Top

Computational Mechanics

Published in:

01-01-2014 | Original Paper

Thermal analysis of 3D composites by a new fast multipole hybrid boundary node method

Authors: Yu Miao, Qiao Wang, Hongping Zhu, Yinping Li

Published in: Computational Mechanics | Issue 1/2014

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper applies the hybrid boundary node method (Hybrid BNM) for the thermal analysis of 3D composites. A new formulation is derived for the inclusion-based composites. In the new formulation, the unknowns of the interfaces are assembled only once in the final system equation, which can reduce nearly one half of degrees of freedom (DOFs) compared with the conventional multi-domain solver when there are lots of inclusions. A new version of the fast multipole method (FMM) is also coupled with the new formulation and the technique is applied to thermal analysis of composites with many inclusions. In the new fast multipole hybrid boundary node method (FM-HBNM), a diagonal form for translation operators is used and the method presented can be applied to the computation of more than 1,000,000 DOFs on a personal computer. Numerical examples are presented to analyze the thermal behavior of composites with many inclusions.

previous article An efficient dynamic load balancing algorithm

next article Space–time computation techniques with continuous representation in time (ST-C)

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Alexander A, Tzeng J (1997) Three dimensional effective properties of composite materials for finite element applications. J Compos Mater 31(5):466–485CrossRef

Islam M, Pramila A (1999) Thermal conductivity of fiber reinforced composites by the fem. J Compos Mater 33(18):1699–1715CrossRef

Nishimura N, Liu Y (2004) Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by the boundary integral equation method. Comput Mech 35(1):1–10CrossRefMATH

Chatterjee J, Henry D, Ma F, Banerjee P (2008) An efficient bem formulation for three-dimensional steady-state heat conduction analysis of composites. Int J Heat Mass Transf 51(5–6):1439–1452CrossRefMATH

Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37(2):229–256CrossRefMATHMathSciNet

Atluri SN, Zhu T (1998) A new meshless local Petrov–Galerkin (mlpg) approach in computational mechanics. Comput Mech 22(2):117–127CrossRefMATHMathSciNet

Mukherjee YX, Mukherjee S (1997) The boundary node method for potential problems. Int J Numer Methods Eng 40(5):797–815CrossRefMATH

Li XL, Zhu J (2009) A Galerkin boundary node method and its convergence analysis. J Comput Appl Math 230(1):314–328CrossRefMATHMathSciNet

Zhang JM, Qin XY, Han X, Li GY (2009) A boundary face method for potential problems in three dimensions. Int J Numer Methods Eng 80(3):320–337CrossRefMATHMathSciNet

10.

Zhang JM, Yao ZH, Li H (2002) A hybrid boundary node method. Int J Numer Methods Eng 53:751–763CrossRefMathSciNet

11.

Zhang JM, Tanaka M, Matsumoto T (2004) Meshless analysis of potential problems in three dimensions with the hybrid boundary node method. Int J Numer Methods Eng 59:1147–1160CrossRefMATHMathSciNet

12.

Miao Y, Wang YH (2005) Development of hybrid boundary node method in two-dimensional elasticity. Eng Anal Boundary Elem 29:703–712CrossRefMATH

13.

Miao Y, Wang YH (2006) Meshless analysis for three-dimensional elasticity with singular hybrid boundary node method. Appl Math Mech 27(6):673–681CrossRefMATH

14.

Miao Y, Wang Q, Liao BH, Zheng JJ (2009) A dual hybrid boundary node method for 2d elastodynamics problems. CMES Comput Model Eng Sci 53(1):1–22MATH

15.

Miao Y, Wang Y, Wang YH (2009) A meshless hybrid boundary-node method for Helmholtz problems. Eng Anal Boundary Elem 33(2):120–127CrossRefMATHMathSciNet

16.

Wang Q, Zheng JJ, Miao Y, Lv JH (2011) The multi-domain hybrid boundary node method for 3d elasticity. Eng Anal Boundary Elem 35(6):803–810CrossRefMATHMathSciNet

17.

Zhang JM, Tanaka M, Matsumoto T (2004) A simplified approach for heat conduction analysis of cnt-based nano-composites. Comput Methods Appl Mech Eng 193(52):5597–5609CrossRefMATH

18.

Singh IV, Tanaka M, Endo M (2007) Thermal analysis of cnt-based nano-composites by element free Galerkin method. Comput Mech 39(6):719–728CrossRefMATH

19.

Rokhlin V (1985) Rapid solution of integral equations of classical potential theory. J Comput Phys 60(2):187–207CrossRefMATHMathSciNet

20.

Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73(2):325–348

21.

Zhang JM, Tanaka M, Endo M (2005) The hybrid boundary node method accelerated by fast multipole expansion technique for 3d potential problems. Int J Numer Methods Eng 63(5):660–680CrossRefMATH

22.

Zhang JM, Tanaka M (2007) Systematic study of thermal properties of cnt composites by the fast multipole hybrid boundary node method. Eng Anal Boundary Elem 31(5):388–401CrossRefMATHMathSciNet

23.

Zhang JM, Tanaka M (2008) Fast hdbnm for large-scale thermal analysis of cnt-reinforced composites. Comput Mech 41(6):777–787CrossRefMATH

24.

Wang Q, Miao Y, Zheng JJ (2010) The hybrid boundary node method accelerated by fast multipole expansion technique for 3d elasticity. Comput Model Eng Sci 70(2):123–151MATHMathSciNet

25.

Wang Q, Miao Y, Zhu HP, Zhang C (2012) An O(N) fast multipole hybrid boundary node method for 3D elasticity. Comput Mater Continua 28(1):1–25MATH

26.

Wang Q, Miao Y, Zhu HP (2013) A fast multipole hybrid boundary node method for composite materials. Comput Mech 51:885–897CrossRefMATHMathSciNet

27.

Kulkarni SS, Telukunta S, Mukherjee S (2003) Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory. Comput Mech 32(4):240–249CrossRefMATH

28.

Liu YJ, Nishimura N, Yao ZH (2005) A fast multipole accelerated method of fundamental solutions for potential problems. Eng Anal Boundary Elem 29(11):1016–1024CrossRefMATH

29.

Greengard L, Rokhlin V (1997) A new version of the fast multipole method for the laplace equation in three dimensions. Acta Numer 6(1):229–269CrossRefMathSciNet

30.

Yoshida K, Nishimura N, Kobayashi S (2001) Application of new fast multipole boundary integral equation method to crack problems in 3d. Eng Anal Boundary Elem 25(4):239–247CrossRefMATH

31.

Nishimura N (2002) Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55:299CrossRef

32.

Shen L, Liu Y (2007) An adaptive fast multipole boundary element method for three-dimensional potential problems. Comput Mech 39(6):681–691CrossRefMATHMathSciNet

33.

Bapat MS, Liu YJ (2010) A new adaptive algorithm for the fast multipole boundary element method. Comput Model Eng Sci 58(2):161–184

34.

Saad Y, Schultz MH (1986) Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869CrossRefMATHMathSciNet

35.

Cheng H, Greengard L, Rokhlin V (1999) A fast adaptive multipole algorithm in three dimensions. J Comput Phys 155(2):468–498CrossRefMATHMathSciNet

36.

Karris AN (1989) An examination of the mori-tanaka effective medium approximation for multiphase composites. J Appl Mech 56:83–88CrossRef

37.

Dunn M, Taya M, Hatta H, Takei T, Nakajima Y (1993) Thermal conductivity of hybrid short fiber composites. J Compos Mater 27(15):1493–1519CrossRef

38.

Landau LD, Lifšic EM, Sykes JB, Bell JS, Kearsley M, Pitaevskii LP (1960) Electrodynamics of continuous media, vol 364. Pergamon Press, OxfordMATH

39.

Yao ZH, Xu JD, Wang HT, Zheng XP (2009) Simulation of CNT composites using fast multipole BEM. J Mar Sci Technol 17:194–202

Title: Thermal analysis of 3D composites by a new fast multipole hybrid boundary node method
Authors: Yu Miao
Qiao Wang
Hongping Zhu
Yinping Li
Publication date: 01-01-2014
Publisher: Springer Berlin Heidelberg
Published in: Computational Mechanics / Issue 1/2014
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-013-0893-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 1/2014

Static analysis of offshore risers with a geometrically-exact 3D beam model subjected to unilateral contact

3D multiscale crack propagation using the XFEM applied to a gas turbine blade

XLME interpolants, a seamless bridge between XFEM and enriched meshless methods

Space–time computation techniques with continuous representation in time (ST-C)

A method based on small amplitude homogenization for detecting defects using elastic waves

Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems