Advances in thermal analysis of heterogeneous materials with hybrid finite element methods

Authors

  • Yi Xiao  Research School of Engineering, Australian National University, Acton, ACT 2601, Australia

Keywords:

Finite Element Method, Fundamental Solution, Functionally graded material, composite materials

Abstract

This paper presents an overview on applications of hybrid finite element method to thermal analysis of heterogeneous materials. Recent developments on the hybrid fundamental solution based finite element model (FEM) of heat transfer in nonlinear functionally graded materials (FGMs) and composite materials are described. Formulations for all cases are derived by means of modified variational functional and fundamental solutions. Generation of elemental stiffness equations from the modified variational principle is also discussed. Finally, a brief summary of the approach is provided

References

  1. J. Reddy, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 47(1-3) (2000) 663-684.
  2. E. Carrera, S. Brischetto, A. Robaldo, Variable kinematic model for the analysis of functionally graded material plates, AIAA journal, 46(1) (2008) 194-203.
  3. J.-H. Kim, G. Paulino, Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, Journal of Applied Mechanics, 69(4) (2002) 502-514.
  4. H. Wang, Q.H. Qin, Y. Kang, A meshless model for transient heat conduction in functionally graded materials, Computational Mechanics, 38(1) (2006) 51-60.
  5. Y. Jiang, J. Ou, Z. Zhang, Q.-H. Qin, Preparation of magnetic and bioactive calcium zinc iron silicon oxide composite for hyperthermia treatment of bone cancer and repair of bone defects, Journal of Materials Science: Materials in Medicine, 22(3) (2011) 721-729.
  6. H.Y. Liu, Q.H. Qin, Y.W. Mai, Theoretical model of piezoelectric fibre pull-out, International Journal of Solids and Structures, 40(20) (2003) 5511-5519.
  7. W. Qiu, Y. Kang, Q. Sun, Q.H. Qin, Y. Lin, Stress analysis and geometrical configuration selection for multilayer piezoelectric displacement actuator, Acta Mechanica Solida Sinica, 17(4) (2004) 323-329.
  8. C.-Y. Lee, Q.H. Qin, G. Walpole, Numerical modeling on electric response of fibre-orientation of composites with piezoelectricity, International Journal of Research and Reviews in Applied Science, 16(3) (2013) 377-386.
  9. V. Kompiš, Z. Murčinková, S. Rjasanow, R. Grzhibovskis, Q.-H. Qin, Computational Simulation Methods for Composites Reinforced by Fibres, Computational Structural Engineering: Proceedings of the International Symposium on Computational Structural Engineering, Held in Shanghai, China, June 22-24, 2009, (2009) 63.
  10. M. Koizumi, FGM activities in Japan, Composites Part B: Engineering, 28(1) (1997) 1-4.
  11. 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 (2016) 228-235.
  12. Q.H. Qin, The Trefftz finite and boundary element method, WIT Press, Southampton, 2000.
  13. Q.H. Qin, Trefftz finite element method and its applications, Applied Mechanics Reviews, 58(5) (2005) 316-337.
  14. Z.-J. Fu, Q.-H. Qin, W. Chen, Hybrid-Trefftz finite element method for heat conduction in nonlinear functionally graded materials, Engineering Computations, 28(5) (2011) 578-599.
  15. Q.H. Qin, H. Wang, Matlab and C programming for Trefftz finite element methods, New York: CRC Press, 2008.
  16. Q.H. Qin, C.X. Mao, Coupled torsional-flexural vibration of shaft systems in mechanical engineering—I. Finite element model, Computers & Structures, 58(4) (1996) 835-843.
  17. H.C. Martin, G.F. Carey, Introduction to finite element analysis: Theory and application, McGraw-Hill New York, 1973.
  18. H. Wang, Y. Xiao, Q.H. Qin, 2D hierarchical heat transfer computational model of natural ber bundle reinforced composite, Scientia Iranica, Transactions B: Mechanical Engineering, 23(1) (2016) 268-276.
  19. K.Z. Ding, Q.H. Qin, M. Cardew-Hall, A New Integration Algorithm for the Finite Element Analysis of Elastic-Plastic Problems, in: Proc. of 9th International Conference on Inspection, Appraisal, Repairs & Maintenance of Structures, Fuzhou, China, 20-21 October, CI-Premier PTY LTD, ISBN: 981-05-3548-1, 2005, pp. 209-216.
  20. Q.H. Qin, Y.W. Mai, BEM for crack-hole problems in thermopiezoelectric materials, Engineering Fracture Mechanics, 69(5) (2002) 577-588.
  21. Q.H. Qin, Y. Huang, BEM of postbuckling analysis of thin plates, Applied Mathematical Modelling, 14(10) (1990) 544-548.
  22. Q.H. Qin, Nonlinear analysis of Reissner plates on an elastic foundation by the BEM, International journal of solids and structures, 30(22) (1993) 3101-3111.
  23. W. Chen, Z.-J. Fu, Q.-H. Qin, Boundary particle method with high-order Trefftz functions, Computers, Materials & Continua (CMC), 13(3) (2010) 201-217.
  24. H. Wang, Q.H. Qin, D. Arounsavat, Application of hybrid Trefftz finite element method to non‐linear problems of minimal surface, International Journal for Numerical Methods in Engineering, 69(6) (2007) 1262-1277.
  25. H. Wang, Q.-H. Qin, X.-P. Liang, Solving the nonlinear Poisson-type problems with F-Trefftz hybrid finite element model, Engineering Analysis with Boundary Elements, 36(1) (2012) 39-46.
  26. L.-L. Cao, Q.-H. Qin, N. Zhao, A new RBF-Trefftz meshless method for partial differential equations, IOP Conference Series: Materials Science and Engineering, 10 (2010) 012217.
  27. Q.H. Qin, Dual variational formulation for Trefftz finite element method of elastic materials, Mechanics Research Communications, 31(3) (2004) 321-330.
  28. H. Wang, Q.-H. Qin, Numerical implementation of local effects due to two-dimensional discontinuous loads using special elements based on boundary integrals, Engineering Analysis with Boundary Elements, 36(12) (2012) 1733-1745.
  29. Q.H. Qin, Formulation of hybrid Trefftz finite element method for elastoplasticity, Applied Mathematical Modelling, 29(3) (2005) 235-252.
  30. Q.-H. Qin, Trefftz plane elements of elastoplasticity with p-extension capabilities, Journal of Mechanical Engineering, 56(1) (2005) 40-59.
  31. Y. Cui, Q.H. Qin, Fracture analysis of mode III problems by Trefftz finite element approach, in: WCCM VI in conjunction with APCOM, 2004, pp. v1-p380.
  32. Y.-h. Cui, Q.H. Qin, J.-S. Wang, Application of HT finite element method to multiple crack problems of Mode I, II and III, Chinese Journal of Engineering Mechanics, 23(3) (2006) 104-110.
  33. Y. Cui, J. Wang, M. Dhanasek, Q.H. Qin, Mode III fracture analysis by Trefftz boundary element method, Acta Mechanica Sinica, 23(2) (2007) 173-181.
  34. C. Cao, Q.H. Qin, A. Yu, Micromechanical Analysis of Heterogeneous Composites using Hybrid Trefftz FEM and Hybrid Fundamental Solution Based FEM, Journal of Mechanics, 29(4) (2013) 661-674.
  35. C. Cao, A. Yu, Q.-H. Qin, Evaluation of effective thermal conductivity of fiber-reinforced composites by boundary integral based finite element method, International Journal of Architecture, Engineering and Construction, 1(1) (2012) 14-29.
  36. M. Dhanasekar, J. Han, Q.H. Qin, A hybrid-Trefftz element containing an elliptic hole, Finite Elements in Analysis and Design, 42(14) (2006) 1314-1323.
  37. Q.-H. Qin, X.-Q. He, Special elliptic hole elements of Trefftz FEM in stress concentration analysis, Journal of Mechanics and MEMS, 1(2) (2009) 335-348.
  38. J. Jirousek, Q.H. Qin, Application of hybrid-Trefftz element approach to transient heat conduction analysis, Computers & Structures, 58(1) (1996) 195-201.
  39. L. Cao, Q.H. Qin, N. Zhao, Application of DRM-Trefftz and DRM-MFS to Transient Heat Conduction Analysis, Recent Patents on Space Technology (Open access), 2 (2010) 41-50.
  40. N. Zhao, L.-L. Cao, Q.-H. Qin, Application of Trefftz Method to Heat Conduction Problem in Functionally Graded Materials, Recent Patents on Space Technology, 1(2) (2011) 158-166.
  41. Q.H. Qin, Hybrid Trefftz finite-element approach for plate bending on an elastic foundation, Applied Mathematical Modelling, 18(6) (1994) 334-339.
  42. Q.H. Qin, Postbuckling analysis of thin plates by a hybrid Trefftz finite element method, Computer Methods in Applied Mechanics and Engineering, 128(1) (1995) 123-136.
  43. Q.H. Qin, Transient plate bending analysis by hybrid Trefftz element approach, Communications in Numerical Methods in Engineering, 12(10) (1996) 609-616.
  44. Q.H. Qin, Postbuckling analysis of thin plates on an elastic foundation by HT FE approach, Applied Mathematical Modelling, 21(9) (1997) 547-556.
  45. F. Jin, Q.H. Qin, A variational principle and hybrid Trefftz finite element for the analysis of Reissner plates, Computers & Structures, 56(4) (1995) 697-701.
  46. J. Jirousek, A. Wroblewski, Q.H. Qin, X. He, A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis, Computer Methods in Applied Mechanics and Engineering, 127(1) (1995) 315-344.
  47. Q.H. Qin, Hybrid-Trefftz Finite-Element Method for Reissner Plates on an Elastic-Foundation, Computer Methods in Applied Mechanics and Engineering, 122(3-4) (1995) 379-392.
  48. Q.H. Qin, S. Diao, Nonlinear analysis of thick plates on an elastic foundation by HT FE with p-extension capabilities, International Journal of Solids and Structures, 33(30) (1996) 4583-4604.
  49. Q.H. Qin, Nonlinear analysis of thick plates by HT FE approach, Computers & Structures, 61(2) (1996) 271-281.
  50. C.-Y. Lee, Q.H. Qin, H. Wang, Trefftz functions and application to 3D elasticity, Computer Assisted Mechanics and Engineering Sciences, 15 (2008) 251-263.
  51. Q.H. Qin, Variational formulations for TFEM of piezoelectricity, International Journal of Solids and Structures, 40(23) (2003) 6335-6346.
  52. Q.H. Qin, Solving anti-plane problems of piezoelectric materials by the Trefftz finite element approach, Computational Mechanics, 31(6) (2003) 461-468.
  53. Q.H. Qin, Mode III fracture analysis of piezoelectric materials by Trefftz BEM, Structural Engineering and Mechanics, 20(2) (2005) 225-240.
  54. Q.H. Qin, Fracture Analysis of Piezoelectric Materials by Boundary and Trefftz Finite Element Methods, WCCM VI in conjunction with APCOM’04, Sept. 5-10, 2004, Beijing, China, (2004).
  55. Q.H. Qin, Trefftz Plane Element of Piezoelectric Plate with p-Extension Capabilities, IUTAM Symposium on Mechanics and Reliability of Actuating Materials, (2006) 144-153.
  56. Q.H. Qin, K.-Y. Wang, Application of hybrid-Trefftz finite element method fractional contact problems, Computer Assisted Mechanics and Engineering Sciences, 15 (2008) 319-336.
  57. K. Wang, Q.H. Qin, Y. Kang, J. Wang, C. Qu, A direct constraint‐Trefftz FEM for analysing elastic contact problems, International Journal for Numerical Methods in Engineering, 63(12) (2005) 1694-1718.
  58. M. Dhanasekar, K.Y. Wang, Q.H. Qin, Y.L. Kang, Contact analysis using Trefftz and interface finite elements, Computer Assisted Mechanics and Engineering Sciences, 13(3) (2006) 457-471.
  59. H. Wang, Q.H. Qin, Hybrid FEM with fundamental solutions as trial functions for heat conduction simulation, Acta Mechanica Solida Sinica, 22(5) (2009) 487-498.
  60. C. Cao, Q.-H. Qin, Hybrid fundamental solution based finite element method: theory and applications, Advances in Mathematical Physics, 2015 (2015).
  61. Q.H. Qin, Fundamental Solution Based Finite Element Method, J Appl Mech Eng, 2 (2013) e118.
  62. Z.-J. Fu, W. Chen, Q.-H. Qin, Hybrid Finite Element Method Based on Novel General Solutions for Helmholtz-Type Problems, Computers Materials and Continua, 21(3) (2011) 187.
  63. Y.-T. Gao, H. Wang, Q.-H. Qin, Orthotropic Seepage Analysis using Hybrid Finite Element Method, Journal of Advanced Mechanical Engineering, 2(1) (2015) 1-13.
  64. H. Wang, Q.H. Qin, Fundamental solution-based hybrid finite element analysis for non-linear minimal surface problems, Recent Developments in Boundary Element Methods: A Volume to Honour Professor John T. Katsikadelis, 309 (2010).
  65. H. Wang, Q.-H. Qin, Fundamental-solution-based hybrid FEM for plane elasticity with special elements, Computational Mechanics, 48(5) (2011) 515-528.
  66. H. Wang, Q.H. Qin, W. Yao, Improving accuracy of opening-mode stress intensity factor in two-dimensional media using fundamental solution based finite element model, Australian Journal of Mechanical Engineering, 10(1) (2012) 41-51.
  67. Q.H. Qin, H. Wang, Special Elements for Composites Containing Hexagonal and Circular Fibers, International Journal of Computational Methods, 12(04) (2015) 1540012.
  68. H. Wang, Q.H. Qin, Special fiber elements for thermal analysis of fiber-reinforced composites, Engineering Computations, 28(8) (2011) 1079-1097.
  69. H. Wang, Q.H. Qin, A fundamental solution based FE model for thermal analysis of nanocomposites, in: Boundary elements and other mesh Reduction methods XXXIII', 33rd International Conference on Boundary Elements and other Mesh Reduction Methods, ed. CA Brebbia and V. Popov, WIT Press, UK, 2011, pp. 191-202.
  70. H. Wang, Q.H. Qin, Implementation of fundamental-solution based hybrid finite element model for elastic circular inclusions, in: Proceedings of the Asia-Pacific Congress for Computational Mechanics, 11th-14th Dec, 2013.
  71. C. Cao, Q.H. Qin, A. Yu, Hybrid fundamental-solution-based FEM for piezoelectric materials, Computational Mechanics, 50(4) (2012) 397-412.
  72. C. Cao, A. Yu, Q.-H. Qin, A new hybrid finite element approach for plane piezoelectricity with defects, Acta Mechanica, 224(1) (2013) 41-61.
  73. H. Wang, Q.H. Qin, Fracture analysis in plane piezoelectric media using hybrid finite element model, in: International Conference of fracture, 2013.
  74. C. Cao, Q.-H. Qin, A. Yu, A new hybrid finite element approach for three-dimensional elastic problems, Archives of Mechanics, 64(3) (2012) 261-292.
  75. L.-L. Cao, Q.-H. Qin, N. Zhao, Hybrid graded element model for transient heat conduction in functionally graded materials, Acta Mechanica Sinica, 28(1) (2012) 128-139.
  76. L. Cao, H. Wang, Q.-H. Qin, Fundamental solution based graded element model for steady-state heat transfer in FGM, Acta Mechanica Solida Sinica, 25(4) (2012) 377-392.
  77. 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 (2012) 12-23.
  78. H. Wang, Q.H. Qin, FE approach with Green’s function as internal trial function for simulating bioheat transfer in the human eye, Archives of Mechanics, 62(6) (2010) 493-510.
  79. H. Wang, Q.H. Qin, Computational bioheat modeling in human eye with local blood perfusion effect, Human Eye Imaging and Modeling, (2012).
  80. 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(05) (2012) 1250027.
  81. Z.-W. Zhang, H. Wang, Q.-H. Qin, Transient bioheat simulation of the laser-tissue interaction in human skin using hybrid finite element formulation, Molecular & Cellular Biomechanics, 9(1) (2012) 31-53.
  82. Z.W. Zhang, H. Wang, Q.H. Qin, Analysis of transient bioheat transfer in the human eye using hybrid finite element model, in: Applied Mechanics and Materials, Trans Tech Publ, 2014, pp. 356-361.
  83. C. Cao, Q.-H. Qin, A. Yu, A novel boundary-integral based finite element method for 2D and 3D thermo-elasticity problems, Journal of Thermal Stresses, 35(10) (2012) 849-876.
  84. Q.H. Qin, H. Wang, Special circular hole elements for thermal analysis in cellular solids with multiple circular holes, International Journal of Computational Methods, 10(04) (2013) 1350008.
  85. H. Wang, Q.-H. Qin, A new special element for stress concentration analysis of a plate with elliptical holes, Acta Mechanica, 223(6) (2012) 1323-1340.
  86. Q.H. Qin, H. Wang, Fundamental solution based FEM for nonlinear thermal radiation problem, in: 12th International Conference on Boundary Element and Meshless Techniques (BeTeq 2011), ed. EL Albuquerque, MH Aliabadi, EC Ltd, Eastleigh, UK, 2011, pp. 113-118.
  87. C. Cao, A. Yu, Q.-H. Qin, A novel hybrid finite element model for modeling anisotropic composites, Finite Elements in Analysis and Design, 64 (2013) 36-47.
  88. C. Cao, A. Yu, Q.H. Qin, Mesh reduction strategy: Special element for modelling anisotropic materials with defects, Boundary Elements and Other Mesh Reduction Methods XXXVI, 56 (2013) 61.
  89. H. Wang, Q.-H. Qin, Fundamental-solution-based finite element model for plane orthotropic elastic bodies, European Journal of Mechanics-A/Solids, 29(5) (2010) 801-809.
  90. H. Wang, L. Cao, Q.-H. Qin, Hybrid Graded Element Model for Nonlinear Functionally Graded Materials, Mechanics of Advanced Materials and Structures, 19(8) (2012) 590-602.
  91. Q.H. Qin, Y. Huang, The study and prospect of solutions on the nonlinear problem of plates, Chinese Journal of Engineering Mechanics, 7(4) (1990) 10-18.
  92. S. Yu, X. Feng, Q.H. Qin, On several problems of macro/micro failure mechanics, Key Engineering Materials, 145 (1998) 51-60.
  93. Q.H. Qin, On nonlinear solutions for dislocations in a bimaterial solid, Structural integrity and fracture: proceedings of the International Conference on Structural Integrity and Fracture, SIF 2002, Perth, Australia, 25-27 September 2002, (2002) 71-79.
  94. X.-C. Hong, Q.H. Qin, Bifurcation of Limit Cycles in a Cubic Hamiltonian System with Some Special Perturbed Terms, International Journal of Mathematical Sciences, 6(2) (2007) 187-198.
  95. X.-C. Hong, Q.-H. Qin, Bifurcation of Limit Cycles in Two Given Planar Polynomial Systems, Recent Advances in Computer Science and Information Engineering, (2012) 705-713.
  96. L. Marin, D. Lesnic, The method of fundamental solutions for nonlinear functionally graded materials, International journal of solids and structures, 44(21) (2007) 6878-6890.
  97. L. Gray, T. Kaplan, J. Richardson, G.H. Paulino, Green’s functions and boundary integral analysis for exponentially graded materials: heat conduction, Journal of Applied Mechanics, 70(4) (2003) 543-549.
  98. L. Gray, T. Kaplan, J. Richardson, G.H. Paulino, Green's functions and boundary integral analysis for exponentially graded materials: heat conduction, Journal of Applied Mechanics, 70(4) (2003) 543-549.
  99. C. Chao, M. Shen, On bonded circular inclusions in plane thermoelasticity, Journal of applied mechanics, 64(4) (1997) 1000-1004.

International Journal of Scientific Research in Science, Engineering and Technology

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2017-12-31

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Volume 2, Issue 2, March-April-2016

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Research Articles

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[1]
Yi Xiao, " Advances in thermal analysis of heterogeneous materials with hybrid finite element methods, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 2, Issue 2, pp.1114-1124, March-April-2016.