Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Structural and Multidisciplinary Optimization
Published in: Structural and Multidisciplinary Optimization 1/2015

01-01-2015 | RESEARCH PAPER

Multiobjective topology optimization of energy absorbing materials

Authors: Raymond A. Wildman, George A. Gazonas

Published in: Structural and Multidisciplinary Optimization | Issue 1/2015

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A method for the multiobjective optimization of local-scale material topology is presented. The topology optimization scheme is based on a constructive solid geometry-like representation, in which convex polygons—defined as the convex hull of arbitrary-length lists of points—are combined using an overlapping function. This data structure is tree-shaped and so genetic programming is used as the optimizer. The forward problem is solved with a multiscale finite element method with automatic cohesive zone insertion to model damage. As a multiscale method, loads and boundary conditions are applied and objective functions measured at a global scale, while the local scale material structure is optimized. The global scale geometry is assumed fixed. Pareto optimal designs are generated, representing optimal tradeoffs between conflicting goals: quasi-static displacement and dynamic strain energy. Results demonstrate the efficacy of the proposed algorithm.
previous article Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters
next article Actuator topology design using the controllability Gramian

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
Ahmed F, Bhattacharya B, Deb K (2013) Constructive Solid Geometry based Topology Optimization using Evolutionary Algorithm. In: Bansal JC, et al. (eds) Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012), Volume 201 of Advances in Intelligent Systems and Computing, Berlin, Germany, pp. 227–238. Springer-Verlag, Berlin
Allaire G, Kohn R (1993) Optimal-design for minimum weight and compliance in plane-stress using extremal microstructures. Eur J Mech A-Solids 12(6):839–878MATHMathSciNet
Allen D, Searcy C (2001) A micromechanical model for a viscoelastic cohesive zone. Int J Fract 107(2):159–176CrossRef
Anghileri M, Chirwa E, Lanzi L, Mentuccia F (2005) An inverse approach to identify the constitutive model parameters for crashworthiness modelling of composite structures. Compos Struct 68(1):65–74CrossRef
Banzhaf W, Nordin P, Keller R E, Francone FD (1999) Genetic programming: an introduction. Morgan Kauffman, Inc., San Francisco
Bendsoe M, Sigmund O (2003) Topology optimization: Theory, Methods and Applications. Engineering Online Library. Springer
Bieri H (1995) Nef polyhedra: A brief introduction. In: Hagen H, Farin G, Noltemeier H (eds) Geometric Modelling, Volume 10 of Computing Supplement, pp. 43–60. Springer, Vienna
Qi C, Yang S, Yang L-J, Wei Z-Y, Lu Z-H (2013) Blast resistance and multi-objective optimization of aluminum foam-cored sandwich panels. Compos Struct 105(0):45–57CrossRef
Chessa J, Smolinski P, Belytschko T (2002) The extended finite element method (XFEM) for solidification problems. Int J Numer Methods Eng 53(8):1959–1977CrossRefMATHMathSciNet
Chiandussi G, Avalle M (2002) Maximisation of the crushing performance of a tubular device by shape optimisation. Comput Struct 80(27–30):2425–2432CrossRef
Cohon J (1978) Multiobjective programming and planning. Academic, New YorkMATH
Cohon JL, Marks DH (1975) A review and evaluation of multiobjective programming techniques. Water Resour Res 11(2):208–219CrossRef
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
Duysinx P, Bendsoe M (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8):1453–1478CrossRefMATHMathSciNet
Goldberg D E (1987) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading
Hamza K, Saitou K (2004) Optimization of constructive solid geometry via a tree-based multi-objective genetic algorithm. In: Deb K, et al. (eds) Genetic and Evolutionary Computation Gecco 2004, Pt 2, Proceedings, Volume 3103 of Lecture Notes in Computer Science, Berlin, Germany, pp. 981–992. Springer-Verlag, Berlin
Huang X, Xie YM, Lu G (2007) Topology optimization of energy-absorbing structures. Int J Crashworthiness 12(6):663–675CrossRefMATH
Huang X, Zhou SW, Xie YM, Li Q (2013) Topology optimization of microstructures of cellular materials and composites for macrostructures. Comput Mater Sci 67:397–407CrossRef
Koza JR (1999) Genetic programming III: Darwinian invention and problem solving. Morgan Kauffman, Inc, San FranciscoMATH
Guo L, Tovar A, Penninger C, Renaud J (2011) Strain-based topology optimisation for crashworthiness using hybrid cellular automata. Int J Crashworthiness 16:239–52CrossRef
Main JA, Gazonas GA (2008) Uniaxial crushing of sandwich plates under air blast: influence of mass distribution. Int J Solids Struct 45(7–8):2297–2321CrossRefMATH
Mei Y, Wang X (2004) A level set method for microstructure design of composite materials. Acta Mechanica Solida Sinica 17(3):239–250MathSciNet
Mozumder C, Renaud JE, Tovar A (2012) Topometry optimisation for crashworthiness design using hybrid cellular automata. Int J Veh Des 60(1–2):100–120CrossRef
Nguyen VP, Stroeven M, Sluys LJ (2011) Multiscale continuous and discontinuous modeling of heterogeneous materials: a review on recent developments. J Multiscale Model 3(4):1–42CrossRefMathSciNet
Qiao P, Yang M, Bobaru F (2008) Impact mechanics and high-energy absorbing materials: review. J Aerosp Eng 21(4):235–248CrossRef
Requicha A, Voelker HB (1977) Constructive solid geometry, TM-25. Technical memorandum. Production Automation Project, University of Rochester
Rueda MAF, Cui L, Gilchrist MD (2009) Optimisation of energy absorbing liner for equestrian helmets. Part I: layered foam liner. Mater Des 30(9):3405–3413CrossRef
Sethian J, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528CrossRefMATHMathSciNet
Sigmund O (1994) Materials with prescribed constitutive parameters - an inverse homogenization problem. Int J Solids Struct 31(17):2313–2329CrossRefMATHMathSciNet
Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248CrossRef
Souza FV, Allen DH (2010) Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model. Mech Time-Dependent Mater 14(2):125–151CrossRef
Souza FV, Allen DH (2011) Modeling the transition of microcracks into macrocracks in heterogeneous viscoelastic media using a two-way coupled multiscale model. Int J Solids Struct 48(22–23):3160–3175CrossRef
Souza F V, Allen D H (2013) Verification of a two-way coupled multiscale finite element code for dynamic/impact problems. Mech Adv Mater Struct 20 (1): 74–90CrossRef
Souza FV, Allen DH, Kim YR (2008) Multiscale model for predicting damage evolution in composites due to impact loading. Compos Sci Technol 68(13, SI):2624–2634CrossRef
Steuer R (1989) Multiple criteria optimization: theory, computation, application. Krieger, Malabar
Weile D, Michielssen E, Goldberg D (1996) Genetic algorithm design of Pareto optimal broadband microwave absorbers. IEEE Trans Electromagn Compat 38(3):518–525CrossRef
Wildman RA, Gazonas GA (2009) Gravitational and magnetic anomaly inversion using a tree-based geometry representation. Geophysics 74(3):I23—I35CrossRef
Wildman RA, Gazonas GA (2011) Genetic Programming-based Phononic Bandgap Structure Design. Technical Report ARL-TR-5733, US Army Research Laboratory
Wildman RA, Weile DS (2007) Geometry reconstruction of conducting cylinders using genetic programming. IEEE Trans Antennas Propag 55(3):629–636CrossRef
Wildman RA, Weile DS (2008) Greedy search and a hybrid local optimization/genetic algorithm for tree-based inverse scattering. Microw Opt Technol Lett 50(3):822–825CrossRef
Wildman RA, Weile DS (2010) Inverse scattering of dielectric cylindrical targets using genetic programming. Electromagnetics 30(1–2, Sp. Iss. SI):222–236CrossRef
Xie Y, Steven G (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896CrossRef
Xie Y, Steven G (1997) Evolutionary structural optimization. Springer
Xu X, Needleman A (1994) Numerical simulations of fast crack-growth in brittle solids. J Mech Phys Solids 42(9):1397–&CrossRefMATH
Xu X, Needleman A (1996) Numerical simulations of dynamic crack growth along an interface. Int J Fract 74(4):289–324CrossRef
Yamagiwa M, Uehara M, Murakami M, Yoneyama M (2010) A reconstruction method for ultrasonic deterioration image by the combination of constructive solid geometry and strongly typed genetic programming. Comput Syst Sci Eng 25(2, SI):161–170
Zohdi T (2002) On the tailoring of microstructures for prescribed effective properties. Int J Fract 118(4):L89—L94
Metadata
Title
Multiobjective topology optimization of energy absorbing materials
Authors
Raymond A. Wildman
George A. Gazonas
Publication date
01-01-2015
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 1/2015
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-014-1117-8

Other articles of this Issue 1/2015

Structural and Multidisciplinary Optimization 1/2015 Go to the issue

RESEARCH PAPER

Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach

RESEARCH PAPER

Continuum shape sensitivity analysis and what-if study for two-dimensional multi-scale crack propagation problems using bridging scale decomposition

INDUSTRIAL APPLICATION

Structure and fluid optimization of the guide vane blade with the decomposition of the optimization problem

RESEARCH PAPER

Application of topological derivative to accelerate genetic algorithm in shape optimization of coupled models

RESEARCH PAPER

A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

MEDICAL AND BIO-ENGINEERING APPLICATIONS

Prediction of crank torque and pedal angle profiles during pedaling movements by biomechanical optimization

Premium Partners

    Image Credits