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PIES with Trimmed Surfaces for Solving Elastoplastic Boundary Problems

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Computational Science – ICCS 2022 (ICCS 2022)

Abstract

The paper presents the strategy for solving elastoplastic problems using a parametric integral equation system (PIES) and a trimming technique. It allows even complex shapes of a plastic zone to be modeled with a single surface and a set of trimming curves. New schemes for integration and approximation of solutions are developed to include changed requirements. However, both of them have kept their advantages. Some examples are solved, and the obtained results are compared with analytical solutions and those received from other numerical methods.

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References

  1. Zienkiewicz, O.C.: The Finite Element Methods. McGraw-Hill, London (1977)

    MATH  Google Scholar 

  2. Aliabadi, M.H.: The Boundary Element Method. Applications in Solids and Structures, vol. 2. Wiley, Chichester (2002)

    MATH  Google Scholar 

  3. Bołtuć, A.: Elastoplastic boundary problems in PIES comparing to BEM and FEM. Comput. Math. Appl. 72(9), 2343–2363 (2016)

    Article  MathSciNet  Google Scholar 

  4. Bołtuć, A.: 2D elastoplastic boundary problems solved by PIES without strongly singular surface integrals. Eur. J. Mech. A-Solid 65, 233–242 (2017)

    Article  MathSciNet  Google Scholar 

  5. Salomon, D.: Curves and Surfaces for Computer Graphics. Springer, New York (2006). https://doi.org/10.1007/0-387-28452-4

    Book  MATH  Google Scholar 

  6. Czarny, O., Huysmans, G.: Bézier surfaces and finite elements for MHD simulations. J. Comput. Phys. 227(16), 7423–7445 (2008)

    Article  MathSciNet  Google Scholar 

  7. Hyun-Jung, K., Yu-Deok, S., Sung-Kie, Y.: Isogeometric analysis for trimmed CAD surfaces. Comput. Method Appl. Mech. Eng. 198, 2982–2995 (2009)

    Article  Google Scholar 

  8. Marussig, B., Hughes, T.J.R.: A review of trimming in isogeometric analysis: challenges, data exchange and simulation aspects. Arch. Comput. Method E 25,1059–1127 (2018)

    Google Scholar 

  9. Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 ACM National Conference, pp. 517–524. Association for Computing Machinery, USA (1968)

    Google Scholar 

  10. Bołtuć, A., Zieniuk, E.: PIES for 2D elastoplastic problems with singular plastic strain fields. Comput. Math. Appl. 103, 53–64 (2021)

    Article  MathSciNet  Google Scholar 

  11. Lubliner, J.: Plasticity Theory. Macmillan Publishing Company, New York (1990)

    MATH  Google Scholar 

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Correspondence to Agnieszka Bołtuć .

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Bołtuć, A., Zieniuk, E. (2022). PIES with Trimmed Surfaces for Solving Elastoplastic Boundary Problems. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13351. Springer, Cham. https://doi.org/10.1007/978-3-031-08754-7_17

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  • DOI: https://doi.org/10.1007/978-3-031-08754-7_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08753-0

  • Online ISBN: 978-3-031-08754-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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