基于滑动Kriging插值的EFG-SBM求解含侧边界的稳态热传导问题

doi:10.16183/j.cnki.jsjtu.2020.215

上海交通大学学报 ›› 2021, Vol. 55 ›› Issue (11): 1483-1492.doi: 10.16183/j.cnki.jsjtu.2020.215

所属专题：《上海交通大学学报》2021年12期专题汇总专辑；《上海交通大学学报》2021年“水利工程”专题

基于滑动Kriging插值的EFG-SBM求解含侧边界的稳态热传导问题

王峰¹^,², 陈佳莉¹^,², 陈灯红³(), 范勇¹^,², 李志远⁴, 何卫平¹^,²

1.三峡大学水利与环境学院,湖北宜昌 443002
2.三峡大学湖北省水电工程施工与管理重点实验室,湖北宜昌 443002
3.三峡大学土木与建筑学院,湖北宜昌 443002
4.大连理工大学建设工程学部,辽宁大连 116024

收稿日期:2020-07-08 出版日期:2021-11-28 发布日期:2021-12-03
通讯作者: 陈灯红 E-mail:d.chen@ctgu.edu.cn
作者简介:王峰(1987-),男,山东省莱阳市人,副教授,从事无网格法及比例边界有限元法研究.
基金资助:
国家自然科学基金(51809154);湖北省教育厅科学技术研究项目(Q20181207);湖北省高等学校优秀中青年科技创新团队计划(T2020005);湖北省水电工程施工与管理重点实验室开放基金(2019KSD04)

Element-Free Galerkin Scaled Boundary Method Based on Moving Kriging Interpolation for Steady Heat Conduction Analysis with Temperatures on Side-Faces

WANG Feng¹^,², CHEN Jiali¹^,², CHEN Denghong³(), FAN Yong¹^,², LI Zhiyuan⁴, HE Weiping¹^,²

1. College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, Hubei, China
2. Hubei Key Laboratory of Construction and Management in Hydropower Engineering, China Three Gorges University, Yichang 443002, Hubei, China
3. College of Civil Engineering and Architecture, China Three Gorges University, Yichang 443002, Hubei, China
4. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China

Received:2020-07-08 Online:2021-11-28 Published:2021-12-03
Contact: CHEN Denghong E-mail:d.chen@ctgu.edu.cn

摘要/Abstract

摘要：

采用基于滑动Kriging插值的无单元伽辽金比例边界法(EFG-SBM)求解侧边界有温度载荷的稳态热传导问题,该方法通过无单元伽辽金法(EFG)和滑动Kriging插值离散环向边界.由于滑动Kriging插值形函数具备Kronecker delta函数插值特性,克服了移动最小二乘逼近难以直接准确施加本质边界条件的不足.作为一种新型的边界型无网格法,EFG-SBM兼有EFG法和比例边界有限元法(SBFEM)的优点.该方法继承了SBFEM的半解析特性,通过引入比例边界坐标系,可将偏微分控制方程环向离散,径向上解析求解.与传统的SBFEM相比,环向边界通过节点进行离散,前处理和后处理简便.通过数值算例可以看出,相比基于拉格朗日多项式的SBFEM,基于滑动Kriging插值的EFG-SBM计算精度更高.相比有限元法(FEM),该方法能更好地反映尖角处热奇异性以及无限域温度分布状态.

关键词: 无单元伽辽金比例边界法, 滑动Kriging插值, 热传导, 比例边界有限元法

Abstract:

The element-free Galerkin scaled boundary method (EFG-SBM) based on moving Kriging (MK) interpolation is used to solve steady heat conduction problems with temperature loads on side-faces, in which the circumferential boundary is discretized based on MK interpolation and the element-free Galerkin (EFG) method. As the shape functions constructed from the MK interpolation possess the Kronecker delta interpolation property, the MK shape functions overcome the shortcomings of moving least squares (MLS) approximation which is difficult to impose essential boundary conditions directly and accurately. As a new boundary-type meshless method, EFG-SBM has advantages of the EFG and scaled boundary finite element method (SBFEM). This method inherits the semi-analytical property of SBFEM by introducing the scaled boundary coordinate system, in which the governing differential equations are weakened in the circumferential direction and can be solved analytically in the radial direction. Unlike the traditional SBFEM, the preprocessing and postprocessing processes of EFG-SBM are simplified since only the nodal data structure is required in the circumferential direction. Numerical examples show that the EFG-SBM based on MK interpolation can obtain a higher accuracy than the SBFEM based on Lagrange polynomials. Compared with the finite element method (FEM), this method can better characterize the thermal singularity at the sharp corner and the temperature distribution of the infinite region.

Key words: element-free Galerkin scaled boundary method (EFG-SBM), moving Kriging (MK) interpolation, heat conduction, scaled boundary finite element method (SBFEM)

中图分类号:

O343.6

王峰, 陈佳莉, 陈灯红, 范勇, 李志远, 何卫平. 基于滑动Kriging插值的EFG-SBM求解含侧边界的稳态热传导问题[J]. 上海交通大学学报, 2021, 55(11): 1483-1492.

WANG Feng, CHEN Jiali, CHEN Denghong, FAN Yong, LI Zhiyuan, HE Weiping. Element-Free Galerkin Scaled Boundary Method Based on Moving Kriging Interpolation for Steady Heat Conduction Analysis with Temperatures on Side-Faces[J]. Journal of Shanghai Jiao Tong University, 2021, 55(11): 1483-1492.

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计算点 (x,y)	理论解	SBFEM解	EFG- SBM解	SBFEM 误差/%	EFG-SBM 误差/%
(5,1)	9.927	9.971	9.927	0.45	0
(5,2)	20.841	20.823	20.842	0.09	0.005
(5,3)	33.830	33.804	33.830	0.08	0
(5,4)	50.184	50.155	50.185	0.06	0.002
(5,5)	71.533	71.509	71.533	0.03	0

基于滑动Kriging插值的EFG-SBM求解含侧边界的稳态热传导问题

Element-Free Galerkin Scaled Boundary Method Based on Moving Kriging Interpolation for Steady Heat Conduction Analysis with Temperatures on Side-Faces

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