A further review of ESO type methods for topology optimization

Structural and Multidisciplinary Optimization - Tập 41 - Trang 671-683 - 2010
Xiaodong Huang1, Yi-Min Xie1
1School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, Australia

Tóm tắt

Evolutionary Structural Optimization (ESO) and its later version bi-directional ESO (BESO) have gained widespread popularity among researchers in structural optimization and practitioners in engineering and architecture. However, there have also been many critical comments on various aspects of ESO/BESO. To address those criticisms, we have carried out extensive work to improve the original ESO/BESO algorithms in recent years. This paper summarizes latest developments in BESO for stiffness optimization problems and compares BESO with other well-established optimization methods. Through a series of numerical examples, this paper provides answers to those critical comments and shows the validity and effectiveness of the evolutionary structural optimization method.

Tài liệu tham khảo

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202 Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Heidelberg Chu DN, Xie YM, Hira A, Steven GP (1996) Evolutionary structural optimization for problems with stiffness constraints. Finite Elem Anal Des 21:239–251 Cui C, Ohmori H, Sasaki M (2005) Structural design by extended ESO method. In: Proceedings of frontiers of computational sciences symposium, Nagoya, Japan, 11–13 October 2005, pp 149–156 Edwards CS, Kim HA, Budd CJ (2007) An evaluative study on ESO and SIMP for optimizing a cantilever tie-beam. Struct Multidisc Optim 34(5):403–414 Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43:1039–1049 Huang X, Xie YM (2008) A new look at the ESO/BESO optimization methods. Struct Multidisc Optim 35(1):89–92 Huang X, Xie YM (2009a) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401. doi:10.1007/s00466-008-0312-0 Huang X, Xie YM (2009b) Evolutionary topology optimization of continuum structures with a local displacement constraint. Struct Multidisc Optim 40:409–416. doi:10.1007/s00158-009-0382-4 Norato JA, Bendsøe MP, Harber RB, Tortorelli DA (2007) A topological derivative method for topology optimization. Struct Multidisc Optim 33:375–386 Ohmori H, Futai H, Iijima T, Muto A, Hasegawa Y (2005) Application of computational morphogenesis to structural design. In: Proceedings of frontiers of computational sciences symposium, Nagoya, Japan, 11–13 October 2005, pp 45–52 Querin OM, Steven GP, Xie YM (1998) Evolutionary structural optimization (ESO) using a bi-directional algorithm. Eng Comput 15:1031–1048 Querin OM, Young V, Steven GP, Xie YM (2000) Computational efficiency and validation of bi-directional evolutionary structural optimization. Comput Methods Appl Mech Eng 189:559–573 Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37:217–237 Rozvany GIN, Querin OM (2002) Combining ESO with rigorous optimality criteria. Int J Veh Des 28:294–299 Rozvany GIN, Zhou M, Sigmund O (1994) Optimization of topology. In: Adeli H (ed) Advances in design optimization. Chapman & Hall, London Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25:495–592 Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120–127 Sigmund O, Petersson J (1998) Numerical instability in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75 Stolpe M, Svanberg K (2001) On the trajectories of penalization methods for topology optimization. Struct Multidisc Optim 21:128–139 Xie YM, Steven GP (1992) Shape and layout optimization via an evolutionary procedure. In: Proceedings of the international conference computational engineering science. Hong Kong, p 421 Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896 Xie YM, Steven GP (1997) Evolutionary structural optimization. Springer, London Yang XY, Xie YM, Steven GP, Querin OM (1999) Bidirectional evolutionary method for stiffness optimization. AIAA J 37(11):1483–1488 Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:197–224 Zhou M, Rozvany GIN (2001) On the validity of ESO type methods in topology optimization. Struct Multidisc Optim 21:80–83