DOI 10.1007/s00158-005-0530-4 RESEARCH PAPER Struct Multidisc Optim (2006) Z.-D. Ma · H. Wang · N. Kikuchi · C. Pierre · B. Raju Experimental validation and prototyping of optimum designs obtained from topology optimization Received: 21 October 2004 / Revised manuscript received: 7 February 2005 / Published online: 19 January 2006  Springer-Verlag 2006 Abstract This paper provides, through both numerical analyses and physical tests, a validation of the optimality of structural designs obtained from a topology optimiza- tion process. Issues related to the manufacturability of the topology-optimized design are first addressed in order to develop structural specimens suitable for experimental val- idation. Multidomain and multistep topology optimization techniques are introduced that, by embedding the designer’s intuition and experience into the design process, allow for the simplification of the design layout and thus for a better manufacturability of the design. A boundary identification method is also proposed that is applied to produce a smooth boundary for the design. An STL (STereo Lithography) file is then generated and used as input to a rapid prototyp- ing machine, and physical specimens are fabricated for the experiments. Finally, the experimental measurements are compared with the theoretical and numerical predictions. Results agree extremely well for the example problems con- sidered, and thus the optimum designs pass both virtual and physical tests. It is also shown that the optimum design ob- tained from topology optimization can be independent of the material used and the dimensions assumed for the structural design problem. This important feature extends the appli- cability of a single optimum design to a range of different designs of various sizes, and it simplifies the prototyping and experimental validation since small, inexpensive prototypes can be utilized. This could result in significant cost savings when carrying out proof-of-concept in the product develop- ment process. Z.-D. Ma (B ) · N. Kikuchi · C. Pierre Department of Mechanical Engineering, University of Michigan, 2250 G. G. Brown Bldg., Ann Arbor, MI 48109-2125, USA E-mail: {mazd, kikuchi, pierre}@umich.edu H. Wang MKP Structural Design Associates, Inc., 3003 Washtenaw Ave., Ann Arbor, MI 48104-5107, USA E-mail: wanghui@mkpsd.com B. Raju U.S. Army Tank-Automotive and Armaments Command Keywords Topology optimization · Experimental valida- tion · Optimal design · Structural dynamics · Noise and vibration Introduction Topology optimization has received extensive attention since the groundbreaking paper of Bendsøe and Kikuchi (1988). To date significant progress has been made using a variety of approaches, as evidenced by the number of com- mercial codes that have been developed and the variety of applications that have been treated (see Rozvany et al. 1994; Bendsøe 1995, 2003; Hassani and Hinton 1999). However, despite the great promise held by topology optimization, there is still a gap between the theory and real engineer- ing design applications. Specifically, laying out an optimum design with the effectiveness and efficiency required of an engineering product remains a considerable challenge. In an effort to fill this gap, we address in this paper some fundamental issues related to the manufacturability and proof-of-concept of new structural designs generated by top- ology optimization. A critical issue in the applicability of topology opti- mization to a practical engineering design problem is the manufacturability of the design. The optimum design ob- tained from a standard topology optimization process tends to be too complicated and without a smooth boundary; it is therefore quite difficult to manufacture. Ambrosio and Buttazzo (1993) first introduced a scheme to simplify the structural shape using a perimeter control, which was further implemented by Haber et al. (1996) with a finite element method. This technique allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale. Sigmund and Petersson (1998) provided a survey of procedures dealing with issues such as checkerboards, mesh dependencies, and local minima occur- ring in the topology optimization processes. The checker- board problem refers to the formation of regions of alternat- ing solid and void elements ordered in a checkerboardlike fashion. The mesh-dependence problem refers to obtaining