A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

doi:10.1088/1674-1056/22/12/120204

中国物理B ›› 2013, Vol. 22 ›› Issue (12): 120204-120204.doi: 10.1088/1674-1056/22/12/120204

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

李庆华, 陈莘莘, 曾骥辉

College of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, China

收稿日期:2013-08-02 修回日期:2013-08-21 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11002054) and the Foundation of Hunan Educational Committee (Grant No. 12C0059).

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

Li Qing-Hua (李庆华), Chen Shen-Shen (陈莘莘), Zeng Ji-Hui (曾骥辉)

College of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, China

Received:2013-08-02 Revised:2013-08-21 Online:2013-10-25 Published:2013-10-25
Contact: Chen Shen-Shen E-mail:chenshenshen@tsinghua.org.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11002054) and the Foundation of Hunan Educational Committee (Grant No. 12C0059).

摘要/Abstract

摘要： A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional (3D) axisymmetric continuously nonhomogeneous functionally graded materials (FGMs). Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional (2D) problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method (FEM) shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

关键词: meshless method, transient heat conduction problem, axisymmetric, functionally graded materials, natural neighbor interpolation

Abstract: A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional (3D) axisymmetric continuously nonhomogeneous functionally graded materials (FGMs). Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional (2D) problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method (FEM) shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

Key words: meshless method, transient heat conduction problem, axisymmetric, functionally graded materials, natural neighbor interpolation

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 44.10.+i (Heat conduction)

李庆华, 陈莘莘, 曾骥辉. A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids[J]. 中国物理B, 2013, 22(12): 120204-120204.

Li Qing-Hua (李庆华), Chen Shen-Shen (陈莘莘), Zeng Ji-Hui (曾骥辉). A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids[J]. Chin. Phys. B, 2013, 22(12): 120204-120204.

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A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

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