Since its introduction, the ground structure method has been used in the derivation of closed–form analytical solutions for optimal structures, as well as providing information on the optimal load–paths. Despite its long history, the method has seen little use in three–dimensional problems or in problems with non–orthogonal domains, mainly due to computational implementation difficulties. This work presents a methodology for ground structure based topology optimization in arbitrary three–dimensional (3D) domains. The proposed approach is able to address concave domains and with the possibility of holes. In addition, an easy–to–use implementation of the proposed algorithm for the optimization of least–weight trusses is described in detail. The method is verified against three–dimensional closed–form solutions available in the literature. By means of examples, various features of the 3D ground structure approach are assessed, including the ability of the method to provide solutions with different levels of detail. The source code for a MATLAB implementation of the method, named GRAND3 — GRound structure ANalysis and Design in 3D, is available in the (electronic) Supplementary Material accompanying this publication.
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The authors appreciate constructive comments and insightful suggestions from the anonymous reviewers. We are thankful to the support from the US National Science Foundation under grant CMMI #1335160. We also acknowledge the support from SOM (Skidmore, Owings and Merrill LLP) and from the Donald B. and Elizabeth M. Willett endowment at the University of Illinois at Urbana–Champaign. Any opinion, finding, conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the sponsors.
Christensen P, Klarbring A (2009) An introduction to structural optimization, 1st edn. Springer, BerlinMATHGoogle Scholar
Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J Mech 3(1):25–52Google Scholar
Ericson C (2004) Real-time collision detection, 1st edn. Morgan Kaufmann, San FranciscoGoogle Scholar
Gerdes D (1994) Strukturoptimierung unter Anwendung der Optimalitätskriterien auf diskretisierte Tragwerke bei besonderer Berücksichtigung der Stabilität (in German). Phd thesis, Universitĺat EssenGoogle Scholar
Gilbert M, Darwich W, Tyas A, Shepherd P (2005) Application of large-scale layout optimization techniques in structural engineering practice. In: 6th world congress of structural and multidisciplinary optimizartion, June:1–10Google Scholar
Gilbert M, Tyas A (2003) Layout optimization of large-scale pin-jointed frames. Eng Comput 20(8):1044–1064CrossRefMATHGoogle Scholar
Lewiński T, Zhou M, Rozvany GIN (1994) Extended exact solutions for least-weight truss layouts–Part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36(5):375–398CrossRefMATHGoogle Scholar
Mazurek A, Baker WF, Tort C (2011) Geometrical aspects of optimum truss like structures. Struct Multidiscip Optim 43(2):231– 242CrossRefGoogle Scholar
Michell AGM (1904) The limits of economy of material in frame-structures. Philosophical Magazine Series 6 8(47):589–597CrossRefMATHGoogle Scholar
Ohsaki M (2010) Optimization of finite dimensional structures, 1st edn. CRC Press, Boca RatonCrossRefGoogle Scholar
Rozvany GIN (1997) On the validity of Prager’s example of nonunique Michell structures. Structural Optimization 13(2–3):191– 194CrossRefGoogle Scholar
Sokół T (2011) A 99 line code for discretized Michell truss optimization written in mathematica. Struct Multidiscip Optim 43(2):181–190CrossRefMATHGoogle Scholar
Stromberg LL, Beghini A, Baker WF, Paulino GH (2010) Application of layout and topology optimization using pattern gradation for the conceptual design of buildings. Struct Multidiscip Optim 43(2):165–180CrossRefGoogle Scholar
Sved G (1954) The minimum weight of certain redundant structures. Austral J Appl Sci 5:1–9Google Scholar
Tyas A, Gilbert M, Pritchard T (2006) Practical plastic layout optimization of trusses incorporating stability considerations. Comput Struct 84(3–4):115–126CrossRefGoogle Scholar
Wright MH (2004) The interior-point revolution in optimization: history, recent developments, and lasting consequences. Bull Am Math Soc 42(1):39–56CrossRefGoogle Scholar
Zegard T, Paulino GH (2014) GRAND – Ground structure based topology optimization on arbitrary 2D domains using MATLAB. Struct Multidiscip Optim 50(5):861–882CrossRefMathSciNetGoogle Scholar