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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Zienkiewicz, O.C.: The Finite Element Methods. McGraw-Hill, London (1977)
Aliabadi, M.H.: The Boundary Element Method. Applications in Solids and Structures, vol. 2. Wiley, Chichester (2002)
Bołtuć, A.: Elastoplastic boundary problems in PIES comparing to BEM and FEM. Comput. Math. Appl. 72(9), 2343–2363 (2016)
Bołtuć, A.: 2D elastoplastic boundary problems solved by PIES without strongly singular surface integrals. Eur. J. Mech. A-Solid 65, 233–242 (2017)
Salomon, D.: Curves and Surfaces for Computer Graphics. Springer, New York (2006). https://doi.org/10.1007/0-387-28452-4
Czarny, O., Huysmans, G.: Bézier surfaces and finite elements for MHD simulations. J. Comput. Phys. 227(16), 7423–7445 (2008)
Hyun-Jung, K., Yu-Deok, S., Sung-Kie, Y.: Isogeometric analysis for trimmed CAD surfaces. Comput. Method Appl. Mech. Eng. 198, 2982–2995 (2009)
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)
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)
Bołtuć, A., Zieniuk, E.: PIES for 2D elastoplastic problems with singular plastic strain fields. Comput. Math. Appl. 103, 53–64 (2021)
Lubliner, J.: Plasticity Theory. Macmillan Publishing Company, New York (1990)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-031-08754-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08753-0
Online ISBN: 978-3-031-08754-7
eBook Packages: Computer ScienceComputer Science (R0)