Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization
This study proposes a methodology to generalize and reduce the computational cost of sensitivity analysis for static linear elastic systems in topology optimization. The process is fully generalized by applying sensitivity analysis in conjunction with the adjoint variable method and automatic differ...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2024-12-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00225/_pdf/-char/en |
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| _version_ | 1832584957677010944 |
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| author | Shun OGAWA Kazuo YONEKURA Katsuyuki SUZUKI |
| author_facet | Shun OGAWA Kazuo YONEKURA Katsuyuki SUZUKI |
| author_sort | Shun OGAWA |
| collection | DOAJ |
| description | This study proposes a methodology to generalize and reduce the computational cost of sensitivity analysis for static linear elastic systems in topology optimization. The process is fully generalized by applying sensitivity analysis in conjunction with the adjoint variable method and automatic differentiation. The design sensitivities can be computed independently of any evaluation function and the material interpolation method for static elastic systems. Furthermore, the issue of excessive computational memory required by automatic differentiation is resolved by utilizing the adjoint variable method. To demonstrate the generality of the proposed method, we focus on multi-material topology optimization for isotropic linear elastic systems, evaluating compliance and maximum stress based on the Lp-norm. Additionally, the extended SIMP and Discrete Material Optimization (DMO) methods are investigated as interpolation schemes for material properties in multi-material problems. Finally, the finite difference method and automatic differentiation are benchmarked against other sensitivity analysis methods, and the proposed method is evaluated in terms of accuracy, computational cost, and memory usage. Moreover, examples of topology optimization for a 3-dimensional problem are presented to demonstrate the applicability of the proposed method to large-scale analyses. |
| format | Article |
| id | doaj-art-cef9b7ad5aa1496abfb1a5f9378dc8ee |
| institution | Kabale University |
| issn | 2187-9761 |
| language | Japanese |
| publishDate | 2024-12-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj-art-cef9b7ad5aa1496abfb1a5f9378dc8ee2025-01-27T08:34:35ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612024-12-019194124-0022524-0022510.1299/transjsme.24-00225transjsmeSensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimizationShun OGAWA0Kazuo YONEKURA1Katsuyuki SUZUKI2Graduate School of Engineering, The University of TokyoGraduate School of Engineering, The University of TokyoGraduate School of Engineering, The University of TokyoThis study proposes a methodology to generalize and reduce the computational cost of sensitivity analysis for static linear elastic systems in topology optimization. The process is fully generalized by applying sensitivity analysis in conjunction with the adjoint variable method and automatic differentiation. The design sensitivities can be computed independently of any evaluation function and the material interpolation method for static elastic systems. Furthermore, the issue of excessive computational memory required by automatic differentiation is resolved by utilizing the adjoint variable method. To demonstrate the generality of the proposed method, we focus on multi-material topology optimization for isotropic linear elastic systems, evaluating compliance and maximum stress based on the Lp-norm. Additionally, the extended SIMP and Discrete Material Optimization (DMO) methods are investigated as interpolation schemes for material properties in multi-material problems. Finally, the finite difference method and automatic differentiation are benchmarked against other sensitivity analysis methods, and the proposed method is evaluated in terms of accuracy, computational cost, and memory usage. Moreover, examples of topology optimization for a 3-dimensional problem are presented to demonstrate the applicability of the proposed method to large-scale analyses.https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00225/_pdf/-char/entopology optimizationmulti-materialsensitivity analysisautomatic differentiationadjoint variable methodfinite element method |
| spellingShingle | Shun OGAWA Kazuo YONEKURA Katsuyuki SUZUKI Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization Nihon Kikai Gakkai ronbunshu topology optimization multi-material sensitivity analysis automatic differentiation adjoint variable method finite element method |
| title | Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| title_full | Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| title_fullStr | Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| title_full_unstemmed | Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| title_short | Sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| title_sort | sensitivity analysis for any functions of static elastic systems using combination of adjoint variable method and automatic differentiation for topology optimization |
| topic | topology optimization multi-material sensitivity analysis automatic differentiation adjoint variable method finite element method |
| url | https://www.jstage.jst.go.jp/article/transjsme/91/941/91_24-00225/_pdf/-char/en |
| work_keys_str_mv | AT shunogawa sensitivityanalysisforanyfunctionsofstaticelasticsystemsusingcombinationofadjointvariablemethodandautomaticdifferentiationfortopologyoptimization AT kazuoyonekura sensitivityanalysisforanyfunctionsofstaticelasticsystemsusingcombinationofadjointvariablemethodandautomaticdifferentiationfortopologyoptimization AT katsuyukisuzuki sensitivityanalysisforanyfunctionsofstaticelasticsystemsusingcombinationofadjointvariablemethodandautomaticdifferentiationfortopologyoptimization |