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Structural optimization of multibody system components described using level set techniques

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Abstract

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure.

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References

  • Arnold M, Brüls O (2007) Convergence of the generalized- α scheme for constrained mechanical systems. Multibody Systems Dynamics 18(2):185–202

    Article  MATH  Google Scholar 

  • Bendsøe M, Kikuchi N (1988) Generating optimal topologies in optimal design using a homogenization method. Computational methods in applied mechanics and engineering 71:197–224

    Article  Google Scholar 

  • Bendsøe M, Sigmund O (2003) Topology optimization: Theory, Methods, and Applications. Springer Verlag, Berlin

    Google Scholar 

  • Bestle D, Seybold J (1992) Sensitivity analysis of constrained multibody systems. Arch Appl Mech 62:181–190

    MATH  Google Scholar 

  • Brüls O, Eberhard P (2008) Sensitivity analysis for dynamic mechanical systems with finite rotations. Int J Numer Methods Eng 74(13):1897–1927

    Article  MATH  Google Scholar 

  • Brüls O, Lemaire E, Duysinx P, Eberhard P (2011) Optimization of multibody systems and their structural components. In: Multibody Dynamics: Computational Methods and Applications, vol 23, pp 49–68. Springer

  • Bruns T, Tortorelli D (1995) Computer-aided optimal design of flexible mechanisms. In: Proceedings of the Twelfth Conference of the Irish Manufacturing Commitee, IMC12, Competitive Manufacturing. University College Cork, Ireland

    Google Scholar 

  • Chung J, Hulbert G (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized- α method. J Appl Mech 60:371–375

    Article  MathSciNet  MATH  Google Scholar 

  • Deaton J, Grandhi R (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38

    Article  MathSciNet  Google Scholar 

  • Duysinx P, Zhang W, Zhong H, Beckers P, Fleury C (1994) Structural shape optimization with error control. In: Proceedings of the 20th ASME Design Automation Conference, Mineapolis

  • Géradin M, Cardona A (2001) Flexible Multibody Dynamics: A Finite Element Approach. John Wiley, New York

    Google Scholar 

  • Haftka R, Grandhi R (1986) Structural shape optimization - a survey. Comput Methods Appl Mech Eng 57:91–106

    Article  MathSciNet  MATH  Google Scholar 

  • Häussler P, Emmrich D, Müller O, Ilzhöfer B, Nowicki L, Albers A (2001) Automated topology optimization of flexible components in hybrid finite element multibody systems using ADAMS/Flex and MSC.Construct. In: Proceedings of the 16th European ADAMS Users’ Conference

  • Häussler P, Minx J, Emmrich D (2004) Topology optimization of dynamically loaded parts in mechanical systems: Coupling of MBS, FEM and structural optimization. In: Proceedings of NAFEMS Seminar Analysis of Multi-Body Systems Using FEM and MBS, Wiesbaden

  • Hong E, You B, Kim C, Park G (2010) Optimization of flexible components of multibody systems via equivalent static loads. Structural Multidisciplinary Optimization 40:549–562

    Article  MathSciNet  MATH  Google Scholar 

  • Kang B, Park G, Arora J (2005) Optimization of flexible multibody dynamic systems using the equivalent static load method. AIAA J 43(4):846–852

    Article  Google Scholar 

  • Kim N, Chang Y (2005) Eulerian shape design sensitivity analysis and optimization with a fixed grid. Comput Methods Appl Mech Eng 194:3291–3314

    Article  MathSciNet  MATH  Google Scholar 

  • Norato J, Haber R, Tortorelli D, Bendsøe M (2004) A geometry projection method for shape optimization. Int J Numer Methods Eng 60:2289–2312

    Article  MATH  Google Scholar 

  • Oral S, Kemal Ider S (1997) Optimum design of high-speed flexible robotic arms with dynamic behavior constraints. Comput Struct 65(2):255–259

    Article  MATH  Google Scholar 

  • Osher S, Sethian J (1988) Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12–49

    Article  MathSciNet  MATH  Google Scholar 

  • Schleupen A, Maute K, Ramm E (2000) Adaptive fe-procedures in shape optimization. Struct Multidiscip Optim 19(4):282– 302

    Article  Google Scholar 

  • Seifried R, Held A (2011) Integrated design approaches for controlled flexible multibody systems. In: Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2011), Washington DC

  • Shapiro V (2007) Semi-analytic geometry with r-functions. Acta Numerica 16:239–303

    Article  MathSciNet  MATH  Google Scholar 

  • Sherif K, Irschik H (2010) Efficient topology optimization of large dynamic finite element systems using fatigue. AIAA J 48(7):1339–1347

    Article  Google Scholar 

  • Sigmund O, Maute K (2013) Topology optimization approaches: A comparative review. Struct Multidiscip Optim 48(6):1031–1055

    Article  MathSciNet  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359– 373

    Article  MathSciNet  MATH  Google Scholar 

  • Tobias C, Fehr J, Eberhard P (2010) Durability-based structural optimization with reduced elastic multibody systems. In: Proceedings of 2 nd International Conference on Engineering Optimization, Lisbon

  • Tromme E, Brüls O, Emonds-Alt J, Bruyneel M, Virlez G, Duysinx P (2013) Discussion on the optimization problem formulation of flexible components in multibody systems. Structural Multidisciplinary Optimization 48:1189–1206

    Article  Google Scholar 

  • Van Dijk N, Maute K, Langelaar M, Van Keulen F (2013) Level-set methods for structural topology optimization: a review. Structural Multidisciplinary Optimization 48:437–472

    Article  MathSciNet  Google Scholar 

  • Van Keulen F, Haftka R, Kim N (2005) Review of options for structural design sensitivity analysis. Part 1: Linear systems. Comput Methods Appl Mech Eng 194:3213–3243

    Article  MathSciNet  MATH  Google Scholar 

  • Van Miegroet L, Duysinx P (2007) Stress concentration minimization of 2D filets using x-fem and level set description. Structural Multidisciplinary Optimization 33:425–438

    Article  Google Scholar 

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Acknowledgments

The first author wishes to acknowledge the LIGHTCAR Project sponsored by the pole of competitiveness “Mecatech” and the Walloon Region of Belgium for their supports (Contract RW-6500).

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Correspondence to Emmanuel Tromme.

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Tromme, E., Tortorelli, D., Brüls, O. et al. Structural optimization of multibody system components described using level set techniques. Struct Multidisc Optim 52, 959–971 (2015). https://doi.org/10.1007/s00158-015-1280-6

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  • DOI: https://doi.org/10.1007/s00158-015-1280-6

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