X-FEM based Topological Optimization Method

Meisam Abdi, Ian Ashcroft, Ricky Wildman

Abstract

This study presents a new algorithm for structural topological optimization by combining the Extended Finite Element Method (X-FEM) with an evolutionary optimization algorithm. Taking advantage of an isoline design approach for boundary representation in a fixed grid domain, X-FEM can be implemented to obtain more accurate results on the boundary during the optimization process. This approach can produce topologies with clear and smooth boundaries without using a remeshing or a moving mesh algorithm. Also, reanalysing the converged solutions in NASTRAN confirms the high accuracy of the proposed method.

References

  1. Allaire, G., Jouve, F., Toader, A. M., 2004. Structural optimisation using sensitivity analysis and a level set method, J. Comp. Phys., 194, pp. 363-393.
  2. Bendsøe, M. P. 1989. Optimal shape design as a material distribution problem. Struct. Optim. 1, pp. 193-202.
  3. Bendsøe, M. P. and Kikuchi, N., 1988. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71, pp. 197-224
  4. Dunning, P., Kim, H. A. and Mullineux, G., 2008. Error analysis of fixed grid formulation for boundary based structural optimisation. In: 7th ASMO UK / ISSMO conference on Engineering Design Optimisation, 7-8 July 2008, Bath, UK.
  5. Gerstenberger, A., Wall. W. A., 2008. An eXtended finite element method/Lagrange multiplier based approach for fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 197, pp.1699- 714.
  6. Huang, X., Xie, Y. M., 2009. Evolutionary Topology Optimisation of Continuum Structures, Wiley.
  7. Lee, D., Park, S., Shin, S., 2007. Node-wise topological shape optimum design for structural reinforced modeling of Michell-type concrete deep beams. J Solid Mech Mater Eng, 1(9), pp. 1085-96.
  8. Maute, K., Ramm, E., 1995. Adaptive topology optimisation. Struct Optim, 10, pp. 100-12.
  9. Miegroet, L. V., Duysinx, P., 2007. Stress concentration minimization of 2D filets using X-FEM and level set description. Structural and Multidisciplinary Optimisation, 33, pp. 425-38.
  10. Querin, O. M., Steven, G. P. and Xie, Y. M., 1988. Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Engineering Computations, 15 ( 8), pp. 1031-1048.
  11. Moës, N., Dolbow, J. and Belytschko, T., 1999. A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering. 46, pp. 131-150.
  12. Sigmund, O., 2001. A 99 line topology optimisation code written in Matlab. Struct Multidiscipl Optim, 21, pp. 120-127.
  13. Sukumar, N., Chopp, D. L., Moës, N. and Belytschko, T., 2001. Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method. Computer Methods in Applied Mechanics and Engineering, 190, pp. 6183-6200.
  14. Victoria, M., Marti, P., Querin, O. M., 2009. Topology design of two-dimensional continuum structures using isolines. Computer and Structures, 87, pp.101-109.
  15. Victoria, M., Querin, O. M., Marti, P., 2010. Topology design for multiple loading conditions of continuum structures using isolines and isosurfaces. Finite Elements in Analysis and Design, 46 , pp. 229-237.
  16. Wang, M. Y., Wang, X., Guo, D., 2003. A level set method for structural topology optimisation. Comput. Meth .Appl. Eng., 192, pp.227-46.
  17. Wei, P., Wang, M.Y., Xing, X., 2010. A study on X-FEM in continuum structural optimization using level set method. Computer-Aided Design, 42, pp. 708-719.
  18. Xie, Y. M. and Steven, G. P., 1993. A simple evolutionary procedure for structural optimization. Computers & Structures, 49, pp. 885-896.
  19. Yang, X. Y., Xie, Y. M., Steven, G. P., and Querin, O. M., 1999. Bidirectional evolutionary method for stiffness optimisation. AIAA J., 37(11), pp.1483-1488.
  20. Zhou, M., Rozvany, G. I. N., 1991. The COG algorithm, Part II: Topological, geometrical and general shape optimisation. Comp. Meth. Appl. Mech. Eng., 89, pp. 309-336.
Download


Paper Citation


in Harvard Style

Abdi M., Ashcroft I. and Wildman R. (2012). X-FEM based Topological Optimization Method . In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012) ISBN 978-989-8565-20-4, pages 466-471. DOI: 10.5220/0004148404660471


in Bibtex Style

@conference{sddom12,
author={Meisam Abdi and Ian Ashcroft and Ricky Wildman},
title={X-FEM based Topological Optimization Method},
booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)},
year={2012},
pages={466-471},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004148404660471},
isbn={978-989-8565-20-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2012)
TI - X-FEM based Topological Optimization Method
SN - 978-989-8565-20-4
AU - Abdi M.
AU - Ashcroft I.
AU - Wildman R.
PY - 2012
SP - 466
EP - 471
DO - 10.5220/0004148404660471