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A COMPARATIVE STUDY ON THE DISPERSION PROPERTIES OF HRK AND RK MESHFREE APPROXIMATIONS FOR KIRCHHOFF PLATE PROBLEM

DONGDONG WANG

Department of Civil Engineering, Xiamen University, Xiamen, Fujian 361005, China

Corresponding author.

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and

ZHENTING LIN

Department of Civil Engineering, Xiamen University, Xiamen, Fujian 361005, China

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https://doi.org/10.1142/S0219876212400154Cited by:8 (Source: Crossref)

Abstract

Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.

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References

T. Belytschko and R. Mullen, Modern Problems in Elastic Wave Propagation, eds. J. Achenbach and J. Miklowitz (Springer-Verlag, 1978) pp. 67–82. Google Scholar
T. Belytschko, Y. Y. Lu and L. Gu, Int. J. Numer. Meth. Eng. 37, 229 (1994). Crossref, Web of Science, Google Scholar
D. Bueche, N. Sukumar and B. Moran, Comput. Mech. 25, 207 (2000). Crossref, Web of Science, Google Scholar
J. S. Chenet al., Comp. Method Appl. M. 139, 195 (1996). Crossref, Web of Science, Google Scholar
M. A. Christon and T. E. Voth, Int. J. Numer. Meth. Eng. 47, 1285 (2000). Crossref, Web of Science, Google Scholar
Y. T. Gu and G. R. Liu, CMES-Comput. Model. Eng. Sci. 2, 463 (2001). Web of Science, Google Scholar
P. Krysl and T. Belytschko, Comput. Mech. 16, 1 (1995). Web of Science, Google Scholar
S. Li and W. K. Liu , Meshfree Particle Methods ( Springer-Verlag , 2004 ) . Google Scholar
G. R. Liu , Mesh Free Methods: Moving Beyond the Finite Element Method , 2nd edn. ( CRC Press , 2009 ) . Crossref, Google Scholar
G. R. Liu and X. L. Chen, J. Sound Vib. 241, 839 (2001). Crossref, Web of Science, Google Scholar
W. K. Liu, S. Jun and Y. F. Zhang, Int. J. Numer. Meth. Fl. 20, 1081 (1995). Crossref, Web of Science, Google Scholar
W. K. Liuet al., Comput. Method. Appl. M. 193, 933 (2004). Crossref, Web of Science, Google Scholar
Y. Liu, Y. C. Hon and K. M. Liew, Int. J. Numer. Meth. Eng. 66, 1153 (2005). Crossref, Web of Science, Google Scholar
H. L. Schreyer, Comput. Methods for Transient Analysis, eds. T. Belytschko and T. J. R. Hughes (Elsevier Science Publishers, 1983) pp. 267–299. Google Scholar
T. E. Voth , D. Wang and J. S. Chen , An analysis of stabilized integration, Galerkin meshfree methods discretizations for advection problems , Proceeding of the 5th World Congress on Computational Mechanics ( 2002 ) . Google Scholar
D. Wang , A stabilized conforming integration procedure for Galerkin meshfree analysis of thin beam and plate , Proceeding of the 10th Enhancement and Promotion of Computational Methods in Engineering and Science ( 2006 ) . Google Scholar
D. Wang and J. S. Chen, Int. J. Numer. Meth. Eng. 74, 368 (2008). Crossref, Web of Science, Google Scholar
D. Wang and Z. Lin, Comput. Mech. 46, 703 (2010). Crossref, Web of Science, Google Scholar
Y. You, J. S. Chen and T. E. Voth, Finite Elem. Anal. Des. 38, 999 (2002). Crossref, Web of Science, Google Scholar