A data‐driven bond‐based peridynamic model derived from group method of data handling neural network with genetic algorithm
In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data ha...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 123; H. 22; S. 5618 - 5651 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Hoboken, USA
John Wiley & Sons, Inc
30.11.2022
Wiley Subscription Services, Inc |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data handling (GMDH) neural network is first developed to explicitly derive the discrete bond‐based peridynamic equation of motion based on measured data in this study rather than traditional complicated mathematical derivation. In order to discover the optimal structure more efficiently and to avoid exhaustive search, genetic algorithm is incorporated into GMDH structure. It is found that the prediction results obtained by GMDH model agree well with measured values both for training and testing data. Moreover, the derived equation of motion is expressed as the product of parameter composed of Young's modulus and length scale and linear combination of displacements of material points in the horizon, which is in accordance with the original bond‐based peridynamic formulation. Furthermore, numerical benchmarks associated with elastic deformation and crack problems are performed and compared with analytical solution or finite element analysis result to verify the validity and feasibility of the proposed model. |
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| AbstractList | In the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data handling (GMDH) neural network is first developed to explicitly derive the discrete bond‐based peridynamic equation of motion based on measured data in this study rather than traditional complicated mathematical derivation. In order to discover the optimal structure more efficiently and to avoid exhaustive search, genetic algorithm is incorporated into GMDH structure. It is found that the prediction results obtained by GMDH model agree well with measured values both for training and testing data. Moreover, the derived equation of motion is expressed as the product of parameter composed of Young's modulus and length scale and linear combination of displacements of material points in the horizon, which is in accordance with the original bond‐based peridynamic formulation. Furthermore, numerical benchmarks associated with elastic deformation and crack problems are performed and compared with analytical solution or finite element analysis result to verify the validity and feasibility of the proposed model. |
| Author | Zhou, Xiao‐Ping Yu, Xiang‐Long |
| Author_xml | – sequence: 1 givenname: Xiang‐Long surname: Yu fullname: Yu, Xiang‐Long organization: Chongqing University – sequence: 2 givenname: Xiao‐Ping orcidid: 0000-0003-1551-6504 surname: Zhou fullname: Zhou, Xiao‐Ping email: xiao_ping_zhou@126.com organization: Chongqing University |
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| CitedBy_id | crossref_primary_10_1016_j_cma_2024_117226 crossref_primary_10_1007_s00466_023_02365_0 crossref_primary_10_1016_j_ijmecsci_2024_109234 crossref_primary_10_1016_j_cma_2024_117268 crossref_primary_10_1016_j_compstruc_2024_107395 crossref_primary_10_1016_j_tafmec_2023_103980 crossref_primary_10_3390_math11061381 crossref_primary_10_1016_j_enganabound_2024_01_004 crossref_primary_10_1016_j_enganabound_2023_08_028 crossref_primary_10_1002_nme_7296 |
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| SubjectTerms | data‐driven model Elastic deformation equation of motion Equations of motion Exact solutions Finite element method Genetic algorithms GMDH neural network Group method of data handling Horizon Modulus of elasticity Neural networks peridynamics Response functions Stiffness |
| Title | A data‐driven bond‐based peridynamic model derived from group method of data handling neural network with genetic algorithm |
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