A Numerical Implementation of Linear Matching Method for the Limit Analysis

Jun-Hyok Ri; Hyon-Sik Hong; Yong-Chol Kim; Jin-Chol Ri

doi:doi:10.11648/j.ajma.20251202.11

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A Numerical Implementation of Linear Matching Method for the Limit Analysis

Jun-Hyok Ri^*

, Hyon-Sik Hong, Yong-Chol Kim, Jin-Chol Ri

Published in American Journal of Mechanics and Applications (Volume 12, Issue 2)

Received: 26 February 2025 Accepted: 3 April 2025 Published: 9 May 2025

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Abstract

ANSYS UserMat and its corresponding special MACRO are developed for implementing the linear matching method (LMM) for the limit analysis by using ANSYS. By this, pre and post-processing for the limit analysis can be done in the sole ANSYS circumstance without a help of any additional programs. Once user creates the FE model and enters the parameters for the LMM analysis by using ANSYS interface, ANSYS then will evaluate the upper and lower bound of limit load automatically. In order to overcome the drawback of LMM which does not give the reliable lower bound of limit load, the elastic compensation method (ECM) for the computation of lower bound of limit load is combined with the LMM so that the converged upper and lower bound of limit load is obtained, respectively. Moreover, a simple method is proposed in order to overcome the numerical difficulty of LMM due to the high gradient of stress state. Some numerical examples were given to validate the proposed method and the corresponding computational system and the reliable stability was shown, as expected.

Published in	American Journal of Mechanics and Applications (Volume 12, Issue 2)
DOI	10.11648/j.ajma.20251202.11
Page(s)	22-32
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

LMM, Limit Analysis, ANSYS UPF

References

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[5]	H. F. Chen, A. R. S. Ponter, Shakedown and limit analyses for 3D structures using the linear matching method. Int. J. Pre. Ves. & Piping, 78(2001) 443-451.
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APA Style

Ri, J., Hong, H., Kim, Y., Ri, J. (2025). A Numerical Implementation of Linear Matching Method for the Limit Analysis. American Journal of Mechanics and Applications, 12(2), 22-32. https://doi.org/10.11648/j.ajma.20251202.11

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ACS Style

Ri, J.; Hong, H.; Kim, Y.; Ri, J. A Numerical Implementation of Linear Matching Method for the Limit Analysis. Am. J. Mech. Appl. 2025, 12(2), 22-32. doi: 10.11648/j.ajma.20251202.11

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AMA Style

Ri J, Hong H, Kim Y, Ri J. A Numerical Implementation of Linear Matching Method for the Limit Analysis. Am J Mech Appl. 2025;12(2):22-32. doi: 10.11648/j.ajma.20251202.11

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@article{10.11648/j.ajma.20251202.11,
  author = {Jun-Hyok Ri and Hyon-Sik Hong and Yong-Chol Kim and Jin-Chol Ri},
  title = {A Numerical Implementation of Linear Matching Method for the Limit Analysis
},
  journal = {American Journal of Mechanics and Applications},
  volume = {12},
  number = {2},
  pages = {22-32},
  doi = {10.11648/j.ajma.20251202.11},
  url = {https://doi.org/10.11648/j.ajma.20251202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20251202.11},
  abstract = {ANSYS UserMat and its corresponding special MACRO are developed for implementing the linear matching method (LMM) for the limit analysis by using ANSYS. By this, pre and post-processing for the limit analysis can be done in the sole ANSYS circumstance without a help of any additional programs. Once user creates the FE model and enters the parameters for the LMM analysis by using ANSYS interface, ANSYS then will evaluate the upper and lower bound of limit load automatically. In order to overcome the drawback of LMM which does not give the reliable lower bound of limit load, the elastic compensation method (ECM) for the computation of lower bound of limit load is combined with the LMM so that the converged upper and lower bound of limit load is obtained, respectively. Moreover, a simple method is proposed in order to overcome the numerical difficulty of LMM due to the high gradient of stress state. Some numerical examples were given to validate the proposed method and the corresponding computational system and the reliable stability was shown, as expected.},
 year = {2025}
}

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TY  - JOUR
T1  - A Numerical Implementation of Linear Matching Method for the Limit Analysis

AU  - Jun-Hyok Ri
AU  - Hyon-Sik Hong
AU  - Yong-Chol Kim
AU  - Jin-Chol Ri
Y1  - 2025/05/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ajma.20251202.11
DO  - 10.11648/j.ajma.20251202.11
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 22
EP  - 32
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20251202.11
AB  - ANSYS UserMat and its corresponding special MACRO are developed for implementing the linear matching method (LMM) for the limit analysis by using ANSYS. By this, pre and post-processing for the limit analysis can be done in the sole ANSYS circumstance without a help of any additional programs. Once user creates the FE model and enters the parameters for the LMM analysis by using ANSYS interface, ANSYS then will evaluate the upper and lower bound of limit load automatically. In order to overcome the drawback of LMM which does not give the reliable lower bound of limit load, the elastic compensation method (ECM) for the computation of lower bound of limit load is combined with the LMM so that the converged upper and lower bound of limit load is obtained, respectively. Moreover, a simple method is proposed in order to overcome the numerical difficulty of LMM due to the high gradient of stress state. Some numerical examples were given to validate the proposed method and the corresponding computational system and the reliable stability was shown, as expected.
VL  - 12
IS  - 2
ER  -

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Author Information

Jun-Hyok Ri

Institute of Mechanics, State Academy of Sciences, Pyongyang, DPR Korea

Contact Email

http://orcid.org/0009-0009-8613-3907
Hyon-Sik Hong

Institute of Mechanics, State Academy of Sciences, Pyongyang, DPR Korea
Yong-Chol Kim

Department of Coal Mining Construction Engineering, Pyongsong University of Coal Mining, Pyongsong, DPR Korea
Jin-Chol Ri

Department of Coal Mining Construction Engineering, Pyongsong University of Coal Mining, Pyongsong, DPR Korea

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Plain Text BibTeX RIS

APA Style

Ri, J., Hong, H., Kim, Y., Ri, J. (2025). A Numerical Implementation of Linear Matching Method for the Limit Analysis. American Journal of Mechanics and Applications, 12(2), 22-32. https://doi.org/10.11648/j.ajma.20251202.11

Copy | Download

ACS Style

Ri, J.; Hong, H.; Kim, Y.; Ri, J. A Numerical Implementation of Linear Matching Method for the Limit Analysis. Am. J. Mech. Appl. 2025, 12(2), 22-32. doi: 10.11648/j.ajma.20251202.11

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AMA Style

Ri J, Hong H, Kim Y, Ri J. A Numerical Implementation of Linear Matching Method for the Limit Analysis. Am J Mech Appl. 2025;12(2):22-32. doi: 10.11648/j.ajma.20251202.11

Copy | Download

@article{10.11648/j.ajma.20251202.11,
  author = {Jun-Hyok Ri and Hyon-Sik Hong and Yong-Chol Kim and Jin-Chol Ri},
  title = {A Numerical Implementation of Linear Matching Method for the Limit Analysis
},
  journal = {American Journal of Mechanics and Applications},
  volume = {12},
  number = {2},
  pages = {22-32},
  doi = {10.11648/j.ajma.20251202.11},
  url = {https://doi.org/10.11648/j.ajma.20251202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20251202.11},
  abstract = {ANSYS UserMat and its corresponding special MACRO are developed for implementing the linear matching method (LMM) for the limit analysis by using ANSYS. By this, pre and post-processing for the limit analysis can be done in the sole ANSYS circumstance without a help of any additional programs. Once user creates the FE model and enters the parameters for the LMM analysis by using ANSYS interface, ANSYS then will evaluate the upper and lower bound of limit load automatically. In order to overcome the drawback of LMM which does not give the reliable lower bound of limit load, the elastic compensation method (ECM) for the computation of lower bound of limit load is combined with the LMM so that the converged upper and lower bound of limit load is obtained, respectively. Moreover, a simple method is proposed in order to overcome the numerical difficulty of LMM due to the high gradient of stress state. Some numerical examples were given to validate the proposed method and the corresponding computational system and the reliable stability was shown, as expected.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A Numerical Implementation of Linear Matching Method for the Limit Analysis

AU  - Jun-Hyok Ri
AU  - Hyon-Sik Hong
AU  - Yong-Chol Kim
AU  - Jin-Chol Ri
Y1  - 2025/05/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ajma.20251202.11
DO  - 10.11648/j.ajma.20251202.11
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 22
EP  - 32
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20251202.11
AB  - ANSYS UserMat and its corresponding special MACRO are developed for implementing the linear matching method (LMM) for the limit analysis by using ANSYS. By this, pre and post-processing for the limit analysis can be done in the sole ANSYS circumstance without a help of any additional programs. Once user creates the FE model and enters the parameters for the LMM analysis by using ANSYS interface, ANSYS then will evaluate the upper and lower bound of limit load automatically. In order to overcome the drawback of LMM which does not give the reliable lower bound of limit load, the elastic compensation method (ECM) for the computation of lower bound of limit load is combined with the LMM so that the converged upper and lower bound of limit load is obtained, respectively. Moreover, a simple method is proposed in order to overcome the numerical difficulty of LMM due to the high gradient of stress state. Some numerical examples were given to validate the proposed method and the corresponding computational system and the reliable stability was shown, as expected.
VL  - 12
IS  - 2
ER  -

Copy | Download