A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 1 : method formulation and testing

Vuga, Gašper (author), Mavrič, Boštjan (author), Šarler, Božidar (author)

A hybrid version of the strong form meshless Radial Basis Function-Finite Difference (RBF-FD) method is introduced for solving thermo-mechanics. The thermal model is spatially discretised with RBF-FD, where trial functions are polyharmonic splines augmented with polynomials. For time discretisation, the explicit Euler method is employed. An extension of RBF-FD, the hybrid RBF-FD, is introduced for solving mechanical problems. The model is one-way coupled, where temperature affects displacements. The thermo-elastoplastic material response is considered where the stress field is generally non-smooth. The hybrid RBF-FD, where the finite difference method is used to discretise the divergence operator from the balance equation, is shown to be successful when dealing with such problems. The mechanical model is introduced in a plane strain and in a generalised plane strain (GPS) assumption. For the first time, this work presents a strong form RBF-FD for GPS problems subjected to integral form constraints. The proposed method is assessed regarding h-convergence and accuracy on the benchmark with heating an elastoplastic square. It is proven to be successful at solving one-way coupled thermo-elastoplastic problems. The proposed novel meshless approach is efficient, accurate, and robust. Its use in an industrial situation is provided in Part 2 of this paper.

• Language: English
• Keywords: thermo-mechanical modelling, von Mises small strain plasticity, hybrid radial basis function generated finite differences, polyharmonic splines
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 58-67
• Numbering: Vol. 159
• PID: 20.500.12556/RUL-152636
• UDC: 539.3:519.6
• ISSN on article: 0955-7997
• DOI: 10.1016/j.enganabound.2023.11.014
• COBISS.SI-ID: 174529795
• Publication date in RUL: 01.12.2023

Record is a part of a journal

• Title: Engineering analysis with boundary elements
• Shortened title: Eng. anal. bound. elem.
• Publisher: Elsevier
• ISSN: 0955-7997
• COBISS.SI-ID: 5605380

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: termo-mehansko modeliranje, von Misesova plastičnost z majhnimi deformacijami, hibridne končne diference generirane z radialnimi baznimi funkcijami, poliharmonični zlepki