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Element nodal computation-based radial integration BEM for non-homogeneous problems

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Abstract

This paper presents a new strategy of using the radial integration boundary element method (RIBEM) to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial integral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.

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References

  1. Gao, X.W.: A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity. International Journal for Numerical Methods in Engineering 66, 1411–1431 (2006)

    Article  MATH  Google Scholar 

  2. Gao, X.W., Davies, T.G.: Boundary Element Programming in Mechanics. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  3. Sladek, J., Sladek, V., Atluri, S.N.: Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. Computational Mechanics 24, 456–462 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Nardini, D., Brebbia, C.A.: A new approach for free vibration analysis using boundary elements. In: Brebbia, C.A., ed. Boundary Elements Methods in Engineering. Springer, Berlin, 312–326 (1982)

    Chapter  Google Scholar 

  5. Gao, X.W.: The radial integration method for evaluation of domain integrals with boundary-only discretization. Engineering Analysis with Boundary Elements 26, 905–916 (2002)

    Article  MATH  Google Scholar 

  6. Gao, X.W.: Evaluation of regular and singular domain integrals with boundary-only discretization-theory and Fortran code. Journal of Computational and Applied Mathematics 175, 265–290 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gao, X.W.: An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals. Computer Methods in Applied Mechanics and Engineering 199, 2856–2864 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, Ch., Cui, M., Wang, J., et al.: 3D crack analysis in functionally graded materials. Engineering Fracture Mechanics 78, 585–604 (2011)

    Article  Google Scholar 

  9. Albuquerque, E.L., Aliabadi, M.H.: A boundary element analysis of symmetric laminated composite shallow shells. Computer Methods in Applied Mechanics and Engineering 199, 2663–2668 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Guo, L., Chen, T., Gao, X.W.: Transient meshless boundary element method for prediction of chloride diffusion in concrete with time dependent nonlinear coefficients. Engineering Analysis with Boundary Elements 36, 104–111 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. AL-Jawary, M.A., Wrobel, L.C.: Radial integration boundary integral and integro-differential equation methods for two-dimensional heat conduction problems with variable coefficients. Engineering Analysis with Boundary Elements 36, 685–695 (2012)

    Article  MathSciNet  Google Scholar 

  12. Hematiyan, M.R., Mohammadi, M., Marin, L., et al.: Boundary element analysis of uncoupled transient thermo-elastic problems with time- and space-dependent heat sources. Applied Mathematics and Computation 218, 1862–1882 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Deng, Q., Li, C.G., Wang, S.L., et al.: A nonlinear complementarity approach for elastoplastic problems by BEM without internal cells. Engineering Analysis with Boundary Elements 35, 313–318 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fata, S.N.: Semi-analytic treatment of the three-dimensional Poisson equation via a Galerkin BIE method. Journal of Com putational and Applied Mathematics 236, 1216–1225 (2011)

    Article  MATH  Google Scholar 

  15. Gao, X.W., Hu, J.X., Cui, M.: A MDBEM based on row elimination-back-substitutionmethod. Chinese Journal of Theoretical and Applied Mechanics 44, 361–368 (2012)

    MathSciNet  Google Scholar 

  16. Gao, X.W., Yang, K.: Thermal stress analysis of functionally graded material structures using boundary element method. Chinese Journal of Theoretical and Applied Mechanics 43, 136–143 (2011)

    MathSciNet  Google Scholar 

  17. Brebbia, C.A., Dominguez, J.: Boundary Elements: An Introductory Course. McGraw-Hill Book Co., London (1992)

    MATH  Google Scholar 

  18. Partridge, P.W., Sensale, B.: Hybrid approximation functions in the dual reciprocity boundary element method. Communications in Numerical Methods in Engineering 13, 83–94 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gao, X.W., Guo, L., Zhang, Ch.: Three-step multi-domain BEM solver for nonhomogeneous material problems. Engineering Analysis with Boundary Elements 31, 965–973 (2007)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 116024, Dalian, China

    Hai-Feng Peng, Kai Yang & Xiao-Wei Gao

Authors
  1. Hai-Feng Peng
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  2. Kai Yang
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  3. Xiao-Wei Gao
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Corresponding author

Correspondence to Xiao-Wei Gao.

Additional information

The project was supported by the National Natural Science Foundation of China (10872050, 11172055) and the Fundamental Research Funds for the Centred Universities (DUT11ZD(G)01).

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Peng, HF., Yang, K. & Gao, XW. Element nodal computation-based radial integration BEM for non-homogeneous problems. Acta Mech Sin 29, 429–436 (2013). https://doi.org/10.1007/s10409-013-0031-4

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  • DOI: https://doi.org/10.1007/s10409-013-0031-4

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