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Error estimation in nonlinear problems based on stress recovery in t-r-refinement strategy by isogeometric method
In this research, stress recovery methods using superconvergent points and equilibrium in patches methods have been used in solving nonlinear problems to achieve more reliable results. These two methods have been compared with the help of the isogeometric analysis method. The performance of these tw...
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| Published in: | European physical journal plus 2023-09, Vol.138 (9), p.839, Article 839 |
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| Main Authors: | , , |
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| container_issue | 9 |
| container_start_page | 839 |
| container_title | European physical journal plus |
| container_volume | 138 |
| creator | Shahini, Ali Ganjali, Ahmad Mirzakhani, Aboozar |
| description | In this research, stress recovery methods using superconvergent points and equilibrium in patches methods have been used in solving nonlinear problems to achieve more reliable results. These two methods have been compared with the help of the isogeometric analysis method. The performance of these two methods in guiding the adaptive solution algorithm based on the movement of control points has been investigated. In the stress recovery methods, error estimation has been considered by assuming the error as a thermal gradient dependent on the energy norm. For this purpose, we carried out modeling of two nonlinear problems based on their analytical solution, and the results have shown that both stress recovery methods used in improving the network of control points have had a desirable effect. The effectiveness of the equilibrium in patches method is more than the method based on superconvergent points in achieving more accurate results, and it can be used as a suitable solution to improve the stress field.
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| doi_str_mv | 10.1140/epjp/s13360-023-04453-9 |
| format | article |
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Phys. J. Plus</stitle><date>2023-09-25</date><risdate>2023</risdate><volume>138</volume><issue>9</issue><spage>839</spage><pages>839-</pages><artnum>839</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>In this research, stress recovery methods using superconvergent points and equilibrium in patches methods have been used in solving nonlinear problems to achieve more reliable results. These two methods have been compared with the help of the isogeometric analysis method. The performance of these two methods in guiding the adaptive solution algorithm based on the movement of control points has been investigated. In the stress recovery methods, error estimation has been considered by assuming the error as a thermal gradient dependent on the energy norm. For this purpose, we carried out modeling of two nonlinear problems based on their analytical solution, and the results have shown that both stress recovery methods used in improving the network of control points have had a desirable effect. The effectiveness of the equilibrium in patches method is more than the method based on superconvergent points in achieving more accurate results, and it can be used as a suitable solution to improve the stress field.
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| subjects | Adaptive algorithms Adaptive control Applied and Technical Physics Atomic Complex Systems Condensed Matter Physics Equilibrium methods Error analysis Exact solutions Geometry Knots Mathematical and Computational Physics Mathematical functions Methods Molecular Optical and Plasma Physics Physics Physics and Astronomy Recovery Regular Article Stress distribution Theoretical |
| title | Error estimation in nonlinear problems based on stress recovery in t-r-refinement strategy by isogeometric method |
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