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Error estimation in nonlinear problems based on stress recovery in t-r-refinement strategy by isogeometric method

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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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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data generated or analyzed during this study are included in this published article, and also the datasets during the current study are available from the corresponding author on reasonable request.]

Notes

  1. Non-Uniform Rational B-Splines.

  2. Isogeometric Analysis.

  3. Remesh Refinement.

  4. Thermal Gradient-based Remesh Refinement.

  5. Recovery Nonlinear Isogeometric Analysis by Equilibrium in Patches.

  6. Recovery Nonlinear Isogeometric Analysis by Superconvergent Points.

  7. Computer-Aided Design.

  8. Unbalanced forces.

  9. Element subdivision (enrichment).

  10. Voronoi tessellation.

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Authors and Affiliations

  1. Department of Civil Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran

    Ali Shahini, Ahmad Ganjali & Aboozar Mirzakhani

Authors
  1. Ali Shahini
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  2. Ahmad Ganjali
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  3. Aboozar Mirzakhani
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Correspondence to Ahmad Ganjali.

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Shahini, A., Ganjali, A. & Mirzakhani, A. Error estimation in nonlinear problems based on stress recovery in t-r-refinement strategy by isogeometric method. Eur. Phys. J. Plus 138, 839 (2023). https://doi.org/10.1140/epjp/s13360-023-04453-9

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