Multi-material robust topology optimization considering uncertainty of material properties
This paper proposes a solution to a multi-material robust topology optimization problem of density type considering material uncertainties based on H1 gradient method. A material interpolation with respect to the density is introduced using the rational approximation of material properties (RAMP) an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Japanese |
| Published: |
The Japan Society of Mechanical Engineers
2021-08-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/87/900/87_21-00138/_pdf/-char/en |
| _version_ | 1811308646488866816 |
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| author | Kohei SHINTANI Hideyuki AZEGAMI Takayuki YAMADA |
| author_facet | Kohei SHINTANI Hideyuki AZEGAMI Takayuki YAMADA |
| author_sort | Kohei SHINTANI |
| collection | DOAJ |
| description | This paper proposes a solution to a multi-material robust topology optimization problem of density type considering material uncertainties based on H1 gradient method. A material interpolation with respect to the density is introduced using the rational approximation of material properties (RAMP) and generalized it for the case with an arbitrary number of materials. Material uncertainty is considered by introducing random variables in the material interpolation scheme. The probability density functions of the random variables are assumed to be given. The topology optimization is formulated using the density which is given by a sigmoid function of the design variable. A weighted sum of the mean and standard deviation of the mean compliance is used as the objective function to control the tradeoff between optimality and robustness. To evaluate statistical moments of the objective function effectively, the univariate dimension reduction (UDR) and the Gauss-type quadrature sampling are introduced. A scheme to solve the robust topology optimization problem is presented using an iterative algorithm based on the H1 gradient method for reshaping. Examples of a two-dimensional cantilever beam under various material uncertainty exhibit the efficiency and flexibility of the approach. The accuracy of UDR is validated by comparing the results to the Monte Carlo approach. |
| first_indexed | 2024-04-13T09:27:01Z |
| format | Article |
| id | doaj.art-b33024051d0d4f37830c6a96c41168ff |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-13T09:27:01Z |
| publishDate | 2021-08-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-b33024051d0d4f37830c6a96c41168ff2022-12-22T02:52:24ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612021-08-018790021-0013821-0013810.1299/transjsme.21-00138transjsmeMulti-material robust topology optimization considering uncertainty of material propertiesKohei SHINTANI0Hideyuki AZEGAMI1Takayuki YAMADA2Graduate School of Engineering, The University of TokyoGraduate School of Information Science, Nagoya UniversityGraduate School of Engineering, The University of TokyoThis paper proposes a solution to a multi-material robust topology optimization problem of density type considering material uncertainties based on H1 gradient method. A material interpolation with respect to the density is introduced using the rational approximation of material properties (RAMP) and generalized it for the case with an arbitrary number of materials. Material uncertainty is considered by introducing random variables in the material interpolation scheme. The probability density functions of the random variables are assumed to be given. The topology optimization is formulated using the density which is given by a sigmoid function of the design variable. A weighted sum of the mean and standard deviation of the mean compliance is used as the objective function to control the tradeoff between optimality and robustness. To evaluate statistical moments of the objective function effectively, the univariate dimension reduction (UDR) and the Gauss-type quadrature sampling are introduced. A scheme to solve the robust topology optimization problem is presented using an iterative algorithm based on the H1 gradient method for reshaping. Examples of a two-dimensional cantilever beam under various material uncertainty exhibit the efficiency and flexibility of the approach. The accuracy of UDR is validated by comparing the results to the Monte Carlo approach.https://www.jstage.jst.go.jp/article/transjsme/87/900/87_21-00138/_pdf/-char/enrobust topology optimizationmulti-materialmaterial uncertaintyh1 gradient methodunivariate dimension reductionrational approximation of material properties |
| spellingShingle | Kohei SHINTANI Hideyuki AZEGAMI Takayuki YAMADA Multi-material robust topology optimization considering uncertainty of material properties Nihon Kikai Gakkai ronbunshu robust topology optimization multi-material material uncertainty h1 gradient method univariate dimension reduction rational approximation of material properties |
| title | Multi-material robust topology optimization considering uncertainty of material properties |
| title_full | Multi-material robust topology optimization considering uncertainty of material properties |
| title_fullStr | Multi-material robust topology optimization considering uncertainty of material properties |
| title_full_unstemmed | Multi-material robust topology optimization considering uncertainty of material properties |
| title_short | Multi-material robust topology optimization considering uncertainty of material properties |
| title_sort | multi material robust topology optimization considering uncertainty of material properties |
| topic | robust topology optimization multi-material material uncertainty h1 gradient method univariate dimension reduction rational approximation of material properties |
| url | https://www.jstage.jst.go.jp/article/transjsme/87/900/87_21-00138/_pdf/-char/en |
| work_keys_str_mv | AT koheishintani multimaterialrobusttopologyoptimizationconsideringuncertaintyofmaterialproperties AT hideyukiazegami multimaterialrobusttopologyoptimizationconsideringuncertaintyofmaterialproperties AT takayukiyamada multimaterialrobusttopologyoptimizationconsideringuncertaintyofmaterialproperties |