Applied Mathematics and Mechanics

, Volume 26, Issue 12, pp 1564–1573 | Cite as

Dual reciprocity boundary element method for flexural waves in thin plate with cutout

  • Suo-wen Gao
  • Yue-sheng Wang
  • Zi-mao Zhang
  • Xing-mi Ma
Article
Received:
Revised:

Abstract

The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy.

Key words

thin plate DRM scattering of flexural wave dynamic stress concentration 

Chinese Library Classification

O347.4 

Document code

A 

2000 Mathematics Subject Classification

74K20 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wang Duo, Ma Xingrui, Liu Diankui. The Newest Advance of Elastodynamics [M]. Science Press, Beijing, 1995, 1–106 (in Chinese).Google Scholar
  2. [2]
    Pao Y H. Dynamical stress concentration in an elastic plate [J]. J Appl Mech, 1962, 29(2): 299–305.MATHGoogle Scholar
  3. [3]
    Liu Diankui, Gai Bingzheng, Tao Guiguan. Application of the method of complex functions to dynamic stress concentrations [J]. Wave Morion, 1982, 4(3):293–304.MathSciNetMATHGoogle Scholar
  4. [4]
    Partridge P W, Brebbia C A, Wrobel L C. Dual Reciprocity Boundary Element Method [M]. Southampton Boston: Comput Mech Pub, 1992, 1–176.Google Scholar
  5. [5]
    Nardini D, Brebbia C A. A new approach to free vibration analysis using boundary elements [A]. In: Brebbia C A (ed). Boundary Elements Methods in Engineering [C]. Springer-Verlag, Berlin, 1982, 312–326.Google Scholar
  6. [6]
    Kogl M, Gaul L. Free vibration analysis of anisotropic solids with the boundary element method[J]. Engineering Analysis with Boundary Elements, 2003, 27(2): 107–114.Google Scholar
  7. [7]
    Rodriguez J J, Power H. H-adaptive mesh refinement strategy for the boundary element method based on local error analysis [J]. Engineering Analysis with Boundary Elements, 2001, 25 (7):565–579.MATHGoogle Scholar
  8. [8]
    Rodriguez J J, Power H. An adaptive dual reciprocity scheme for the numerical solution of the Poisson equation[J]. Engineering Analysis with Boundary Elements,2002,26(4):283–300.MATHGoogle Scholar
  9. [9]
    Chien C C, Chen Y H, Chuang C C. Dual reciprocity BEM analysis of 2D transient elastody-namic problems by time-discontinuous Galerkin FEM[J]. Engineering Analysis with Boundary Elements,2003,27(6):611–624.MATHGoogle Scholar
  10. [10]
    Itagaki M. Advanced dual reciprocity method based on polynomial source and its application to eigenvalue problem for nonuniform media [J]. Engineering Analysis with Boundary Elements, 2000,24(2): 169–176.MATHGoogle Scholar
  11. [11]
    Chen J T, Kuo S R, Chung I L, et al. Study on the true and spurious eigensolutions of two-diamensional cavities using the dual multiple reciprocity method[J]. Engineering Analysis with Boundary Elements, 2003,27(7):655–670.MATHGoogle Scholar
  12. [12]
    Singh K M, Tanaka M. Dual reciprocity boundary element analysis of inverse heat conduction problems[J]. Comput Methods Appl Mech Engrg,2001,190(40/41):5283–5295.MATHGoogle Scholar
  13. [13]
    Albuquerque E L, Sollero P, Aliabadi M H. The boundary element method applied to time dependent problems in anisotropic materials[J]. Internat J Solids and Structres,2002,39(5):1405–1422.MATHGoogle Scholar
  14. [14]
    Albuquerque E L, Sollero P, Fedelinski P. Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems [J]. Computers and Structures, 2003,81(17):1703–1713.Google Scholar
  15. [15]
    Chen W, Hon Y C. Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems [J]. Comput Methods Appl Mech Engrg,2003,192(15):1859–1875.MATHGoogle Scholar
  16. [16]
    Gao Suowen, Wang Benli, Ma Xingrui. Scattering of elastic wave and dynamic stress concentrations in the thin plate with a circular hole[J]. Engineering Mechanics,2001,23(2):14–20 (in Chinese).MATHGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2005

Authors and Affiliations

  • Suo-wen Gao
    • 1
  • Yue-sheng Wang
    • 1
  • Zi-mao Zhang
    • 1
  • Xing-mi Ma
    • 2
  1. 1.Institute of Engineering MechanicsBeijing Jiaotong UniversityBeijingP. R. China
  2. 2.China Aerospace Science and Technology CorporationBeijingP. R. China

Personalised recommendations