Free-form optimization of a frame structure for strength maximization
In this paper, we present a parameter-free free-form optimization method for the strength design problem of a frame structure. The maximum von Mises stress is minimized under a given volume constraint. The strength design problems are formulated as distributed-parameter optimization problems under t...
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The Japan Society of Mechanical Engineers
2017
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oai:doaj.org-article:5d5e94de710641a890a84ed167c8bcc82021-11-26T07:02:12ZFree-form optimization of a frame structure for strength maximization2187-974510.1299/mej.17-00014https://doaj.org/article/5d5e94de710641a890a84ed167c8bcc82017-03-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/4/2/4_17-00014/_pdf/-char/enhttps://doaj.org/toc/2187-9745In this paper, we present a parameter-free free-form optimization method for the strength design problem of a frame structure. The maximum von Mises stress is minimized under a given volume constraint. The strength design problems are formulated as distributed-parameter optimization problems under the assumptions that each member is varied in the off-axis direction to the centroidal-axis and the cross section is not varied with respect to the iteration process. The issue of non-differentiability inherent in this min-max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional by using the Kreisselmeier-Steinhauser function. The shape gradient functions and optimality conditions theoretically derived are applied to the free-form optimization method for frames. With this method, the smooth optimal free-form of a frame structure is determined without any shape design parameterization, while minimizing the objective functional. Design examples are presented to demonstrate the validity of this free-form optimization method for strength design problems of a frame structure.Zhiqiang WUMasatoshi SHIMODAKei HISATOMIJin-Xing SHIThe Japan Society of Mechanical Engineersarticleshape optimizationframe structurefree-form optimizationvon mises stressstrength designkreisselmeier-steinhauser functionmin-max problemMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 4, Iss 2, Pp 17-00014-17-00014 (2017) |
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DOAJ |
language |
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topic |
shape optimization frame structure free-form optimization von mises stress strength design kreisselmeier-steinhauser function min-max problem Mechanical engineering and machinery TJ1-1570 |
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shape optimization frame structure free-form optimization von mises stress strength design kreisselmeier-steinhauser function min-max problem Mechanical engineering and machinery TJ1-1570 Zhiqiang WU Masatoshi SHIMODA Kei HISATOMI Jin-Xing SHI Free-form optimization of a frame structure for strength maximization |
description |
In this paper, we present a parameter-free free-form optimization method for the strength design problem of a frame structure. The maximum von Mises stress is minimized under a given volume constraint. The strength design problems are formulated as distributed-parameter optimization problems under the assumptions that each member is varied in the off-axis direction to the centroidal-axis and the cross section is not varied with respect to the iteration process. The issue of non-differentiability inherent in this min-max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional by using the Kreisselmeier-Steinhauser function. The shape gradient functions and optimality conditions theoretically derived are applied to the free-form optimization method for frames. With this method, the smooth optimal free-form of a frame structure is determined without any shape design parameterization, while minimizing the objective functional. Design examples are presented to demonstrate the validity of this free-form optimization method for strength design problems of a frame structure. |
format |
article |
author |
Zhiqiang WU Masatoshi SHIMODA Kei HISATOMI Jin-Xing SHI |
author_facet |
Zhiqiang WU Masatoshi SHIMODA Kei HISATOMI Jin-Xing SHI |
author_sort |
Zhiqiang WU |
title |
Free-form optimization of a frame structure for strength maximization |
title_short |
Free-form optimization of a frame structure for strength maximization |
title_full |
Free-form optimization of a frame structure for strength maximization |
title_fullStr |
Free-form optimization of a frame structure for strength maximization |
title_full_unstemmed |
Free-form optimization of a frame structure for strength maximization |
title_sort |
free-form optimization of a frame structure for strength maximization |
publisher |
The Japan Society of Mechanical Engineers |
publishDate |
2017 |
url |
https://doaj.org/article/5d5e94de710641a890a84ed167c8bcc8 |
work_keys_str_mv |
AT zhiqiangwu freeformoptimizationofaframestructureforstrengthmaximization AT masatoshishimoda freeformoptimizationofaframestructureforstrengthmaximization AT keihisatomi freeformoptimizationofaframestructureforstrengthmaximization AT jinxingshi freeformoptimizationofaframestructureforstrengthmaximization |
_version_ |
1718409719440211968 |