a 199-line matlab code for pareto-optimal tracing in topology optimization.pdf

Struct Multidisc Optim (2010) 42:665–679 DOI 10.1007/s00158-010-0534-6 EDUCATIONAL ARTICLE A 199-line Matlab code for Pareto-optimal tracing in topology optimization Krishnan Suresh Received: 11 March 2010 / Revised: 7 June 2010 / Accepted: 10 June 2010 / Published online: 16 July 2010 c Springer-Verlag 2010 Abstract The paper ‘A 99-line topology optimization code and level-set (Allaire et al. 2004; Burger et al. 2004; Wang written in Matlab’ by Sigmund (Struct Multidisc Optim et al. 2003), now exist. If a well-defined objective can 21(2):120–127, 2001) demonstrated that SIMP-based topol- be articulated, such methods can systematically generate ogy optimization can be easily implemented in less than insightful designs for complex engineering problems. hundred lines of Matlab code. The published method and In this paper, we discuss a new and robust topology opti- code has been used even since by numerous researchers mization method for multi-objective problems, based on to advance the field of topology optimization. Inspired by the concept of topological sensitivity (Feijóo et al. 2003; the above paper, we demonstrate here that, by exploit- Novotny et al. 2003, 2005, 2006; Belytschko et al. 2003; ing the notion of topological-sensitivity (an alternate to Sokolowski and Zochowski 1999, 2003; Eschenauer et al. SIMP), one can generate Pareto-optimal topologies in about 1994; Céa et al. 2000). A salient feature of the proposed twice the number of lines of Matlab code. In other words, method is that, for compliance problems, one can trace optimal topologies for various volume fractions can be gen- the Pareto-optimal frontier (see Fig. 1) in a computation- erated in a hi