Full Article - Open Access.

Idioma principal

Bi-directional Evolutionary Topology Optimization for Multiphysics Problems with Frequency Response Minimization

Vicente, W. M.; Picelli, R.; Pavanello, R.;

Full Article:

This work presents a topology optimization for frequency responses in multiphysics problems involving fluid-structure interaction. A mixed formulation (u/p) is used, in which the pressure and displacement are governed by Helmholtz equation and the elasticity equation, respectively. The optimization method used in this work is the Bi-directional Evolutionary Structural Optimization (BESO), which consists in a successive elimination and replacement of elements in the design domain. The feasible space of solution is defined initially and through a sensitivity analysis of the frequency response functions the evolutionary algorithm remove or add solid elements. The sensitivity analysis is described for the dynamic problems and the sensitivity numbers are evaluated for several conditions. The formulation implemented in FORTRAN aims to determine the optimum topology in order to minimize the displacement and/or pressure in specific parts of the system for a certain range of frequency excitation. A number of final topologies for vibroacoustic problems are shown, as well as their intermediary topologies and evolutionary history. The results show that this methodology can be applied to this type of problem with good efficiency.

Full Article:

Palavras-chave: Frequency Response Functions, Topology Optimization, BESO Method,


DOI: 10.5151/meceng-wccm2012-20131

Referências bibliográficas
  • [1] Bendsoe, M. P. and Sigmund, O., “Topology Optimization - Theory, Methods and Applications”. Berlin, Heidelberg, Springer-Verlag, 2003.
  • [2] Diaz, A. A. and Kikuchi, N., “Solutions to shape and topology eigenvalue optimization using a homogenization method”. Int. J. Numer. Methods. Eng. 35, 1487-1502, 199
  • [3] Ma, Z. D. and Kikuchi, N. and Cheng, H. C., “Topological design for vibrating structures”. Comp. Meth. App. Mech. 121, 259-280, 1995.
  • [4] Yoon, G. H., “Topology Optimization for stationary fluid-structure interaction problems using a new monolithic formulation”. Int J Numer Meth Eng 82, 591-616, 2010.
  • [5] Silva, F. I. and Pavanello, R., “Synthesis of porous-acoustic absorbing systems by an evolutionary optimization method”. Eng Optimiz 42, 887-905, 2010.
  • [6] Sigmund, O. and Clausen, P. M., “Topology optimization using a mixed formulation: An alternative way to solve pressure load problems”. Comput Methods Appl Mech Eng 196, 1874-1889, 2007.
  • [7] Xie, Y. M., Steven, G. P., “A simple evolutionary procedure for structural optimization”. Comput Struct 49, 885-896, 1993.
  • [8] Querin, O. M. and Steven, G. P., “Evolutionary structural optimisation (ESO) using a bidirectional algorithm”. Eng Comput 15, 1031-1048, 199
  • [9] Huang, X. and Xie, Y. M, “Convergent and mesh-independent solutions for the bidirectional evolutionary structural optimization method”. Finite Elem Anal Des 43, 1039- 1049, 2007.
  • [10] Huang, X. and Xie, Y. M, “Evolutionary topological optimization of vibrating continuum structures for natural frequencies”. Comput Struct 88, 357-364, 20
  • [11] Rozvany, G. I. N., “A critical review of established methods of structural topology optimization”. Struct Multidiscip Optimiz 37, 217-237, 2009.
  • [12] Huang, X. and Xie, Y. M, “A further review of ESO type methods for topology optimization”. Comput Struct 41, 671-683, 2010.
  • [13] Xie, Y. and Huang, X., “Evolutionary Topology Optimzation of Continuum Structures: Methods and Applications”. West Sussex, John Wiley Sons, 1st edition, 2010.
  • [14] Yoon, G. H., Sondergaard, J. and Sigmund, O., “Topology optimization of acousticstructure interaction problems using a mixed finite element formulation”. Int J Numer Meth Eng 70, 1049-1075, 2007.
  • [15] Davidsson, P., “Structure-acoustic analysis; Finite element modelling and reduction methods”. Doctoral Thesis. Lund University, Lund, Sweden, 2004.
  • [16] Nha Chu, D. and Xie, Y. M. and Hira, A. and Steven, G. P., “Evolutionary structural optimization for problems with stiffness constraints”. Finite Elem Anal Des 21, 239- 251, 1996.
  • [17] Sigmund, O. and Peterson, J., “Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima”. Struct Optimiz 16, 68-75, 1998.
  • [18] Xie, Y. M. and Steven, G. P., “Evolutionary structural optimization for dynamic problems”. Comp. Struct. 6, 1067-1073, 1996.
Como citar:

Vicente, W. M.; Picelli, R.; Pavanello, R.; "Bi-directional Evolutionary Topology Optimization for Multiphysics Problems with Frequency Response Minimization", p. 4846-4861 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-20131

últimos 30 dias | último ano | desde a publicação