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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 81
Edited by: B.H.V. Topping
Paper 118

Topology Optimisation using the SERA Method with a BESO Bias on Element Admission

R.N. Brodie, O.M. Querin and D.C. Barton

School of Mechanical Engineering, University of Leeds, United Kingdom

Full Bibliographic Reference for this paper
R.N. Brodie, O.M. Querin, D.C. Barton, "Topology Optimisation using the SERA Method with a BESO Bias on Element Admission", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 118, 2005. doi:10.4203/ccp.81.118
Keywords: structural optimisation, SERA, ESO, BESO, topology, hard-kill methods, element rejections, element admission.

"By slowly removing inefficient material from a structure, the shape of the structure evolves towards an optimum" [1]. This is the simple concept of Evolutionary Structural Optimisation (ESO). The ESO strategy uses an iterative material removal method in an attempt to recreate processes seen in nature. Structural topologies are generated by 'removing' elements that are not being used efficiently according to some response parameter. the Bi-directional Evolutionary Structural Optimisation (BESO) facilitates the reintroduction of elements around elements with a high response parameter [2].

Various problems have been reported with the ESO strategy including the lack of optimality and inefficiency of solution time [3]. The Sequential Element Rejection and Admission (SERA) method [4], is the next step in the development of the ESO methods. SERA is aimed at addressing the problems highlighted with the ESO method.

Instead of removing material, as in the ESO approach, the SERA method changes the stiffness of rejected elements to near zero. This material with negligible stiffness is termed `virtual' material. The stress level in the virtual material is used as an admission criteria to dictate element introduction into the real material domain. With this ground structure admission criteria, topologies can be 'grown' from the virtual material into real material. Similarly like the traditional ESO approach, material can be removed from the real into the virtual material. The final topology is constructed from all real material present at the end of the optimisation.

This paper presents the implementation of the SERA method using a BESO like element admission process. The elemental admission criteria is evaluated by filtering the criteria of real material into the virtual material domain. Through this approach the elements bordering real material are more likely to be admitted into the design domain than the rest of the virtual elements. This results in material being added around the parts of the structure that have the highest value for the driving criteria.

The SERA method was implemented using MATLAB. Results are given. It has been observed that this new method of SERA optimisation yields topologies that compare favourably with those produced by other optimisation methods.

Xie, Y.M.; Steven, G.P.; "Shape and layout optimisation via an evolutionary procedure", Proc. Int. Conf. Comp. Engrg. p. 471. Hong Kong University, 1992.
Querin, O.M.; Steven, G.P.; Xie, Y.M.; "Evolutionary Structural Optimisation (ESO) using bi-directional algorithm". Eng. Comp. 15, 1031-1048, 1998. doi:10.1108/02644409810244129
Zhou, M.; Rozvany, G.I.N.; "On the validity of ESO type methods in topology optimisation", Struct. multidisc. Optim. 21 , 80-83, 2001. doi:10.1007/s001580050170
Brodie, R.N., Querin, O.M., Rozvany, G.I.N., Barton, D.C; "Development and application of the SERA method for topology optimisation", 5th ASMO-UK / ISSMO Conference on Engineering Design Optimization, 2004.

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