AN IMPROVED BEM-LSM COUPLING-BASED TOPOLOGY OPTIMIZATION
DOI:
https://doi.org/10.26512/ripe.v2i6.21471Palavras-chave:
BEM-LSM coupling. Topology Optimization. Boundary Element Method.Resumo
Topology Optimization (TO) is recognized as an important approach during early stages of structural concept. It allows the designer for finding higher performance solutions taking into account the limitation of natural resources. Most computational TO procedures are based on domain methods, in which feasible solutions are searched in relaxed design space. In such a case, jagged faces and grey-scale interpolations often lead to artificial stresses along the optimization. This study presents an algorithm for two-dimensional structural analysis, which overcomes such a difficulty. In addition it allows addressing both shape and topology changes. The coupling between Level Set Method and Boundary Element Method provides precise topologies along the whole optimization process. A benchmark example is used to illustrate its accuracy. The advantages of the proposed procedures are summarized as follows. Firstly, it is a gradient-based approach requiring information only at the boundary. Secondly, it leads to lower computational effort if compared to other available methodologies. The presented formulation shows efficiency and brings out new research perspectives.
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Abe K., Kazama S., Koro K., 2007. A boundary element approach for topology optimization problem using the level set method. Communications in numerical methods in engineering, v. 23, p. 405-416.
Allaire G., Jouve F., Toader A-M., 2004. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, v.194, p.363-393.
Alliabadi M.H. The boundary element method. Applications in solids and structures. v. 2, New York: J. Wiley, 2002.
Bendsoe M.P., 1989. Optimal shape design as a material distribution problem. Structural Optimization, v.1, p.193-202.
Bendsoe M.P., Kikuchi N., 1988. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, v. 71, p.197-224.
Brebbia C.A., Dominguez J. Boundary Elements: An Introductory Course, Southampton: McGraw Hill, 1989.
Marczak R.J., 2007. Topology optimization and boundary elements ”“ a preliminary implementation for linear heat transfer. Engineering Analysis with Boundary Elements, v.31, p.793-802.
Osher S., Sethian J.A. Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Journal of Computational Physics, v.79, p. 12-49, 1988.
Rozvany G.I.N., 2009. A critical review of established methods of structural topology optimization. Struct Multidisc Optim, v. 37, p.217-237.
Sethian J.A., 1999. Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer visions, and material science, ed.2, Cambridge Universty Press, New York.
Sethian J.A., Wiegmann A., 2000. Structural Boundary Design via Level Set and Immersed Interface Methods. Journal of Computational Physics, v.163, p.489-528.
Sigmund O., Maute K., 2013. Topology optimization approaches - A comparative review. Struct Multidisc Optim, v. 48, p.1031-1055.
Tai K., Fenner R.T., 1996. Optimum shape design and positioning of features using the boundary integral equation method. International Journal for Numerical Methods in Engineering, v.39, p.1985-2003.
Ullah B., Trevelyan J., Ivrissimtzis I., 2015. A three-dimensional implementation of the boundary element and level set based strucutral optimization. Engineering Analysis with Boundary Elements, v. 58, p.176-194.
Ullah B., Trevelyan J., Matthews P.C., 2014. Structural optimization based on the boundary element and level set methods. Computer and Structures, v.137, p.14-30.
Yamada T. et al., 2010. A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput. Methods Appl. Mech. Engrg. v.199, p.2876-2891.
Yamasaki S., Yamada T., Matsumoto T., 2013. An immersed boundary element method for level-set based topology optimization. International Journal for Numerical Methods in Engineering, v. 93, p.960-988.
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