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Structural and Multidisciplinary Optimization

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24.07.2020 | Research Paper

Topology optimization of structural systems based on a nonlinear beam finite element model

verfasst von: Navid Changizi, Gordon P. Warn

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 5/2020

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Abstract

A method for the topology optimization of structures composed of nonlinear beam elements based on a hysteretic finite element modeling approach is presented. In the context of the optimal design of structures composed of truss or beam elements, studies reported in the literature have mostly considered linear elastic material behavior. However, certain applications require consideration of the nonlinear response of the structural system to the given external forces. Particular to the methodology suggested in this paper is a hysteretic beam finite element model in which the inelastic deformations are governed by principles of mechanics in conjunction with first-order nonlinear ordinary differential equations. The nonlinear ordinary differential equations determine the onset of inelastic deformations and the approximation of the signum function in the differential equation with the hyperbolic tangent function permits the derivation of analytical sensitivities. The objective of the optimization problem is to minimize the volume of the system such that a system-level displacement satisfies a specified constraint value. This design problem is analogous to that of seismic design where inelastic deformations are permitted, yet sufficient stiffness is required to limit the overall displacement of the system to a specified threshold. The utility of the method is demonstrated through numerical examples for the design of two structural frames and a comparison with the solution from the topology optimization assuming linear elastic material behavior. The comparisons show that the nonlinear design is either comprised of a lower volume for a given level of performance, or offers better performance for a given volume in comparison with optimized linear design.

Vorheriger Artikel Time-variant reliability analysis via approximation of the first-crossing PDF

Nächster Artikel Genetic algorithm-based inverse design of elastic gridshells

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Achtziger W, Bendsøe MP (1995) Design for maximal flexibility as a simple computational model of damage. Struct Optim 10(3–4):258–268CrossRef

Alberdi R, Khandelwal K (2017) Topology optimization of pressure dependent elastoplastic energy absorbing structures with material damage constraints. Finite Elem Anal Des 133:42–61MathSciNetCrossRef

Alberdi R, Zhang G, Li L, Khandelwal K (2018) A unified framework for nonlinear path-dependent sensitivity analysis in topology optimization. Int J Numer Methods Eng, vol 115

American Institute of Steel Construction (2015) Steel construction manual shapes database

Amir M, Papakonstantinou K, Warn G (2019) A consistent timoshenko hysteretic beam finite element model. Int J Non-Linear Mech, vol 119

Asadpoure A, Tootkaboni M, Guest J K (2011) Robust topology optimization of structures with uncertainties in stiffness–application to truss structures. Comput Struct 89(11):1131–1141CrossRef

ASCE (2017) Minimum design loads for buildings and other structures. American Society of Civil Engineers, Reston, asce/sei 7–16 edition

Baber T T, Noori M N (1985) Random vibration of degrading, pinching systems. J Eng Mech 111(8):1010–1026CrossRef

Baber T T, Wen Y-K (1981) Random vibration hysteretic, degrading systems. J Eng Mech Div 107(6):1069–1087

Bathe K-J (2006) Finite element procedures. Klaus-Jurgen Bathe

Bendsoe MP, Sigmund O (2004) Topology optimization: theory, methods and applications. Springer, BerlinCrossRef

Boese K D, Kahng A B, Muddu S (1994) A new adaptive multi-start technique for combinatorial global optimizations. Oper Res Lett 16(2):101–114MathSciNetCrossRef

Bouc R (1967) Forced vibration of mechanical systems with hysteresis. In: Proceedings of the fourth conference on non-linear oscillation. Prague, p 315

Casciati F (1989) Stochastic dynamics of hysteretic media. Struct Saf 6(2–4):259–269CrossRef

Changizi N, Jalalpour M (2017a) Robust topology optimization of frame structures under geometric or material properties uncertainties. Struct Multidiscip Optim 56(4):791–807

Changizi N, Jalalpour M (2017b) Stress-based topology optimization of steel-frame structures using members with standard cross sections: gradient-based approach. J Struct Eng 143(8):04017078

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

Erlicher S, Point N (2004) Thermodynamic admissibility of Bouc–Wen type hysteresis models. C R Mec 332(1):51–57CrossRef

Foliente G C (1995) Hysteresis modeling of wood joints and structural systems. J Struct Eng 121 (6):1013–1022CrossRef

Gömöry F, Vojenčiak M, Pardo E, Šouc J (2009) Magnetic flux penetration and AC loss in a composite superconducting wire with ferromagnetic parts. Supercond Sci Technol 22(3):034017CrossRef

James K A, Waisman H (2014) Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model. Comput Methods Appl Mech Eng 268:614–631MathSciNetCrossRef

James K A, Waisman H (2015) Topology optimization of structures under variable loading using a damage superposition approach. Int J Numer Methods Eng 101(5):375–406MathSciNetCrossRef

Kim T, Rook T, Singh R (2003) Effect of smoothening functions on the frequency response of an oscillator with clearance non-linearity. J Sound Vib 263(3):665–678MathSciNetCrossRef

Klarbring A, Strömberg N (2013) Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidiscip Optim 47(1):37–48MathSciNetCrossRef

Kleiber M (1993) Shape and non-shape structural sensitivity analysis for problems with any material and kinematic non-linearity. Comput Methods Appl Mech Eng 108(1–2):73–97CrossRef

Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605–620

Li L, Khandelwal K (2017) Topology optimization of geometrically nonlinear trusses with spurious eigenmodes control. Eng Struct 131:324–344CrossRef

Li L, Zhang G, Khandelwal K (2017) Design of energy dissipating elastoplastic structures under cyclic loads using topology optimization. Struct Multidiscip Optim 56(2):391–412MathSciNetCrossRef

Li L, Zhang G, Khandelwal K (2018) Failure resistant topology optimization of structures using nonlocal elastoplastic-damage model. Struct Multidiscip Optim, vol 58

Luo Y, Wang M Y, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRef

Martí R, Lozano JA, Mendiburu A, Hernando L (2016) Multi-start methods. In: Handbook of heuristics, pp 1–21

Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91CrossRef

Miche U (1904) The limits of economy of material in frame structure. Philos Mag 8:589–597CrossRef

Nakshatrala P, Tortorelli D (2015) Topology optimization for effective energy propagation in rate-independent elastoplastic material systems. Comput Methods Appl Mech Eng 295:305–326MathSciNetCrossRef

Nakshatrala P B, Tortorelli D, Nakshatrala K (2013) Nonlinear structural design using multiscale topology optimization. Part i: static formulation. Comput Methods Appl Mech Eng 261:167–176MathSciNetCrossRef

Pedersen C B (2003) Topology optimization design of crushed 2d-frames for desired energy absorption history. Struct Multidiscip Optim 25(5–6):368–382CrossRef

Pedersen C B (2004) Crashworthiness design of transient frame structures using topology optimization. Comput Methods Appl Mech Eng 193(6–8):653–678CrossRef

Ramos A S, Paulino G H (2015) Convex topology optimization for hyperelastic trusses based on the ground-structure approach. Struct Multidiscip Optim 51(2):287–304MathSciNetCrossRef

Rozvany GI, Lewinski T (2014) Topology optimization in structural and continuum mechanics. Springer, New YorkCrossRef

Schwarz S, Maute K, Ramm E (2001) Topology and shape optimization for elastoplastic structural response. Comput Methods Appl Mech Eng 190(15–17):2135–2155CrossRef

Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, Technical University of Denmark, Denmark

Sivaselvan M V, Reinhorn A M (2000) Hysteretic models for deteriorating inelastic structures. J Eng Mech 126(6):633–640CrossRef

Swan C C, Kosaka I (1997) Voigt-reuss topology optimization for structures with nonlinear material behaviors. Int J Numer Methods Eng 40(20):3785–3814MathSciNetCrossRef

The MathWorks Inc. (2018) MATLAB- Optimization toolbox, Version 8.1. The MathWorks Inc., Natick

Tortorelli D A (1992) Sensitivity analysis for non-linear constrained elastostatic systems. Int J Numer Methods Eng 33(8):1643–1660CrossRef

Triantafyllou S P, Koumousis V K (2011) An inelastic timoshenko beam element with axial–shear–flexural interaction. Comput Mech 48(6):713–727MathSciNetCrossRef

Triantafyllou S, Koumousis V (2012) Small and large displacement dynamic analysis of frame structures based on hysteretic beam elements. J Eng Mech 138(1):36–49CrossRef

Tsay J, Arora J (1990) Nonlinear structural design sensivitity analysis for path dependent problems. Part 1: general theory. Comput Methods Appl Mech Eng 81(2):183–208CrossRef

Wallin M, Jönsson V, Wingren E (2016) Topology optimization based on finite strain plasticity. Struct Multidiscip Optim 54(4):783– 793MathSciNetCrossRef

Yuge K, Kikuchi N (1995) Optimization of a frame structure subjected to a plastic deformation. Struct Optim 10(3–4):197–208CrossRef

Yuge K, Iwai N, Kikuchi N (1999) Optimization of 2-d structures subjected to nonlinear deformations using the homogenization method. Struct Optim 17(4):286–299CrossRef

Zhang G, Li L, Khandelwal K (2017a) Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements. Struct Multidiscip Optim 55(6):1965–1988

Zhang X, Ramos A S, Paulino G H (2017b) Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme. Struct Multidiscip Optim 55(6):2045– 2072

Zhang X S, Paulino G H, Ramos A S (2018) Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity. Struct Multidiscip Optim 57(1):161–182MathSciNetCrossRef

Titel: Topology optimization of structural systems based on a nonlinear beam finite element model
verfasst von: Navid Changizi
Gordon P. Warn
Publikationsdatum: 24.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 5/2020
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-020-02636-x

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