. & Voruganti, H. K. “Geometric Modeling For Isogeometric Analysis”, Proceedings of ICTACEM 2014 International Conference on Theoretical, Applied, Computational and Experimental Mechanics.
[5] Hartman “About Isogeometric analysis and the new NURBS-based Finite elements in LS-DYNA” 8th European LS-DYNA Users Conference, May 23 & 24 2011, Strasbourg, France.
[6] Hassani et. el. “An Isogeometric approach to structural topology optimization by optimality criteria” Struct Multidisc Optim (2012) 45:223–233. doi 10.1007/s00158-011-0680-5.
[7] Hughes TJR, et al. “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement”, Comput Methods in Appl Mech Eng. 2005; 194: 4135–4195p.
[8] Laura De Lorenzis, “Some recent issues and open issues on interface modelling in Civil Engineering Structures”, Materials and Structures, 2012, 45:477-503. 
[9] Luis F. R. Espatha, Alexandre L. Braunb And Armando M. Awruchb "An Introduction To Isogeometric Analysis Applied To Solid Mechanics" Mecánica Computacional Vol XXX, Págs. 1955-1975 (Artículo Completo) 1-4 November, 2011 Oscar Möller, Javier W. Signorelli, Mario A. Storti (Eds.)
[10] Lee, J. S., An, Y. N., & Chang, K. (2010, October). “Optimum structural design based on isogeometric analysis method”, In Strategic Technology (IFOST), 2010 International Forum on (pp. 377-381). IEEE.
[11] M. P. Bendsoe, O. Sigmund, "Material interpolation schemes in topology optimization", Archive of Applied Mechanics 69 (1999) 635-654.
[12] Ming-Hsiu Hsu & Yeh-Liang Hsu (2005a) “Generalization of two- and three dimensional structural topology optimization”, Engineering Optimization, 37:1, 83-102, DOI: 10.1080/03052150412331271208
[13] Ming-Hsiu Hsu, Yeh-Liang Hsu, "Interpreting three-dimensional structural topology optimization results", Computers and Structures, doi:10.1016/j.compstruc.2004.09.005
[14] Mohammad Hossein Abolbashari, Shadi Keshavarzmanesh, “On various aspects of application of the evolutionary structural optimization method for 2D and 3D continuum structures”, Finite Elements in Analysis and Design, 42 (2006) 478 – 491.
[15] Mateus Rauen et. Al., “Isogeometric analysis of free vibration of bars”, 22nd International Congress of Mechanical Engineering, November 3-7, SP, Brazil, 2013. 
[16] Milos Jockovic “Free vibration analysis of beam element using Isogeometric analysis”, 4th International conference on Contemporary achievements in Civil Engineering, 22nd April, 2016, Serbia. UDK: 519. 957 : 534.1. doi:10.14415/konferencijaGFS 2016.026.
[17] Mit Shah, Ravi Katukum (2015a) “Stress analysis without meshing Isogeometric analysis finite element method” UG Summer Internship, Boeing, India, International Conference on Innovations in Computer Science and Technology, ICICSIT 2015. 
[18] Mit Shah, Ravi Katukam (2015b) "Stress Analysis Without Meshing Iso-Geometric Analysis Finite Element Method (IGAFEM)" Boeing Summer Internship Project.
[19] Nagy Attila et. al. “On the variation formulation of stress constraints in Isogeometric design” Computational Methods in Applied Mechanics and Engineering, 199(2010) 2687-2696.
[20] N.Valizadeh, S.Sh.Ghorashi, S.Mohammadi, S.Shojaee, H.Ghasemzadeh- “An Improved Isogeometric Analysis Using the Lagrande Multiplier Method”, European Conference on extended finite element, June 29-30 July1, 2011.
[21] Reddy, A. A., Kumar, C. N., Reddy, K. A., & Chandrasekhar, K. N. V. (2017). “Optimisation of Steel Transmission Tower Structure Using Firefly Algorithm”, i-manager’s Journal on Structural Engineering, 6(2), 9-19.
[22] Vinh Phu Nguyen, Stephane P.A. Bordasa, Timon Rabczuk, "Isogeometric Analysis: An Overview and Computer Implementation Aspects" Mathematics and Computers in Simulation, Volume 117, November 2015, Pages 89-116,
[23] X.-S. Yang,“Firefly algorithm, Levy flights and global optimization”, in: Research and Development in Intelligent Systems XXVI (Eds M. Bramer, R. Ellis, M. Petridis), Springer London, pp. 209-218 (2010).
[24] X.-S. Yang, “Firefly algorithms for multimodal optimization”, in: Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, Vol. 5792, pp. 169-178 (2009).
[25] Xin-She Yang,"Swarm intelligence based algorithms: a critical analysis", Evol. Intel. (2014) 7:17–28, DOI 10.1007/s12065-013-0102-2
[26] Yeh-Liang Hsu, Ming-Sho Hsu, Chuan-Tang Chen, "Interpreting results from topology optimisation using density contours", Computers and Structures 79(2001) 1049-1058
[27] Weisse, T., 2009, Global optimisation algorithms – Theory and Applications.