Volume 8, Issue 5
Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

Bin Chen, Wen Chen & Xing Wei

Adv. Appl. Math. Mech., 8 (2016), pp. 810-826.

Published online: 2018-05

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  • Abstract

This article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

  • Keywords

Inverse problems, parameter identification, meshless method, singular boundary method, Levenberg-Marquardt method.

  • AMS Subject Headings

62P30, 65M32, 65K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-810, author = {}, title = {Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {810--826}, abstract = {

This article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m904}, url = {http://global-sci.org/intro/article_detail/aamm/12118.html} }
TY - JOUR T1 - Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 810 EP - 826 PY - 2018 DA - 2018/05 SN - 8 DO - http://dor.org/10.4208/aamm.2015.m904 UR - https://global-sci.org/intro/aamm/12118.html KW - Inverse problems, parameter identification, meshless method, singular boundary method, Levenberg-Marquardt method. AB -

This article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

Bin Chen, Wen Chen & Xing Wei. (2020). Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method. Advances in Applied Mathematics and Mechanics. 8 (5). 810-826. doi:10.4208/aamm.2015.m904
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