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1.
A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity : Application to cooling of hot-rolled steel bars on a cooling bed
Gašper Vuga, Boštjan Mavrič, Umut Hanoglu, Božidar Šarler, 2024, original scientific article

Abstract: This paper represents Part 2 of the parallel paper Part 1, where the strong form hybrid RBF-FD method was developed for solving thermo-elasto-plastic problems. It addresses the industrial application of this novel meshless method to steel bars cooling on a cooling bed (CB) where the formation of residual stress is of primary interest. The study investigates the impact of the distance between the bars and the distance to the heat shield above the CB on radiative heat fluxes and, consequently, on thermo-mechanical response. The thermal model is solved on bars cross-section with a RBF-FD method where augmented polyharmonic splines are used for the local approximation. View factors, computed with a Monte-Carlo method, are included in radiative heat fluxes. The thermal solution is incrementally applied on a mechanical model that assumes a generalised plane strain state and captures bars bending. The study employs a hybrid RBF-FD method to resolve a nonlinear discontinuous mechanical problem successfully. The simulation of the process shows how different process parameters influence the thermo-mechanical response of the bars.
Keywords: steel bars, cooling bed, thermo-mechanical modelling, hybrid radial basis function, generated finite differences, residual stresses
Published in DiRROS: 28.02.2024; Views: 120; Downloads: 69
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2.
A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 1 : method formulation and testing
Gašper Vuga, Boštjan Mavrič, Božidar Šarler, 2024, original scientific article

Abstract: 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.
Keywords: thermo-mechanical modelling, von Mises small strain plasticity, hybrid radial basis function generated finite differences, polyharmonic splines
Published in DiRROS: 28.02.2024; Views: 122; Downloads: 65
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