System-based approaches for structural optimization of flexible mechanisms

Tromme, Emmanuel; Held, Alexander; Duysinx, Pierre; Bruls, Olivier

doi:10.1007/s11831-017-9215-6

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System-based approaches for structural optimization of flexible mechanisms

Tromme, Emmanuel; Held, Alexander; Duysinx, Pierre et al.

2018 • In Archives of Computational Methods in Engineering, 25 (817-844)

Peer reviewed

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https://hdl.handle.net/2268/213368

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10.1007/s11831-017-9215-6

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Keywords :

Structural optimization; Flexible multibody dynamics; Weakly and fully coupled methods

Abstract :

[en] This paper reviews the state-of-the-art methods to perform structural optimization of flexible mechanisms. These methods are based on a system-based approach, i.e. the formulation of the design problem incorporates the time response of the mechanism that is obtained from a dynamic simulation of the flexible multibody system. The system-based approach aims at considering as precisely as possible the effects of nonlinear dynamic loading under various operating conditions. Also, the optimization process enhances most existing studies which are limited to (quasi-) static or frequency domain loading conditions. This paper briefly introduces flexible multibody system dynamics and structural optimization techniques. Afterwards, the two main methods, named the weakly and the fully coupled methods, that couple both disciplines are presented in details and the influence of the multibody system formalism is analyzed. The advantages and drawbacks of both methods are discussed and future possible research areas are mentioned.

Disciplines :

Mechanical engineering
Aerospace & aeronautics engineering

Author, co-author :

Tromme, Emmanuel; Toyota Central R&D Labs, Inc.

Held, Alexander; Hamburg University of Technology > Institute of Mechanics and Ocean Engineering

Duysinx, Pierre ; Université de Liège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres

Bruls, Olivier ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques

Language :

English

Title :

System-based approaches for structural optimization of flexible mechanisms

Publication date :

2018

Journal title :

Archives of Computational Methods in Engineering

ISSN :

1134-3060

Publisher :

International Center for Numerical Methods in Engineering, Barcelona, Spain

Volume :

Issue :

817-844

Peer reviewed :

Peer reviewed

Available on ORBi :

since 03 August 2017

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6 (4 by ULiège)

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Bibliography

Afimiwala K, Mayne R (1974) Optimal design of an impact absorber. J Eng Ind 96:124–130. doi:10.1115/1.3438286
Albers A, Häussler P (2005) Topology optimization of dynamic loaded parts using multibody simulation and durability analysis. In: Proceedings of the Nafems Seminar: optimization in structural mechanics, Wiesbaden, Germany
Albers A, Emmrich D, Häussler P (2002) Automated structural optimization of flexible components using msc.adams/flex and msc.nastran sol200. In: Proceedings of the 1st European MSC.ADAMS Users’ Conference, Germany
Albers A, Ottnad J, Häussler P, Minx J (2007) Structural optimization of components in controlled mechanical systems. In: Proceedings of the 6th international conference on multibody systems, nonlinear dynamics, and control, Las Vegas, Nevada, USA
Ambrósio J, Neto M, Leal R (2007) Optimization of a complex flexible multibody systems with composite materials. Multibody Syst Dyn 18(2):117–144. doi:10.1007/s11044-007-9086-y
Amir O, Stolpe M, Sigmund O (2010) Efficient use of iterative solvers in nested topology optimization. Struct Multidiscip Optim 42(1):55–72. doi:10.1007/s00158-009-0463-4
Ashrafiuon H, Mani N (1990) Analysis and optimal design of spatial mechanical systems. J Mech Des 112(2):200–207. doi:10.1115/1.2912593
Bastos G Jr, Brüls O (2015) An integrated control-structure design for manipulators with flexible links. IFAC-PapersOnLine 48(11):156–161. doi:10.1016/j.ifacol.2015.09.176
Bastos G Jr, Seifried R, Brüls O (2013) Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach. Multibody Sys Dyn 30(3):359–376. doi:10.1007/s11044-013-9361-z
Bauchau O (2011) Flexible multibody dynamics. Springer, Netherlands. doi:10.1007/978-94-007-0335-3
Bauchau O, Trainelli L (2003) The vectorial parameterization of rotation. Nonlinear Dyn 32(1):71–92. doi:10.1023/A:1024265401576
Bauchau O, Damilano G, Theron N (1995) Numerical integration of non-linear elastic multi-body systems. Int J Numer Methods Eng 38(16):2727–2751. doi:10.1002/nme.1620381605
Beckers P (1991) Recent developments in shape sensitivity analysis: the physical approach. Eng Optim 18(1–3):67–78. doi:10.1080/03052159108941012
Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer Verlag, Berlin. doi:10.1007/978-3-662-05086-6
Bestle D, Eberhard P (1992) Analyzing and optimizing multibody systems. J Struct Mech 20(1):67–92. doi:10.18419/opus-4555
Bestle D (1992) Sensitivity analysis of constrained multibody systems. Arch Appl Mech 62:181–190. doi:10.1007/BF00787958
Bletzinger KU, Firl M, Linhard J, Wüchner R (2010) Optimal shapes of mechanically motivated surfaces. Comput Methods Appl Mech Eng 199(5–8):324–333. doi:10.1016/j.cma.2008.09.009
Bobrow J, Dubowsky S, Gibson J (1985) Time-optimal control of robotic manipulators along specified paths. Int J Robot Res 4:3–17. doi:10.1177/027836498500400301
Bottasso C, Croce A (2004) Optimal control of multibody systems using an energy preserving direct transcription method. Multibody Syst Dyn 12:17–45. doi:10.1023/B:MUBO.0000042931.61655.73
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Braibant V, Fleury C (1984) Shape optimal design using b-splines. Comput Methods Appl Mech Eng 44(3):247–267. doi:10.1016/0045-7825(84)90132-4
Brüls O, Cardona A (2010) On the use of Lie group time integrators in multibody dynamics. J Comput Nonlinear Dyn 5(3):0310002. doi:10.1115/1.4001370
Brüls O, Eberhard P (2008) Sensitivity analysis for dynamic mechanical systems with finite rotations. Int J Numer Methods Eng 74(13):1897–1927. doi:10.1002/nme.2232
Brüls O, Lemaire E, Duysinx P, Eberhard p (2011) Optimization of multibody systems and their structural components. Multibody dynamics: computational methods and applications. Springer, New York, pp 49–68. doi:10.1007/978-90-481-9971-6_3
Brüls O, Cardona A, Arnold M (2012) Lie group generalized- α time integration of constrained flexible multibody systems. Mech Mach Theory 48:121–137. doi:10.1016/j.mechmachtheory.2011.07.017
Bruns T, Tortorelli D (1995) Computer-aided optimal design of flexible mechanisms. Proceedings of the Twelfth Conference of the Irish Manufacturing Commitee, IMC12, Competitive Manufacturing. University College Cork, Cork, pp 29–36
Bruyneel M, Duysinx P, Fleury C (2002) A family of MMA approximations for structural optimization. Struct Multidiscip Optim 24:263–276. doi:10.1007/s00158-002-0238-7
Cardona A (1989) An integrated approach to mechanism analysis. PhD thesis, Université de Liège
Cardona A, Geradin M (1989) Time integration of the equations of motion in mechanism analysis. Comput Struct 33(3):801–820. doi:10.1016/0045-7949(89)90255-1
Cardoso J, Arora J (1992) Design sensitivity analysis of nonlinear dynamic response of structural and mechanical systems. Struct Optim 4(1):37–46. doi:10.1007/BF01894079
Cassis J, Schmit L (1976) Optimum structural design with dynamic constraints. J Struct Div 102(10):2053–2071
Choe U, Gang S, Sin M, Park G (1996) Transformation of a dynamic load into an equivalent static load and shape optimization of the road arm in self-propelled howitzer. Korean Soc Mech Eng 20(12):3767–3781. doi:10.22634/KSME-A.1996.20.12.3767
Choi W, Park G (1999) Transformation of dynamic loads into equivalent static loads based on modal analysis. Int J Numer Methods Eng 46(1):29–43. doi:10.1002/(SICI)1097-0207(19990910)46:1h29::AID-NME661i3.0.CO;2-D
Choi W, Park G (2002) Structural optimization using equivalent static loads at all time intervals. Comput Methods Appl Mech Eng 191(19–20):2105–2122. doi: 10.1016/S0045-7825(01)00373-5
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. doi:10.1115/1.2900803
Cleghorn W, Fenton R, Tabarrok B (1981) Optimum design of high-speed flexible mechanisms. Mech Mach Theory 16(4):399–406. doi:10.1016/0094-114X(81)90013-6
Collard J, Duysinx P, Fisette P (2010) Optimal synthesis of planar mechanisms via an extensible-link approach. Struct Multidiscip Optim 42(3):403–415. doi:10.1007/s00158-010-0500-3
Colson B, Bruyneel M, S Grihon, Raick C (2010) Optimisation methods for advanced design of aircraft panels: a comparison. Optim Eng 11(4):583–596. doi:10.1007/s11081-008-9077-8
Crisfield M, Jelenic G (1999) Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc R Soc Lond A 455:1125–1147. doi:10.1098/rspa.1999.0352
Cugnon F, Cardona A, Selvi A, Paleczny C, Pucheta M (2009) Synthesis and optimization of flexible mechanisms. In: Bottasso C (ed) Multibody dynamics, computational methods in applied sciences, vol 12. Springer, Netherlands, p 81. doi:10.1007/978-1-4020-8829-2_5
Deaton J, Grandhi R (2014) A survey of structural and multidisciplinary continuum topology optimization: post. Struct Multidiscip Optim 49(1):1–38. doi:10.1007/s00158-013-0956-z
Dias J, Pereira M (1997) Sensitivity analysis of rigid-flexible multibody systems. Multibody Syst Dyn 1(3):303–322. doi:10.1023/A:1009790202712
Ding J, Pan Z (2008) Second-order sensitivity analysis of multibody systems described by differential/algebraic equations: adjoint variable approach. Int J Comput Math 85(6):899–913. doi:10.1080/00207160701519020
Dong G (2012) Topology optimization for multi-functional components in multibody dynamics systems. PhD thesis, The University of Michigan
Dong G, Ma Z, Hulbert G, Kikuchi N, Arepally S, Vunnan M, Lou K (2011) Efficient sensitivity analysis for multibody dynamics systems using an iterative steps method with application in topology optimization. In: Proceedings of the ASME 2011 international design engineering technical conferences & computers and information in engineering conference IDETC/CIE, Washington, DC, USA. doi:10.1115/DETC2011-47578
Dopico D, Zhu Y, Sandu A (2015) Direct and adjoint sensitivity analysis of ordinary differential equation multibody formulations. J Comput Nonlinear Dyn 10(1):011012. doi:10.1115/1.4026492
Dunn J, Bertsekas D (1989) Efficient dynamic programming implementations of newton’s method for unconstrained optimal control problems. J Optim Theory Appl 63(1):23–38. doi:10.1007/BF00940728
Eich-Soellner E, Führer C (1998) Numerical methods in multibody dynamics. Springer, New York. doi:10.1007/978-3-663-09828-7
Erdman A, Sandor G (1991) Mechanism design, analysis and synthesis, 2nd edn. Prentice-Hall, Englewood Cliffs
Erdman A, Sandor G, Oakberg R (1972) A general method for kineto-elastodynamic analysis and synthesis of mechanisms. J Eng Ind 94(4):1193–1205. doi:10.1115/1.3428335
Eschenauer H, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–390. doi:10.1115/1.1388075
Etman L (1997) Optimization of multibody systems using approximation concepts. PhD thesis, Technische Universiteit Eindhoven
Etman L, Van Campen D, Schoofs A (1998) Design optimization of multibody systems by sequential approximation. Multibody Syst Dyn 2(4):393–415. doi:10.1023/A:1009780119839
Feng T, Arora J, Haug E (1977) Optimal structural design under dynamic loads. Int J Numer Methods Eng 11(1):39–52. doi:10.1002/nme.1620110106
Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Numer Methods Eng 23:409–428. doi:10.1002/nme.1620230307
Forrester A, Keane A (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(13):50–79. doi:10.1016/j.paerosci.2008.11.001
Forsgren A, Gill P, Wright M (2002) Interior methods for nonlinear optimization. SIAM Rev 44(4):525–597. doi:10.1137/S0036144502414942
Fox R, Kapoor M (1970) Structural optimization in the dynamic regime: a computational approach. AIAA J 8:1798–1804. doi:10.2514/3.5993
Fraeijs De Veubeke B (1976) The dynamics of flexible bodies. Int J Eng Sci 14:895–913. doi:10.1016/0020-7225(76)90102-6
Friberg O (1991) A method for selecting deformation modes in flexible multibody dynamics. Int J Numer Methods Eng 32(8):1637–1655. doi:10.1002/nme.1620320808
García-Vallejo D, Mayo J, Escalona J, Dominguez J (2004) Efficient evaluation of the elastic forces and the jacobian in the absolute nodal coordinate formulation. Nonlinear Dyn 35(4):313–329
Géradin M, Cardona A (2001) Flexible multibody dynamics: a finite element approach. Wiley, New York
Ghandriz T, Führer C, Elmqvist H (2017) Structural topology optimization of multibody systems. Multibody Syst Dyn 39(1):135–148. doi:10.1007/s11044-016-9542-7
Grandhi R, Haftka R, Watson L (1986) Design-oriented identification of critical times in transient response. AIAA J 24(4):649–656. doi:10.2514/3.9321
Haftka R, Gürdal Z, Haftka R, Gürdal Z (1992) Elements of structural optimization, 3rd edn. Springer, Netherlands. doi:10.1007/978-94-011-2550-5
Hansen J (2002) Synthesis of mechanisms using time-varying dimensions. Multibody Syst Dyn 7(1):127–144. doi:10.1023/A:1015247821899
Hansen J, Tortorelli D (1996) An efficient method for synthesis of mechanisms using an optimization method. In: Bestle D, Schiehlen W (eds) IUTAM symposium on optimization of mechanical systems, solid mechanics and its applications, vol 43. Springer, Netherlands, pp 129–138. doi:10.1007/978-94-009-0153-7_17
Hansen M (1992) A general procedure for dimensional synthesis of mechanisms. Mech Des Synth 46:67–71
Hansen M, Hansen J (1998) An efficient method for synthesis of planar multibody systems including shape of bodies as design variables. Multibody Syst Dyn 2(2):115–143. doi:10.1023/A:1009758123449
Haug E, Arora J (1979) Applied optimal design: mechanical and structural systems. Wiley, New York
Haug E, Mani N (1984) Design sensitivity analysis and optimization of dynamically driven systems. Computer aided analysis and optimization of mechanical system dynamics. Springer, New York, pp 555–635. doi:10.1007/978-3-642-52465-3_21
Haug E, Sohoni V (1984) Design sensitivity analysis and optimization of kinematically driven systems. In: Haug E (ed) Computer aided analysis and optimization of mechanical system dynamics, vol 9., NATO ASI SeriesSpringer, Berlin, pp 499–554. doi:10.1007/978-3-642-52465-3_20
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, Germany
Held A (2014) On structural optimization of flexible multibody systems. PhD thesis, Institut für Technische und Numerische Mechanik, Universität Stuttgart
Held A, Seifried R (2013) Gradient-based optimization of flexible multibody systems using the absolute nodal coordinate formulation. Proceedings of the ECCOMAS thematic conference multibody dynamics. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb Croatia, pp 1–8
Held A, Knüfer S, Seifried R (2016) Structural sensitivity analysis of flexible multibody systems modeled with the floating frame of reference approach using the adjoint variable method. Multibody Syst Dyn. doi:10.1007/s11044-016-9540-9
Hilber H, Hughes T, Taylor R (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq Eng Struct Dyn 5(3):283–292. doi:10.1002/eqe.4290050306
Hong E, You B, Kim C, Park G (2010) Optimization of flexible components of multibody systems via equivalent static loads. Struct Multidiscip Optim 40:549–562. doi:10.1007/s00158-009-0384-2
Hong UP (2003) Determination of the crash pulse and optimization of the crash components using the response surface approximate optimization. Proc Inst of Mech Eng Part D 217(3):203–213. doi:10.1243/09544070360550408
Hsieh C, Arora J (1984) Design sensitivity analysis and optimization of dynamic response. Comput Methods Appl Mech Eng 43(2):195–219. doi:10.1016/0045-7825(84)90005-7
Hughes T (1987) The finite element method: linear static and dynamic finite element analysis. Prentice-Hall, Upper Saddle River
Hussein B, Negrut D, Shabana AA (2008) Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dyn 54(4):283–296. doi:10.1007/s11071-007-9328-9
Ider S, Amirouche F (1989) Nonlinear modeling of flexible multibody systems dynamics subjected to variable constraints. J Appl Mech 56(2):444–450. doi:10.1115/1.3176103
Ilzhöfer B, O Müller PH, Emmrich D, Allinger P (2000) Shape optimization based on parameters from lifetime prediction. In: Proceedings of the Nafems Seminar: fatigue analysis, Wiesbaden, Germany
Imam I, Sandor G (1975) High-speed mechanism design—a general analytical approach. J Eng Ind 97(2):609–628. doi:10.1115/1.3438626
Jensen O, Hansen J (2006) Dimensional synthesis of spatial mechanisms and the problem of non-assembly. Multibody Syst Dyn 15(2):107–133. doi:10.1007/s11044-005-9000-4
Jung U, Park G (2015) A new method for simultaneous optimum design of structural and control systems. Comput Struct 160:90–99. doi:10.1016/j.compstruc.2015.08.006
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. doi:10.2514/1.4294
Kang B, Park G, Arora J (2006) A review of optimization of structures subjected to transient loads. Struct Multidiscip Optim 31(2):81–95. doi:10.1007/s00158-005-0575-4
Kang B, Shyy Y, Hong Q (2007) Implementation of equivalent static load method in flexible multibody dynamic systems. In: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, COEX Seoul, Korea
Kawamoto A (2005) Path-generation of articulated mechanisms by shape and topology variations in non-linear truss representation. Int J Numer Methods Eng 64(12):1557–1574. doi:10.1002/nme.1407
Kocer F, Arora J (2002) Optimal design of latticed towers subjected to earthquake loading. J Struct Eng 128(2):197–204. doi:10.1061/(ASCE)0733-9445(2002)128:2(197)
Kurtaran H, Eskandarian A (2001) Design optimization of multi-body systems under impact loading by response surface methodology. Proc Inst Mech Eng Part K 215(4):173–185. doi:10.1243/1464419011544457
Kurtaran H, Eskandarian A, Marzougui D, Bedewi N (2002) Crashworthiness design optimization using successive response surface approximations. Comput Mech 29(4–5):409–421. doi:10.1007/s00466-002-0351-x
Lee H, Park G (2015) Nonlinear dynamic response topology optimization using the equivalent static loads method. Comput Methods Appl Mech Eng 283:956–970. doi:10.1016/j.cma.2014.10.015
Leyendecker S, Ober-Blöbaum S, Marsden J, Ortiz M (2010) Discrete mechanics and optimal control for constrained systems. Optim Control Appl Methods 31:505–528. doi:10.1002/oca.912
Marklund P, Nilsson L (2001) Optimization of a car body component subjected to side impact. Struct Multidiscip Optim 21(5):383–392. doi:10.1007/s001580100117
McCarthy J, Soh G (2011) Geometric design of linkages. Springer, New York. doi:10.1007/978-1-4419-7892-9
Minnaar R, Tortorelli D, Snyman J (2001) On non-assembly in the optimal dimensional synthesis of planar mechanisms. Struct Multidiscip Optim 21:345–354. doi:10.1007/s001580100113
Nocedal J, Wright S (2006) Numerical optimization, 2nd edn. Springer, New York. doi:10.1007/978-0-387-40065-5
Oral S, Kemal Ider S (1997) Optimum design of high-speed flexible robotic arms with dynamic behavior constraints. Comput Struct 65(2):255–259. doi:10.1016/S0045-7949(96)00269-6
Park G (2007) Analytic methods for design practice. Springer, London. doi:10.1007/978-1-84628-473-1
Park G, Kang B (2003) Validation of a structural optimization algorithm transforming dynamic loads into equivalent static loads. J Optim Theory Appl 118(1):191–200. doi:10.1023/A:1024799727258
Pereira M, Dias J (2003) Optimization of rigid and flexible multibody systems with application to vehicle dynamics and crashworthiness. In: Schiehlen W, Valasek M (eds) Virtual nonlinear multibody systems, vol 103., NATO ASI SeriesSpringer, Netherlands, pp 363–382. doi:10.1007/978-94-010-0203-522
Pierson B (1972) A survey of optimal structural design under dynamic constraints. Int J Numer Methods Eng 4(4):491–499. doi:10.1002/nme.1620040404
Pucheta M, Cardona A (2007) An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection. Multibody Syst Dyn 18(2):233–258. doi:10.1007/s11044-007-9087-x
Queipo N, Haftka R, Shyy W, Goel T, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1):1–28. doi:10.1016/j.paerosci.2005.02.001
Saravanos D (1990) Optimum structural design of robotic manipulators with fiber reinforced composite materials. Comput Struct 36:119–132. doi:10.1016/0045-7949(90)90181-Z
Schittkowski K (1986) NLPQL: A fortran subroutine solving constrained nonlinear programming problems. Ann Oper Res 5(2):485–500. doi:10.1007/BF02022087
Schwertassek R, Wallrapp O, Shabana AA (1999) Flexible multibody simulation and choice of shape functions. Nonlinear Dyn 20(4):361–380. doi:10.1023/A:1008314826838
Sedlaczek K, Gaugele T, Eberhard P (2005) Topology optimized synthesis of planar kinematic rigid body mechanisms. In: Proceedings of the ECCOMAS thematic conference on multibody dynamics, Madrid, Spain
Seifried R (2012) Two approaches for feedforward control and optimal design of underactuated multibody systems. Multibody Syst Dyn 27(1):75–93. doi:10.1007/s11044-011-9261-z
Seifried R, Held A (2011) Integrated design approaches for controlled flexible multibody systems. In: Proceedings of the ASME 2011 international design engineering technical conferences and computers and information in engineering conference (IDETC/CIE 2011), Washington DC, USA, pp 347–354. doi:10.1115/DETC2011-47707
Shabana A (1997) Flexible multibody dynamics: review of past and recent developments. Multibody Syst Dyn 1(2):189–222. doi:10.1023/A:1009773505418
Shabana A (2013) Dynamics of multibody systems, 4th edn. Cambridge University Press, England
Shabana AA (1996) An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Tech. Rep. MBS96-1-UIC. Department of Mechanical Engineering, University of Illinois at Chicago, Chicago
Sherif K, Irschik H (2010) Efficient topology optimization of large dynamic finite element systems using fatigue. AIAA J 48(7):1339–1347. doi:10.2514/1.45196
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524. doi:10.1080/08905459708945415
Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48(6):1031–1055. doi:10.1007/s00158-013-0978-6
Simo J, Tarnow N (1992a) Conserving algorithms for nonlinear dynamics. New methods in transient analysis, vol 246. ASME, New York, pp 41–50
Simo J, Tarnow N (1992b) The discrete energy-momentum method. conserving algorithms for nonlinear elastodynamics. Zeitschrift für angewandte Mathematik und Physik ZAMP 43(5):757–792. doi:10.1007/BF00913408
Simo J, Tarnow N, Doblare M (1995) Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms. Int J Numer Methods Eng 38(9):1431–1473. doi:10.1002/nme.1620380903
Simpson T, Toropov V, Balabanov V, Viana F (2008) Design and analysis of computer experiments in multidisciplinary design optimization: A review of how far we have come—or not. In: Proceedings of the 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, British Columbia, Canada. doi:10.2514/6.2008-5802
Sohoni V, Haug E (1982) A state space technique for optimal design of mechanisms. J Mech Des 104(4):792–798. doi:10.1115/1.3256438
Sonneville V, Brüls O (2014) A formulation on the special Euclidean group for dynamic analysis of multibody systems. J Comput Nonlinear Dyn 9(4):041002–041008. doi:10.1115/1.4026569
Sonneville V, Cardona A, Brüls O (2014) Geometrically exact beam finite element formulated on the special Euclidean group SE(3). Comput Methods Appl Mech Eng 268:451–474
Stolpe M (2014) On the equivalent static loads approach for dynamic response structural optimization. Struct Multidiscip Optim 50:921–926. doi:10.1007/s00158-014-1101-3
Sun J, Tian Q, Hu H (2016) Structural optimization of flexible components in a flexible multibody system modeled via ANCF. Mech Mach Theory 104:59–80. doi:10.1016/j.mechmachtheory.2016.05.008
Sun J, Tian Q, Hu H (2016b) Topology optimization based on level set for a flexible multibody system modeled via ancf. Struct Multidiscip Optim 1:1–19. doi:10.1007/s00158-016-1558-3
Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. I J Numer Methods Eng 24:359–373. doi:10.1002/nme.1620240207
Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12(2):555–573. doi:10.1137/S1052623499362822
Tobias C, Fehr J, Eberhard P (2010) Durability-based structural optimization with reduced elastic multibody systems. In: Proceedings of 2nd International Conference on engineering optimization, Lisbon, Portugal
Tortorelli D (1992) Sensitivity analysis for non-linear constrained elastostatic systems. Int J Numer Methods Eng 33(8):1643–1660. doi:10.1002/nme.1620330807
Tortorelli D, Michaleris P (1994) Design sensitivity analysis: overview and review. Inverse Prob Eng 1(1):71–105. doi:10.1080/174159794088027573
Tromme E (2015) Structural optimization of flexible components within a multibody dynamics approach. PhD thesis, Université de Liège
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. Struct Multidiscip Optim 48(6):1189–1206. doi:10.1007/s00158-013-0952-3
Tromme E, Brüls O (2015a) Weakly and fully coupled methods for structural optimization of flexible mechanisms. Multibody Syst Dyn 38(4):391–417. doi:10.1007/s11044-015-9493-4
Tromme E, Tortorelli D, Brüls O, Duysinx P (2015b) Structural optimization of multibody system components described using level set techniques. Struct Multidiscip Optim 52(5):959–971. doi:10.1007/s00158-015-1280-6
Tromme E, Sonneville V, Brüls O, Duysinx P (2016) On the equivalent static load method for flexible multibody systems described with a nonlinear finite element formalism. Int J Numer Methods Eng 108(6):646–664. doi:10.1002/nme.5237
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. doi:10.1016/j.cma.2005.02.002
Verscheure D, Demeulenaere B, Swevers J, De Schutter J, Diehl M (2009) Time-optimal path tracking for robots: a convex optimization approach. IEEE Trans Autom Control 54:2318–2327. doi:10.1109/TAC.2009.2028959
Von Stryk O (1998) Optimal control of multibody systems in minimal coordinates. ZAMM J Appl Math Mech 78:1117–1120. doi:10.1002/zamm.199807815124
Wang Q (2006) A study of alternative formulations for optimization of structural and mechanical systems subjected to static and dynamic loads. PhD thesis, The University of Iowa
Wasfy T, Noor A (1996) Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements. Comput Methods Appl Mech Eng 138(1–4):187–211. doi:10.1016/S0045-7825(96)01113-9
Wehage R, Haug E (1982) Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. J Mech Des 104(1):247–255. doi:10.1115/1.3256318
Willmert K (1974) Optimum design of a linear multi-degree-of-freedom shock isolation system. J Eng Ind 94(2):465–471. doi:10.1115/1.3428177
Witteveen W, Puchner K, Sherif K, Irschik H (2009) Efficient topology optimization for large and dynamically loaded fe models. In: Proceedings of the IMAC-XXVII: conference and exposition on structural dynamics, Orlando, Florida, USA
Wright M (2005) The interior-point revolution in optimization: History, recent developments, and lasting consequences. Bull Am Math Soc 42:39–56. doi:10.1090/S0273-0979-04-01040-7
Zienkiewicz O, Campbell J (1973) Shape optimization and sequential linear programming. In: Gallagher RH, Zienkiewicz OC (eds) Optimum structural design. Wiley, New York, pp 109–126