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Erschienen in: Structural and Multidisciplinary Optimization 6/2015

01.06.2015 | Research Paper

A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations

verfasst von: Hu Liu, Weihong Zhang, Tong Gao

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2015

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Abstract

This work is focused on the topology optimization related to harmonic responses for large-scale problems. A comparative study is made among mode displacement method (MDM), mode acceleration method (MAM) and full method (FM) to highlight their effectiveness. It is found that the MDM results in the unsatisfactory convergence due to the low accuracy of harmonic responses, while MAM and FM have a good accuracy and evidently favor the optimization convergence. Especially, the FM is of superiority in both accuracy and efficiency under the excitation at one specific frequency; MAM is preferable due to its balance between the computing efficiency and accuracy when multiple excitation frequencies are taken into account.

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Literatur
Zurück zum Zitat Alvin KF (1997) Efficient computation of eigenvector sensitivities for structural dynamics. AIAA J 35:1760–1766MATHCrossRef Alvin KF (1997) Efficient computation of eigenvector sensitivities for structural dynamics. AIAA J 35:1760–1766MATHCrossRef
Zurück zum Zitat Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224CrossRef Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224CrossRef
Zurück zum Zitat Besselink B et al (2013) A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J Sound Vib 332:4403–4422CrossRef Besselink B et al (2013) A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J Sound Vib 332:4403–4422CrossRef
Zurück zum Zitat Chen MT, Ali A (1998) An efficient and robust integration technique for applied random vibration analysis. Comput Struct 66:785–798MATHCrossRef Chen MT, Ali A (1998) An efficient and robust integration technique for applied random vibration analysis. Comput Struct 66:785–798MATHCrossRef
Zurück zum Zitat Cornwell RE, Craig RR, Johnson CP (1983) On the application of the mode-acceleration method to structural engineering problems. Earthq Eng Struct Dyn 11:679–688CrossRef Cornwell RE, Craig RR, Johnson CP (1983) On the application of the mode-acceleration method to structural engineering problems. Earthq Eng Struct Dyn 11:679–688CrossRef
Zurück zum Zitat Díaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35:1487–1502MATHCrossRef Díaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35:1487–1502MATHCrossRef
Zurück zum Zitat Dickens JM, Nakagawa JM, Wittbrodt MJ (1997) A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Comput Struct 62:985–998MATHCrossRef Dickens JM, Nakagawa JM, Wittbrodt MJ (1997) A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Comput Struct 62:985–998MATHCrossRef
Zurück zum Zitat Du JB, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim 34:91–110MATHMathSciNetCrossRef Du JB, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidisc Optim 34:91–110MATHMathSciNetCrossRef
Zurück zum Zitat Grimes RG, Lewis JG, Simon HD (1994) A shifted block lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J Matrix Anal Appl 15:228–272MATHMathSciNetCrossRef Grimes RG, Lewis JG, Simon HD (1994) A shifted block lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J Matrix Anal Appl 15:228–272MATHMathSciNetCrossRef
Zurück zum Zitat Gu JM, Ma ZD, Hulbert GM (2000) A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors. Finite Elem Anal Des 36:261–278MATHCrossRef Gu JM, Ma ZD, Hulbert GM (2000) A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors. Finite Elem Anal Des 36:261–278MATHCrossRef
Zurück zum Zitat Jensen JS (2007) Topology optimization of dynamics problems with Padé approximants. Int J Numer Methods Eng 72:1605–1630MATHCrossRef Jensen JS (2007) Topology optimization of dynamics problems with Padé approximants. Int J Numer Methods Eng 72:1605–1630MATHCrossRef
Zurück zum Zitat Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253:687–709CrossRef Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253:687–709CrossRef
Zurück zum Zitat Kang Z, Zhang XP, Jiang SG, Cheng GD (2012) On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidisc Optim 46:51–67MATHMathSciNetCrossRef Kang Z, Zhang XP, Jiang SG, Cheng GD (2012) On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidisc Optim 46:51–67MATHMathSciNetCrossRef
Zurück zum Zitat Liu H, Zhang WH, Zhu JH (2013) Structural topology optimization and frequency influence analysis under harmonic force excitations. Chin J Theor Appl Mech 45:588–597MathSciNet Liu H, Zhang WH, Zhu JH (2013) Structural topology optimization and frequency influence analysis under harmonic force excitations. Chin J Theor Appl Mech 45:588–597MathSciNet
Zurück zum Zitat Olhoff N, Du JB (2005) Topological design of continuum structures subjected to forced vibration. Proceedings of 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, Brazil Olhoff N, Du JB (2005) Topological design of continuum structures subjected to forced vibration. Proceedings of 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, Brazil
Zurück zum Zitat Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidisc Optim 20:2–11CrossRef Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidisc Optim 20:2–11CrossRef
Zurück zum Zitat Shu L, Wang MY, Fang ZD, Ma ZD, Wei P (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330:5820–5834CrossRef Shu L, Wang MY, Fang ZD, Ma ZD, Wei P (2011) Level set based structural topology optimization for minimizing frequency response. J Sound Vib 330:5820–5834CrossRef
Zurück zum Zitat Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75CrossRef Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75CrossRef
Zurück zum Zitat Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22:116–124CrossRef Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22:116–124CrossRef
Zurück zum Zitat Svanberg K (1995) A globally convergent version of MMA without line search. In: First World Congress of Structural and Multidisciplinary Optimization. Pergamon Press, Goslar, pp 9–16 Svanberg K (1995) A globally convergent version of MMA without line search. In: First World Congress of Structural and Multidisciplinary Optimization. Pergamon Press, Goslar, pp 9–16
Zurück zum Zitat Tcherniak D (2002) Topology optimization of resonating structures using SIMP method. Int J Numer Methods Eng 54:1605–1622MATHCrossRef Tcherniak D (2002) Topology optimization of resonating structures using SIMP method. Int J Numer Methods Eng 54:1605–1622MATHCrossRef
Zurück zum Zitat Wilson EL, Yuan MW, Dickens JM (1982) Dynamic analysis by direct superposition of Ritz vectors. Earthq Eng Struct Dyn 10:813–821CrossRef Wilson EL, Yuan MW, Dickens JM (1982) Dynamic analysis by direct superposition of Ritz vectors. Earthq Eng Struct Dyn 10:813–821CrossRef
Zurück zum Zitat Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199:1744–1763MATHCrossRef Yoon GH (2010) Structural topology optimization for frequency response problem using model reduction schemes. Comput Methods Appl Mech Eng 199:1744–1763MATHCrossRef
Zurück zum Zitat Yu Y, Jang IG, Kwak BM (2013) Topology optimization for a frequency response and its application to a violin bridge. Struct Multidisc Optim 48:627–636MathSciNetCrossRef Yu Y, Jang IG, Kwak BM (2013) Topology optimization for a frequency response and its application to a violin bridge. Struct Multidisc Optim 48:627–636MathSciNetCrossRef
Zurück zum Zitat Zhu JH, Beckers P, Zhang WH (2010) On the multi-component layout design with inertial force. J Comput Appl Math 234:2222–2230MATHCrossRef Zhu JH, Beckers P, Zhang WH (2010) On the multi-component layout design with inertial force. J Comput Appl Math 234:2222–2230MATHCrossRef
Metadaten
Titel
A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations
verfasst von
Hu Liu
Weihong Zhang
Tong Gao
Publikationsdatum
01.06.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 6/2015
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-014-1218-4

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