×

A new boundary-type meshfree method with RBFI for 2D thermo-elastic problems. (English) Zbl 1524.74109

Summary: The particular and homogeneous solutions of two-dimension (2D) thermal-elastic problems are expressed by using the virtual boundary element method (VBEM) and the superposition principle. Accordingly, two matrix equations are needed and formed for particular and homogeneous solutions by the novel nonsingular boundary element method with the radial basis function interpolation (RBFI), namely virtual boundary meshfree Galerkin method (VBMGM). Considering the boundary conditions of heat conduction and combining the Galerkin method, virtual source functions of particular solutions can be solved by first using VBMGM. Applying boundary conditions of transformation, virtual source functions of homogeneous solutions can be obtained by second employing VBMGM. The coefficients of two matrix equations are symmetrical. Formed equations are nonsingular and have merits of virtual boundary element method, meshfree method, and Galerkin method. The detailed expressions, calculation steps, and simplified flow chart are given in detail, that is convenient for other scholars to study other more complex thermo-elastic problems through the method of this paper. Three examples are calculated. Comparing their calculation results with other methods, the stability and the precision of VBMGM for 2D thermal-elastic problems are validated.

MSC:

74F05 Thermal effects in solid mechanics
74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N38 Boundary element methods for boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yildirim, A.; Yarimpabuc, D.; Celebi, K., Transient thermal stress analysis of functionally graded annular fin with free base, J. Therm. Stresses, 43, 9, 1138-1149 (2020)
[2] Pu, J.; Wang, W.; Wang, J. H.; Wu, W. L.; Wang, M., Experimental study of free-stream turbulence intensity effect on overall cooling performances and solid thermal deformations of vane laminated end-walls with various internal pin-fin configurations, Appl. Therm. Eng., 173, 1-17 (2020)
[3] Zheng, B. J.; Yang, Y.; Gao, X. W.; Zhang, C., Dynamic fracture analysis of functionally graded materials under thermal shock loading by using the radial integration boundary element method, Comput. Struct., 201, 468-476 (2018)
[4] Yang, K.; Feng, W. Z.; Peng, H. F.; Lv, J., A new analytical approach of functionally graded material structures for thermal stress BEM analysis, Int. Commun. Heat Mass Transf., 62, 26-32 (2015)
[5] Liu, Y. J.; Li, Y. X.; Huang, S., A fast multipole boundary element method for solving two-dimensional thermoelasticity problems, Comput. Mech., 54, 3, 821-831 (2014) · Zbl 1311.74035
[6] Shiah, Y. C.; Tuan, N. A.; Hematiyan, M. R., Thermal stress analysis of 3d anisotropic materials involving domain heat source by the boundary element method, J. Mech., 35, 6, 839-850 (2019)
[7] Hajesfandiari, A.; Hadjesfandiari, A. R.; Dargush, G. F., Boundary element formulation for steady state plane problems in size-dependent thermoelasticity, Eng. Anal. Bound. Elem., 82, 210-226 (2017) · Zbl 1403.74026
[8] Burgess, G.; Mahajerin, E., A comparison of the boundary element and superposition methods, Comput. Struct., 19, 5-6, 697-705 (1984) · Zbl 0552.73075
[9] Sun, H. C.; Zhang, L. Z.; Xu, Q.; Zhang, Y. M., Nonsingularity Boundary Element Methods (1999), Dalian. Univ. Technol. Press: Dalian. Univ. Technol. Press Dalian, (in Chinese)
[10] Xu, Q.; Sun, H. C., Unified way for dealing with three-dimensional problems of solid elasticity, Appl. Math. Mech. (English Ed.), 22, 12, 1357-1367 (2001) · Zbl 1143.74385
[11] Xu, Q.; Zhang, Z. J.; Si, W., Virtual boundary meshless least square collocation method for calculation of 2D multi-domain elastic problems, Eng. Anal. Bound. Elem., 36, 5, 696-708 (2012) · Zbl 1351.74165
[12] Yang, D. S.; Xu, Q., Virtual boundary meshless least square integral method with moving least squares approximation for 2D elastic problem, Eng. Anal. Bound. Elem., 37, 3, 616-623 (2013) · Zbl 1297.74162
[13] Yang, D. S.; Ling, J., Calculating the single-domain heat conduction with heat source problem by virtual boundary meshfree Galerkin method, Int. J. Heat Mass Transf., 92, 610-616 (2016)
[14] Yang, D. S.; Ling, J.; Wang, H. Y.; Chen, T. Y.; Du, Y. D.; Chen, S. G.; Zhang, K. Q., Calculating the multi-domain transient heat conduction with heat source problem by virtual boundary meshfree Galerkin method, Numer. Heat Transf., Part B, Fundam., 74, 1, 465-479 (2018)
[15] Yang, D. S.; Ling, J.; Wang, H. Y.; Huang, Z. H., Calculating 3-D multi-domain heat conduction problems by the virtual boundary element-free Galerkin method, Numer. Heat Transf., Part B, Fundam., 77, 3, 215-227 (2020)
[16] Hematiyan, M. R.; Mohammadi, M.; Tsai, C. C., The method of fundamental solutions for anisotropic thermoelastic problems, Appl. Math. Model., 95, 200-218 (2021) · Zbl 1481.74033
[17] Mohammadi, M.; Hematiyan, M. R., Analysis of transient uncoupled thermoelastic problems involving moving point heat sources using the method of fundamental solutions, Eng. Anal. Bound. Elem., 123, 122-132 (2021) · Zbl 1464.74405
[18] Mohammadi, M.; Hematiyan, M. R.; Shiah, Y. C., An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media, J. Theor. Appl. Mech., 56, 4, 1123-1137 (2018)
[19] Marin, L.; Karageorghis, A.; Lesnic, D.; Johansson, B. T., The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data, Inverse Probl. Sci. Eng., 25, 5, 652-673 (2017) · Zbl 1369.65135
[20] Marin, L.; Karageorghis, A.; Lesnic, D., Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity, Int. J. Solids Struct., 91, 127-142 (2016)
[21] Karageorghis, A.; Lesnic, D.; Marin, L., A moving pseudo-boundary MFS for void detection in two-dimensional thermoelasticity, Int. J. Mech. Sci., 88, 276-288 (2014)
[22] Marin, L.; Karageorghis, A., The MFS-MPS for two-dimensional steady-state thermoelasticity problems, Eng. Anal. Bound. Elem., 37, 7-8, 1004-1020 (2013) · Zbl 1287.74009
[23] Liu, Q. G.; Sarler, B., A non-singular method of fundamental solutions for two-dimensional steady-state isotropic thermoelasticity problems, Eng. Anal. Bound. Elem., 75, 89-102 (2017) · Zbl 1403.74312
[24] Cao, C. Y.; Qin, Q. H.; Yu, A. B., A novel boundary-integral based finite element method for 2d and 3d thermo-elasticity problems, J. Therm. Stresses, 35, 10, 849-876 (2012)
[25] Chen, B.; Chen, W.; Cheng, A. H.D.; Wei, X., The singular boundary method for two-dimensional static thermoelasticity analysis, Comput. Math. Appl., 72, 11, 2716-2730 (2016) · Zbl 1368.74072
[26] Yang, D. S.; Ling, J., A novel boundary-type element-free method for 3D thermal analysis in inhomogeneous media with variable thermal source, Comput. Math. Appl., 80, 12, 3123-3136 (2020) · Zbl 1455.74093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.