Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure)
In this study, we propose a topology optimization method for dynamic problems to control the deformation of the structure. To derive a structure that minimizes the deformation due to transient loads for an isotropic linear elastic model, the strain energy and the squared norm of dynamic compliance a...
| Main Authors: | , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2021-01-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/87/893/87_20-00382/_pdf/-char/en |
| _version_ | 1797989050304430080 |
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| author | Shun OGAWA Takayuki YAMADA |
| author_facet | Shun OGAWA Takayuki YAMADA |
| author_sort | Shun OGAWA |
| collection | DOAJ |
| description | In this study, we propose a topology optimization method for dynamic problems to control the deformation of the structure. To derive a structure that minimizes the deformation due to transient loads for an isotropic linear elastic model, the strain energy and the squared norm of dynamic compliance are set as objective functions. The topology optimization method applies a density method based on the RAMP method. In the case of the density method, since a optimal structure is obtained by an optimization algorithm based on the gradient method, it is necessary to formulate design sensitivity equations that can appropriately take into account the target optimization problem. A generalized sensitivity analysis method is proposed by introducing the adjoint method and applying Newmark’s β method, which considers the displacement as an unknown quantity , and considering the equations of motion. Furthermore, the accuracy of the sensitivity is verified by using the finite difference method as a benchmark, and it is shown that the proposed design sensitivity has high accuracy. Finally, as a numerical example, we derive optimal structures for several optimization problems and discuss the optimization problem settings to obtain a structure that can control vibrations. The validity of the proposed method is demonstrated by deriving the optimal structure to control the vibration. |
| first_indexed | 2024-04-11T08:14:05Z |
| format | Article |
| id | doaj.art-c015d103d76b46698bba320d5a4cc3bb |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-11T08:14:05Z |
| publishDate | 2021-01-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-c015d103d76b46698bba320d5a4cc3bb2022-12-22T04:35:14ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612021-01-018789320-0038220-0038210.1299/transjsme.20-00382transjsmeTopology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure)Shun OGAWA0Takayuki YAMADA1Department of Mechanical Engineering, The University of TokyoDepartment of Strategic Studies, Institute of Engineering Innovation, The University of TokyoIn this study, we propose a topology optimization method for dynamic problems to control the deformation of the structure. To derive a structure that minimizes the deformation due to transient loads for an isotropic linear elastic model, the strain energy and the squared norm of dynamic compliance are set as objective functions. The topology optimization method applies a density method based on the RAMP method. In the case of the density method, since a optimal structure is obtained by an optimization algorithm based on the gradient method, it is necessary to formulate design sensitivity equations that can appropriately take into account the target optimization problem. A generalized sensitivity analysis method is proposed by introducing the adjoint method and applying Newmark’s β method, which considers the displacement as an unknown quantity , and considering the equations of motion. Furthermore, the accuracy of the sensitivity is verified by using the finite difference method as a benchmark, and it is shown that the proposed design sensitivity has high accuracy. Finally, as a numerical example, we derive optimal structures for several optimization problems and discuss the optimization problem settings to obtain a structure that can control vibrations. The validity of the proposed method is demonstrated by deriving the optimal structure to control the vibration.https://www.jstage.jst.go.jp/article/transjsme/87/893/87_20-00382/_pdf/-char/entopology optimizationdensity methodrampanalytical sensitivity analysisdynamic analysisfinite element method |
| spellingShingle | Shun OGAWA Takayuki YAMADA Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) Nihon Kikai Gakkai ronbunshu topology optimization density method ramp analytical sensitivity analysis dynamic analysis finite element method |
| title | Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) |
| title_full | Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) |
| title_fullStr | Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) |
| title_full_unstemmed | Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) |
| title_short | Topology optimization of transient response problems using step by step integration method (Formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure) |
| title_sort | topology optimization of transient response problems using step by step integration method formulation of analytical sensitivity with displacement as an unknown quantity and synthesis of vibration control structure |
| topic | topology optimization density method ramp analytical sensitivity analysis dynamic analysis finite element method |
| url | https://www.jstage.jst.go.jp/article/transjsme/87/893/87_20-00382/_pdf/-char/en |
| work_keys_str_mv | AT shunogawa topologyoptimizationoftransientresponseproblemsusingstepbystepintegrationmethodformulationofanalyticalsensitivitywithdisplacementasanunknownquantityandsynthesisofvibrationcontrolstructure AT takayukiyamada topologyoptimizationoftransientresponseproblemsusingstepbystepintegrationmethodformulationofanalyticalsensitivitywithdisplacementasanunknownquantityandsynthesisofvibrationcontrolstructure |