Topology Optimization of Geometrically Non-Linear Structures Using Iso-XFEM Method

Abstract:

Iso-XFEM is an evolutionary-based topology optimization method which couples the extended finite element method (X-FEM) with an isoline/isosurface optimization approach, enabling a smooth and accurate representation of the design boundary in a fixed-grid finite element mesh. This paper investigates the application of the Iso-XFEM method to the topology optimization of structures which experience large deformation. The total Lagrangian formulation of the finite element method is employed to model the geometrically non-linear behaviour and equilibrium is found by implementing the Newton-Raphson method in each evolution. A cantilever beam is considered as a test case and the Iso-XFEM solutions obtained from linear and non-linear designs are compared with bi-directional evolutionary structural optimization (BESO) solutions.

• Periodical: Key Engineering Materials (Volume 627)
• Pages: 121-124
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.627.121
• Online since: September 2014
• Authors: M. Abdi*, I. Ashcroft, Ricky D. Wildman
• Keywords: Geometrically Non-Linear, Isoline, Topology Optimization, X-FEM

References

[1] X. Huang, Y. M. Xie: Evolutionary Topology Optimisation of Continuum Structures, Wiley, (2009)

[2] Y.M. Xie and G.P. Steven: Computers & Structures, Vol. 49 (1993), pp.885-896

[3] M.Zhou, G.I.N. Rozvany: Comp. Meth. Appl. Mech. Eng., Vol. 89 (1991), pp.309-336

[4] M. Abdi, R. Wildman, I. Ashcroft: Engineering Optimization, Vol. 46 (2014), pp.628-647

[5] M. Abdi, I. Ashcroft, R. Wildman: Vol. 256 (2014), pp.277-289

[6] N. Moës, J. Dolbow, and T. Belytschko: Vol. 46 (1999), p.131–150

[7] N. Sukumar, D. L. Chopp, N. Moës and T. Belytschko: Computer Methods in Applied Mechanics and Engineering, Vol. 190 (2001), p.6183–6200

DOI: 10.1016/s0045-7825(01)00215-8

[8] K. J. Bathe: Finite element procedures. Klaus-Jurgen Bathe (2006)