![](bg6.png)
examples presented in this paper show the accuracy
and efficiency of the proposed algorithm.
ACKNOWLEDGEMENTS
The authors are grateful for the funding provided by
Loughborough University.
REFERENCES
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.
Bendsøe, M. P. 1989. Optimal shape design as a material
distribution problem. Struct. Optim. 1, pp. 193–202.
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
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.
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.
Huang, X., Xie, Y. M., 2009. Evolutionary Topology
Optimisation of Continuum Structures, Wiley.
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.
Maute, K., Ramm, E., 1995. Adaptive topology
optimisation. Struct Optim, 10, pp. 100–12.
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.
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.
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.
Sigmund, O., 2001. A 99 line topology optimisation code
written in Matlab. Struct Multidiscipl Optim, 21, pp.
120–127.
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.
Victoria, M., Martı´, P., Querin, O. M., 2009. Topology
design of two-dimensional continuum structures using
isolines. Computer and Structures, 87, pp.101–109.
Victoria, M., Querin, O. M., Mart
ı´, 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.
Wang, M. Y., Wang, X., Guo, D., 2003. A level set
method for structural topology optimisation. Comput.
Meth .Appl. Eng., 192, pp.227-46.
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.
Xie, Y. M. and Steven, G. P., 1993. A simple evolutionary
procedure for structural optimization. Computers &
Structures, 49, pp. 885-896.
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.
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.
X-FEMbasedTopologicalOptimizationMethod
471