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

doi:10.16183/j.cnki.jsjtu.2020.215

Abstract

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)

CLC Number:

O343.6

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