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New series expansions for fundamental solutions of linear elastostatics in 2D

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Abstract

Series expansions of fundamental solutions are essential to algorithms and analysis of the null field method (NFM) and to analysis of the method of fundamental solutions (MFS). For linear elastostatics, new Fourier series expansions of FS are derived, directly from integration. The new expansions of the FS are simpler than those in Chen et al. (J Mech 26(3):393–401, 2010), thus facile to application in NFM and MFS. The new series expansions of FS in this paper are important to both theory and computation of linear elastostatics. Some computation of the MFS for linear elastostatics is provided, where the expansions of fundamental solutions are a basis tool in analysis. Numerical results of a simple example are reported, accompanied with error analysis.

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References

  1. Chen G, Zhou J (1992) Boundary element methods. Academic Press, New York

    MATH  Google Scholar 

  2. Chen JT, Kuo SR, Lin JH (2002) Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticity. Eng Anal Bound Elem 26: 1669–1681

    Google Scholar 

  3. Chen JT, Shen WC, Wu AC (2006) Null-field integral equations for stress field around circular holes under antiplane shear. Eng Anal Bound Elem 30: 205–217

    Article  MATH  Google Scholar 

  4. Chen JT, Lee CF, Chen JL, Lin JH (2002) An alternative method for degenerate scale problem in boundary element methods for two-dimensional Laplace equation. Eng Anal Bound Elem 26: 559–569

    Article  MATH  Google Scholar 

  5. Chen JT, Lee YT, Chou KH (2010) Revisit of two classical elasticity problems by using the null-fields integration equations. J Mech 26(3): 393–401

    Article  Google Scholar 

  6. Chen JT, Lee YT, Lee JW (2010) Torsional rigidity of an elliptic bar with multiple elliptic inclusions using a null-field integral approach. Comput Mech 46: 511–519

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen JT, Lee JW, Lee SY (2010) Analytical and numerical investigation for true and spurious eigensolutions of an elliptical membrane using the real-part dual BEM. Technical report

  8. Crouch SL, Mogilevskaya SG (2003) On the use of Somigliana’s formula and Fourier series for elasticity problems with circular boundaries. Int J Numer Methods Eng 58: 537–578

    Article  MATH  Google Scholar 

  9. Gradsheyan IS, Ryzhik ZM (1965) Tables of integrals, series and products. Academic Press, New York

    Google Scholar 

  10. Hsiao GC, Wendland WL (2008) Boundary integral equations. Springer, Berlin

    Book  MATH  Google Scholar 

  11. Li ZC (1998) Combined methods for elliptic equations with singularities, interfaces and infinities. Kluwer, Boston

    MATH  Google Scholar 

  12. Li ZC (2009) Method of fundamental solutions for annular shaped domains. J Comput Appl Math 228: 355–372

    Article  MathSciNet  MATH  Google Scholar 

  13. Li ZC (2010) Error analysis for hybrid Trefttz methods coupling traction conditions in linear elastostatics. Numer Methods PDE (accepted)

  14. Li ZC, Lee MG, Chiang JY (2010) Error analysis of the method of fundamental solutions for linear elastostatics. Technical report, National Sun Yat-sen University, Kaohsiung, Taiwan

  15. Li ZC, Chien CS, Huang HT (2007) Effective condition number for finite difference method. J Comput Appl Math 198: 208–235

    Article  MathSciNet  MATH  Google Scholar 

  16. Li ZC, Huang J, Huang HT (2010) Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation. Computing 88: 1–29

    Article  MathSciNet  MATH  Google Scholar 

  17. Li ZC, Liaw CP, Huang HT, Lee MG (2010) The null-field method of Dirichlet problems Laplace’s equation on circular domains with circular holes. Technical report, National Sun Yat-sen University, Kaohsiung, Taiwan

  18. Li ZC, Lu TT, Hu HY, Cheng AHD (2008) Trefftz and collocation methods. WIT Press, Southampton

    MATH  Google Scholar 

  19. Mogilevskaya SG, Linkov AM (1998) Complex fundamental solutions and complex variables boundary element method in elasticity. Comput Mech 22: 88–92

    Article  MathSciNet  MATH  Google Scholar 

  20. Qin QH (2000) The Trefftz finite and boundary element method. WIT Press, Southampton

    MATH  Google Scholar 

  21. Yu DH (2002) Natural boundary integral method and its applications. Science Press/Kluwer, Beijing/New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Zi-Cai Li

  2. Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Zi-Cai Li

  3. Department of Applied Statistics, Chung Hua University, Hsin-Chu, Taiwan

    Zi-Cai Li & Ming-Gong Lee

  4. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Jeng-Tzong Chen

Authors
  1. Zi-Cai Li
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  2. Ming-Gong Lee
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  3. Jeng-Tzong Chen
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Correspondence to Ming-Gong Lee.

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Li, ZC., Lee, MG. & Chen, JT. New series expansions for fundamental solutions of linear elastostatics in 2D. Computing 92, 199–224 (2011). https://doi.org/10.1007/s00607-010-0137-5

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  • DOI: https://doi.org/10.1007/s00607-010-0137-5

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