Abstract
In this study, extended finite element (X-FEM) is implemented to represent topology optimization of continuum structures in a fixed grid design domain. An evolutionary optimization algorithm is used to gradually remove inefficient material from the design space during the optimization process. In the case of 2D problems, evolution of the design boundary which is supper-imposed on the fixed grid finite element framework is captured using isolines of structural performance. The proposed method does not need any remeshing approach as the X-FEM scheme can approximate the contribution of boundary elements in the finite element frame work of the problem. Therefore the converged solutions come up with clear and smooth boundaries which need no further interpretation. This approach is then extended to 3D by using a 3D X-FEM scheme implemented on isosurface topology design.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdi, M., Wildman, R., Ashcroft, I.: Evolutionary topology optimization using X-FEM and isolines. Engineering Optimization (in press, 2013)
Allaire, G., Jouve, F., Toader, A.M.: Structural optimisation using sensitivity analysis and a level set method. J. Comp. Phys. 194, 363–393 (2004)
Aremu, A., Ashcroft, I., Wildman, R., Hague, R., Tuck, C., Brackett, D.: The effects of BESO parameters on an industrial designed component for additive manufacture. Proc. IMechE Part B: J. Engineering Manufacture (2012) (in press)
Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45(5), 601–620 (1999)
Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193–202 (1989)
Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 71, 197–224 (1988)
Dunning, P., Kim, H.A., Mullineux, G.: Error analysis of fixed grid formulation for boundary based structural optimisation. In: 7th ASMO UK / ISSMO Conference on Engineering Design Optimisation, Bath, UK, July 7-8 (2008)
Lee, D., Park, S., Shin, S.: Node-wise topological shape optimum design for structural reinforced modeling of Michell-type concrete deep beams. J. Solid Mech. Mater. Eng. 1(9), 1085–1096 (2007)
Li, L., Wang, M.Y., Wei, P.: XFEM schemes for level set based structural optimization. Frontiers of Mechanical Engineering 7(4), 335–356 (2012)
Maute, K., Ramm, E.: Adaptive topology optimisation. Struct. Optim. 10, 100–112 (1995)
Miegroet, L.V., Duysinx, P.: Stress concentration minimization of 2D Filets using X-FEM and level set description. Structural and Multidisciplinary Optimisation 33, 425–438 (2007)
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 46, 131–150 (1999)
Querin, O.M., Steven, G.P., Xie, Y.M.: Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Engineering Computations 15(8), 1031–1048 (1988)
Sigmund, O.: A 99 line topology optimisation code written in Matlab. Struct. Multidiscipl. Optim. 21, 120–127 (2001)
Sukumar, N., Chopp, D.L., Moës, N., Belytschko, T.: Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method. Computer Methods in Applied Mechanics and Engineering 190, 6183–6200 (2001)
Victoria, M., MartÃ, P., Querin, O.M.: Topology design of two-dimensional continuum structures using isolines. Computer and Structures 87, 101–109 (2009)
Wang, M.Y., Wang, X., Guo, D.: A level set method for structural topology optimisation. Comput. Meth. Appl. Eng. 192, 227–246 (2003)
Wei, P., Wang, M.Y., Xing, X.: A study on X-FEM in continuum structural optimization using level set method. Computer-Aided Design 42, 708–719 (2010)
Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Computers & Structures 49, 885–896 (1993)
Yang, X.Y., Xie, Y.M., Steven, G.P., Querin, O.M.: Bidirectional evolutionary method for stiffness optimisation. AIAA J. 37(11), 1483–1488 (1999)
Zhou, M., Rozvany, G.I.N.: The COG algorithm, Part II: Topological, geometrical and general shape optimisation. Comp. Meth. Appl. Mech. Eng. 89, 309–336 (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Abdi, M., Ashcroft, I., Wildman, R. (2014). An X-FEM Based Approach for Topology Optimization of Continuum Structures. In: Obaidat, M., Filipe, J., Kacprzyk, J., Pina, N. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 256. Springer, Cham. https://doi.org/10.1007/978-3-319-03581-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-03581-9_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03580-2
Online ISBN: 978-3-319-03581-9
eBook Packages: EngineeringEngineering (R0)