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n-sided polygonal hybrid finite elements involving element boundary integrals only for anisotropic thermal analysis

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.
Rocznik
Strony
109--137
Opis fizyczny
Bibliogr. 42 poz., rys. kolor.
Twórcy
autor
  • School of Traffic Engineering, Huanghe Jiaotong University, Jiaozuo, China, 454950
autor
  • Henan Province Engineering Laboratory for High Temperature and Wear Materials, School of Material Science & Engineering, Henan University of Technology, Zhengzhou, China, 450001
autor
  • College of Civil Engineering, Henan University of Technology, Zhengzhou, China, 450001
autor
  • College of Civil Engineering, Henan University of Technology, Zhengzhou, China, 450001
Bibliografia
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  • 2. R.L. McMasters, J.V. Beck, A two-dimensional cylindrical transient conduction solution using green’s functions, Journal of Heat Transfer, 136, 10, 101301 (8 pages), 2014.
  • 3. K.D. Cole, D.H.Y. Yen, Green’s functions, temperature and heat flux in the rectangle, International Journal of Heat and Mass Transfer, 44, 20, 3883–3894, 2001.
  • 4. H. Gu, J.F. Hunt, Two-dimensional finite element heat transfer model of softwood. Part II. Macrostructural effects, Wood Science and Technology, 38, 4, 599–608, 2006.
  • 5. M. Trcala, A 3D transient nonlinear modelling of coupled heat, mass and deformation fields in anisotropic material, International Journal of Heat and Mass Transfer, 55, 17–18, 4588–4596, 2012.
  • 6. M.I. Azis, D.L. Clements, Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM, Engineering Analysis with Boundary Elements, 32, 12, 1054–1060, 2008.
  • 7. S. Ishiguro, H. Nakajima, M. Tanaka, Analysis of two-dimensional steady-state heat conduction in anisotropic solids by boundary element method using analog equation method and Green’s theorem, Transactions of the Japan Society of Mechanical Engineers, Series A, 74, 740, 477–483, 2008.
  • 8. F.J. Wang, Q.S. Hua, C.S. Liu, Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation, Applied Mathematics Letters, 84, 130–136, 2018.
  • 9. N. Salam, A. Haddade, D.L. Clements, M.I. Azis, A boundary element method for a class of elliptic boundary value problems of functionally graded media, Engineering Analysis with Boundary Elements, 84, 186–190, 2017.
  • 10. H. Wang, Q.H. Qin, Y.L. Kang, A meshless model for transient heat conduction in functionally graded materials, Computational Mechanics, 38, 1, 51–60, 2005.
  • 11. J. Sladek, V. Sladek, P.H. Wen, B. Hon, Inverse heat conduction problems in threedimensional anisotropic functionally graded solids, Journal of Engineering Mathematics, 75, 1, 157–171, 2012.
  • 12. J.P. Zhang, G.Q. Zhou, S.G. Gong, S.S. Wan, Transient heat transfer analysis of anisotropic material by using element-free Galerkin method, International Communications in Heat and Mass Transfer, 84, 134–143, 2017.
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  • 14. Q.H. Qin, Trefftz Finite and Boundary Element Method, WIT Press, Southampton, 2000.
  • 15. S. Lu, J. Liu, G. Lin, P. Zhang, Modified scaled boundary finite element analysis of 3D steady-state heat conduction in anisotropic layered media, International Journal of Heat and Mass Transfer, 108, 2462–2471, 2017.
  • 16. N. Sukumar, A. Tabarraei, Conforming polygonal finite elements, International Journal for Numerical Methods in Engineering, 61, 12, 2045–2066, 2004.
  • 17. A. Tabarraei, N. Sukumar, Application of polygonal finite elements in linear elasticity, International Journal of Computational Methods, 3, 4, 503–520, 2006.
  • 18. G. Manzini, A. Russo, N. Sukumar, New perspectives on polygonal and polyhedral finite element methods, Mathematical Models and Methods in Applied Sciences, 24, 8, 1665–1699, 2014.
  • 19. H. Wang, Q.H. Qin, Hybrid FEM with fundamental solutions as trial functions for heat conduction simulation, Acta Mechanica Solida Sinica, 22, 5, 487–498, 2009.
  • 20. H. Wang, Q.H. Qin, Fundamental-solution-based hybrid FEM for plane elasticity with special elements, Computational Mechanics, 48, 5, 515–528, 2011.
  • 21. H. Wang, Q.H. Qin, Boundary integral based graded element for elastic analysis of 2D functionally graded plates, European Journal of Mechanics – A/Solids, 33, 12–23, 2012.
  • 22. H. Wang, Q.H. Qin, A new special element for stress concentration analysis of a plate with elliptical holes, Acta Mechanica, 223, 6, 1323–1340, 2012.
  • 23. H. Wang, Q.H. Qin, A new special coating/fiber element for analyzing effect of interface on thermal conductivity of composites, Applied Mathematics and Computation, 268, 311–321, 2015.
  • 24. H. Wang, Q.H. Qin, C.Y. Lee, n-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization, Applied Mathematical Modelling, 66, 97–117, 2019.
  • 25. H. Wang, Q.-H. Qin, Y. Xiao, Special n -sided Voronoi fiber/matrix elements for clustering thermal effect in natural-hemp-fiber-filled cement composites, International Journal of Heat and Mass Transfer, 92, 228–235, 2016.
  • 26. H. Wang, Q.H. Qin, Fundamental-solution-based finite element model for plane orthotropic elastic bodies, European Journal of Mechanics – A/Solids, 29, 5, 801–809, 2010.
  • 27. H. Wang, Q.H. Qin, A fundamental solution-based finite element model for analyzing multi-layer skin burn injury, Journal of Mechanics in Medicine and Biology, 12, 5, 1250027, 2012.
  • 28. Z. She, K.Y. Wang, P.C. Li, Hybrid Trefftz polygonal elements for heat conduction problems with inclusions/voids, Computers & Mathematics with Applications, 2019.
  • 29. Z. She, K.Y. Wang, P.C. Li, Thermal analysis of multilayer coated fiber-reinforced composites by the hybrid Trefftz finite element method, Composite Structures, 224, 110992, 2019.
  • 30. K.Y. Wang, P.C. Li, D.Z. Wang, Trefftz-type FEM for solving orthotropic potential problems, Latin American Journal of Solids and Structures, 11, 2537–2554, 2014.
  • 31. J.C. Zhou, K.Y. Wang, P.C. Li, A hybrid fundamental-solution-based 8-node element for axisymmetric elasticity problems, Engineering Analysis with Boundary Elements, 101, 297–309, 2019.
  • 32. J.C. Zhou, K.Y. Wang, P.C. Li, Hybrid fundamental solution based finite element method for axisymmetric potential problems with arbitrary boundary conditions, Computers & Structures, 212, 72–85, 2019.
  • 33. J.C. Zhou, K.Y. Wang, P.C. Li, X.D. Miao, Hybrid fundamental solution based finite element method for axisymmetric potential problems, Engineering Analysis with Boundary Elements, 91, 82–91, 2018.
  • 34. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basic and Fundamentals, Elsevier, New York, 2005.
  • 35. F.C. Buroni, R.J. Marczak, M. Denda, A. Sáez, A formalism for anisotropic heat transfer phenomena: foundations and Green’s functions, International Journal of Heat and Mass Transfer, 75, 399–409, 2014.
  • 36. R.J. Marczak, M. Denda, New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media, International Journal of Heat and Mass Transfer, 54, 15, 3605–3612, 2011.
  • 37. F. Aurenhammer, R. Klein, D.T. Lee, Voronoi Diagrams and Delaunay Triangulations, World Scientific, Singapore, 2013.
  • 38. A. Okabe, B. Boots, K. Sugihara, S.N. Chiu, D.G. Kendall, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, Boston, 2000.
  • 39. Q. Du, D. Wang, Anisotropic centroidal Voronoi tessellations and their applications, SIAM Journal on Scientific Computing, 26, 3, 737–761, 2005.
  • 40. Q. Du, V. Faber, M. Gunzburger, Centroidal Voronoi tessellations: applications and algorithms, SIAM Review, 41, 4, 637–676, 1999.
  • 41. Q.H. Qin, The Trefftz Finite and Boundary Element Method, WITpress Boston, Southampton, 2000.
  • 42. K.N. Chau, K.N. Chau, T. Ngo, K. Hackl, H. Nguyen-Xuan, A polytree-based adaptive polygonal finite element method for multi-material topology optimization, Computer Methods in Applied Mechanics and Engineering, 332, 712–739, 2018.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f87d43d4-302f-4072-832e-a5130e91497f
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