A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson...

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Main Authors: Lin Zhang, D. M. Li, Cen-Ying Liao, Li-Rui Tian
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/14/2259
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author Lin Zhang
D. M. Li
Cen-Ying Liao
Li-Rui Tian
author_facet Lin Zhang
D. M. Li
Cen-Ying Liao
Li-Rui Tian
author_sort Lin Zhang
collection DOAJ
description A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated.
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institution Kabale University
issn 2227-7390
language English
publishDate 2025-07-01
publisher MDPI AG
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series Mathematics
spelling doaj-art-e0abad18a72c4706b14fde95a9a2d95c2025-08-20T03:58:30ZengMDPI AGMathematics2227-73902025-07-011314225910.3390/math13142259A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling ProblemsLin Zhang0D. M. Li1Cen-Ying Liao2Li-Rui Tian3School of Physics and Mechanics, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, ChinaA meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated.https://www.mdpi.com/2227-7390/13/14/2259quasi-convex reproducing kernel (QCRK) approximationquasi-convex reproducing kernel particle method (QCRKPM)steady-state thermo-mechanic coupling problemsmeshless/meshfree methodsheat conduction
spellingShingle Lin Zhang
D. M. Li
Cen-Ying Liao
Li-Rui Tian
A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
Mathematics
quasi-convex reproducing kernel (QCRK) approximation
quasi-convex reproducing kernel particle method (QCRKPM)
steady-state thermo-mechanic coupling problems
meshless/meshfree methods
heat conduction
title A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
title_full A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
title_fullStr A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
title_full_unstemmed A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
title_short A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
title_sort quasi convex rkpm for 3d steady state thermomechanical coupling problems
topic quasi-convex reproducing kernel (QCRK) approximation
quasi-convex reproducing kernel particle method (QCRKPM)
steady-state thermo-mechanic coupling problems
meshless/meshfree methods
heat conduction
url https://www.mdpi.com/2227-7390/13/14/2259
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