Top

Structural and Multidisciplinary Optimization

Published in:

01-11-2011 | Research Paper

Topology design with negative masks using gradient search

Author: Anupam Saxena

Published in: Structural and Multidisciplinary Optimization | Issue 5/2011

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

search-config

AI-assisted search

Off

Abstract

Previous implementations of the Material Mask Overlay Scheme (MMOS) (Saxena, ASME J Mech Des 130(8):1–9, 2009, 2010; Jain and Saxena, ASME J Mech Des 132(6):1–10, 2010) use stochastic search to achieve well connected, perfectly binary topologies but are computationally expensive. Here, a gradient search is employed to lay the negative masks over the design region. A continuous material assignment model is presented and studied. This investigation is motivated by the following goals: (a) reduction in the number of evaluations thereby making the search computationally efficient compared to the previous implementations, (b) obtaining as close to well-connected binary topologies as possible, and (c) influence of various parameters on the quality of solutions and existence of gray cells.

previous article Diffuse response surface model based on moving Latin hypercube patterns for reliability-based design optimization of ultrahigh strength steel NC milling parameters

next article Ensemble of surrogates with recursive arithmetic average

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

Available only for authorised users

Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidisc Optim 43:1–16. doi:10.1007/s00158-010-0594-7 CrossRef

Bendsøe MP (1995) Optimization of structural topology, shape and material. Springer, Berlin

Bendsøe D, Kikuchi D (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224CrossRef

Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158MathSciNetMATHCrossRef

Bruns TE, Tortorelli DA (2001) Topology optimization of nonlinear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190:3443–3459MATHCrossRef

Challis VJ (2010) A discrete level-set topology optimization code written in Matlab. Struct Multidisc Optim 41:453–464MathSciNetCrossRef

Epelman MA (2010) Sequential Quadratic Programming (SQP). Lecture notes on IOE 511/Math 562 at http://www-personal.umich.edu/~mepelman/teaching/IOE511/511notes.pdf. Accessed 9 Dec 2010

Guest J (2009) Topology optimization with multiple phase projection. Comput Methods Appl Mech Eng 199(1–4):123–135. doi:10.1016/j.cma.2009.09.023 MathSciNetCrossRef

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 61:238–254MATHCrossRef

Hull P, Canfield S (2006) Optimal synthesis of compliant mechanisms using subdivision and commercial FEA. ASME J Mech Des 128:337–348CrossRef

Jain C, Saxena A (2010) An improved material-mask overlay strategy for topology optimization of structures and compliant mechanisms. ASME J Mech Des 132(6):1–10. doi:10.1115/1.4001530 CrossRef

Jakiela MJ, Chapman C, Duda J, Adewuya A, Saitou K (2000) Continuum structural topology design with genetic algorithms. Comput Methods Appl Mech Eng 186:339–356MathSciNetMATHCrossRef

Langelaar M (2007) The use of convex uniform honeycomb tessellations in structural topology optimization. In: Proceedings of the 7th world congress on structural and multidisciplinary optimization. Seoul, South Korea, 21–25 May 2007

Luo JZ, Luo Z, Chen SK, Tong LY, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198:318–331MATH

Mankame N, Ananthasuresh GK (2007) Synthesis of contact-aided compliant mechanisms for non-smooth path generation. Int J Numer Methods Eng 69(12):2564–2605MATHCrossRef

Pedersen CBW, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50:2683–2705MATHCrossRef

Poulsen TA (2003) A new scheme for imposing minimum length scale in topology optimization. Int J Numer Methods Eng 57:741–760MathSciNetMATHCrossRef

Rahmatallah SF, Swan CC (2004) A Q4/Q4 continuum structural topology optimization implementation. Struct Multidisc Optim 27:130–135CrossRef

Rai AK, Saxena A, Mankame ND (2007) Synthesis of path generating compliant mechanisms using initially curved frame elements. ASME J Mech Des 129:1056–1063CrossRef

Rai AK, Saxena A, Mankame ND (2009) Unified synthesis of compact planar path-generating linkages with rigid and deformable members. Struct Multidisc Optim 41:863–879. doi:10.1007/s00158-009-0458-1 CrossRef

Reddy BVS, Nagendra, Saxena A (2010) Automated design of contact-aided compliant mechanisms using initially curved frame elements. ASME Design Engineering and Technical Conferences, Montre’al, Canada, 15–18 Aug 2009, #DETC-29172

Saxena A (2009) A material-mask overlay strategy for continuum topology optimization of compliant mechanisms using honeycomb discretization. ASME J Mech Des 130(8):1–9. doi:10.1115/1.2936891

Saxena A (2010) On an adaptive mask overlay topology synthesis method. ASME Design Engineering and Technical Conferences, Montre’al, Canada, 15–18 Aug 2009, DETC2010-29113

Saxena A, Ananthasuresh GK (2000) On an optimality property of compliant topologies. Struct Multidisc Optim 19:36–49CrossRef

Saxena A, Ananthasuresh GK (2001) Topology synthesis of compliant mechanisms for nonlinear force-deflection and curved path specification. Trans ASME-R J Mech Des 123(1):33–42CrossRef

Saxena R, Saxena A (2003) On honeycomb parameterization for topology optimization of compliant mechanisms. ASME Design Engineering Technical Conferences, Design Automation Conference, Chicago, IL, 2–6 Sept 2003, paper #. DETC2002/DAC-48806

Saxena R, Saxena A (2007) On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms. Finite Elem Anal Des 43(14):1082–1098CrossRef

Sethian JA, Wiegmann A (2000) Structural boundary via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetMATHCrossRef

Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120–127CrossRef

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424CrossRef

Talischi C, Paulino GH, Le CH (2009) Honeycomb Wachspress finite elements for structural topology optimization. Struct Multidisc Optim 37(6):569–583MathSciNetCrossRef

Wang MY, Chen SK, Wang XM, Mei YL (2005) Design of multi-material compliant mechanisms using level set methods. ASME J Mech Des 127:941–956CrossRef

Wang F, Lazarov BS, Sigmund O (2010) On projection methods, convergence and robust formulations in topology optimitation. Struct Multidisc Optim. doi:10.1007/s00158-010-0602-y

Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside funtions. Struct Multidisc Optim 41:495–505MathSciNetCrossRef

Yin L, Ananthasuresh GK (2001) Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Struct Multidisc Optim 23:49–62CrossRef

Yin L, Ananthasuresh GK (2003) Design of distributed compliant mechanisms. Mech Based Des Struct Mach 31(2):151–179CrossRef

Yoon G, Kim Y, Bendsoe M, Sigmund O (2004) Hinge – free topology optimization with embedded translation – invariant differentiable wavelet shrinkage. Struct Multidisc Optim 27:139–150CrossRef

Title: Topology design with negative masks using gradient search
Author: Anupam Saxena
Publication date: 01-11-2011
Publisher: Springer-Verlag
Published in: Structural and Multidisciplinary Optimization / Issue 5/2011
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-011-0649-4

Springer Professional

Abstract

Please log in to get access to your license.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 5/2011

To bee or not to bee—comments on “Discrete optimum design of truss structures using artificial bee colony algorithm”

Reliability-based design optimization using kriging surrogates and subset simulation

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

Diffuse response surface model based on moving Latin hypercube patterns for reliability-based design optimization of ultrahigh strength steel NC milling parameters

Author’s reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article “On symmetry and non-uniqueness in exact topology optimization” by George I. N. Rozvany (2011, Struct Multidisc Optim 43:297–317)

Optimal design of a class of symmetric plane frameworks of least weight

Premium Partners