In-plane material filters for the discrete material optimization method

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• 作者：René S?rensen ; Erik Lund
• 关键词：Discrete material optimization ; In ; plane material filter ; Density filter ; Laminated composite structures
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：52
• 期：4
• 页码：645-661
• 全文大小：3,661 KB
• 参考文献：Ahmad S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved elements. Int J Numer Methods Eng 2:419-51CrossRef
  Arora J, Wang Q (2005) Review of formulations for structural and mechanical system optimization. Struct Multidiscip Optim 30(4):251-72MATH MathSciNet CrossRef
  Bends?e MP (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1(4):193-02CrossRef
  Bends?e MP, Sigmund O (2003) Topology Optimization, 2nd edn. Springer
  Blasques JP, Stolpe M (2012) Multi-material topology optimization of laminated composite beam cross sections. Compos Struct 94(11):3278-289CrossRef
  Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143-158MATH MathSciNet CrossRef
  Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26-7)
  Chin CM, Fletcher R (1999) On the global convergence of an slp-filter algorithm that takes eqp steps. Numerical Analysis Report NA/199, Department of Mathematics, University of Dundee, Scotland
  Fletcher R, Leyffer S, Toint PL (1998) On the global convergence of an slp-filter algorithm. Numerical Analysis Report NA/183, Department of Mathematics, University of Dundee, Scotland
  Guest JK, Prévost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238-54MATH CrossRef
  Hvejsel C, Lund E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43(6):811-25MATH CrossRef
  Hvejsel C, Lund E, Stolpe M (2011) Optimization strategies for discrete multi-material stiffness optimization. Struct Multidiscip Optim 44(2):149-63CrossRef
  IBM ILOG (2013) IBM ILOG CPLEX Optimization Studio V12.5. http://?www.?ibm.?com
  Lazarov BS, Schevenels M, Sigmund O (2011) Robust design of large-displacement compliant mechanisms. Mech Sci 2(2):175-82CrossRef
  Lund E, Stegmann J (2005) On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy 8(1):109-24CrossRef
  Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization. John Wiley
  Panda S, Natarajan R (1981) Analysis of laminated composite shell structures by finite element method. Comput Struct 14(3-4):225-30MATH CrossRef
  Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4-5):401-24CrossRef
  S?rensen SN, S?rensen R, Lund E (2014) DMTO - a method for discrete material and thickness optimization of laminated composite structures. Struct Multidiscip Optim 50(1):25-7CrossRef
  Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009-027MATH CrossRef
  Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22(2):116-24CrossRef
  Svanberg K, Sv?rd H (2013) Density filters for topology optimization based on the pythagorean means. Struct Multidiscip Optim 48(5):859-75MathSciNet CrossRef
  Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767-84MATH CrossRef
  Zhou M, Fleury R (2012) Composite Optimization - Ply Drop-Rate Constraints for Concepts and Detailed Design. In: Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM), Beijing
  Zhou M, Fleury R, Kemp M (2011) Optimization of Composits - Recent Advances and Application. The 7th Altair CAE Technology Conference, Altair
  
• 作者单位：René S?rensen (1)
  Erik Lund (1)
  
  1. Department of Mechanical and Manufacturing Engineering, Aalborg University, Fibigerstraede 16, 9220, Aalborg East, Denmark
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488

文摘

This paper presents in-plane material filters for the Discrete Material Optimization method used for optimizing laminated composite structures. The filters make it possible for engineers to specify a minimum length scale which governs the minimum size of areas with constant material continuity. Consequently, engineers can target the available production methods, and thereby increase its manufacturability while the optimizer is free to determine which material to apply together with an optimum location, shape, and size of these areas with constant material continuity. By doing so, engineers no longer have to group elements together in so-called patches, so to statically impose a minimum length scale. The proposed method imposes the minimum length scale through a standard density filter known from topology optimization of isotropic materials. This minimum length scale is generally referred to as the filter radius. However, the results show that the density filter alone gives designs with large measures of non-discreteness. In order to obtain near discrete designs an additional threshold projection filter is applied, so to push the physical design variables towards their discrete bounds. However, because the projection filter is a non-linear function of the design variables, the projected variables have to be re-scaled in a final so-called normalization filter. This is done to prevent the optimizer in creating superior, but non-physical pseudo-materials. The method is demonstrated on a series of minimum compliance examples together with a minimum mass example, and the results show that the method is indeed capable of imposing a minimum length scale onto the optimized layup. Keywords Discrete material optimization In-plane material filter Density filter Laminated composite structures