A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function

Chen, J.T.; Chen, I.L.; Chen, K.H.; Lee, Y.T.; Yeh, Yi-Lin

doi:10.1016/s0955-7997(03)00106-1

Cited by 98 publications

(36 citation statements)

References 39 publications

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“…Unlike the MFS, the collocation and source points of the SBM are coincident and are placed on the physical boundary without the need of fictitious boundary. The interpolation formula of the SBM is given by (6) where α j are the unknown coefficients, q ii are defined as the origin intensity factor. Eqn (6) of the SBM differs from eqn (5) of the MFS in that the fundamental solution at origin is replaced by q ii when the collocation point x i and source point x j coincide (i = j).…”

Section: Formulation Of Singular Boundary Methodsmentioning

confidence: 99%

“…In comparison with the boundary element method, a variety of boundary-type meshless methods have been developed. For instance, the method of fundamental solutions (MFS) [1][2][3][4], boundary knot method [5], boundary collocation method [6], boundary node method [7,8], regularized meshless method (RMM) [9,10], and modified method of fundamental solution [11] etc.…”

Section: Introductionmentioning

confidence: 99%

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A method of fundamental solution without fictitious boundary

Chen¹,

Wang²

2009

Mesh Reduction Methods

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This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solution (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation points of the SBM coincide on the physical boundary without the requirement of fictitious boundary. In order to avoid the singularity at origin, this method proposes an inverse interpolation technique to evaluate the singular diagonal elements of the interpolation matrix. This study tests the SBM successfully to three benchmark problems, which shows that the method has rapid convergent rate and is numerically stable.

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Section: Formulation Of Singular Boundary Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A method of fundamental solution without fictitious boundary

Chen¹,

Wang²

2009

Mesh Reduction Methods

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“…Since there is no singularity in (5) or (6), all collocation knots are placed on physical boundary and can be used as either source or response points. By using the non-singular general solution (5) or (6), the solution of Equation (1) or Equation (4) can be approximated by…”

Section: Formulation Of Bkmmentioning

confidence: 99%

“…Recent years have witnessed a research boom in boundary meshless methods, such as the method of fundamental solutions (MFS) [1,2], boundary knot method (BKM) [3,4], boundary collocation method [5,6], boundary node method [7,8], and modified MFS [9][10][11] etc. In particular, the BKM is found to produce very accurate solution of the Helmholtz and modified Helmholtz problems.…”

Section: Introductionmentioning

confidence: 99%

Investigation of regularized techniques for boundary knot method

Wang

Chen

Jiang

2009

Numer Methods Biomed Eng

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SUMMARYThis study investigates regularization techniques for the boundary knot method (BKM). We consider three regularization methods and two approaches for the determination of the regularization parameter. Our numerical experiments show that Tikhonov regularization in conjunction with generalized cross-validation approach outperforms the other regularization techniques in the BKM solution of Helmholtz and modified Helmholtz problems.

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“…Numerical methods are fallen back on to solve the real problem. A large number of investigators have studied the problem numerically, e.g., Beskos (1991), Hutchinson (1988), Chen et al (2004) and Lee et al (2002). Until recent years, the meshless method was adopted to solve the plate eigenproblem.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and treatment for the true and spurious eigenequations of circular plates by the meshless method using radial basis function

Chen

Lee

Chen

et al. 2004

Journal of the Chinese Institute of Engineers

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In this paper, a meshless method for solving the eigenproblems of plate vibration using the radial basis function (RBF) is proposed. By employing the RBF in the imaginary-part fundamental solution, spurious eigenequations in conjunction with the true ones are obtained at the same time. Mathematical analysis for the appearance of spurious eigenequations by using degenerate kernel and circulant is done through a circular plate for a discrete system. In order to obtain the true and spurious eigenequations, six ( C 2 4 ) formulations (either two combinations from the four types of potentials, single, double, triple and quadruple) of meshless methods are employed in conjunction with the SVD technique. The spurious eigenequation in each formulation is found and is filtered out by using the SVD updating technique. Three cases, clamped, simply-supported and free circular plates, are demonstrated to check the validity of the meshless methods.

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A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function

Cited by 98 publications

References 39 publications

A method of fundamental solution without fictitious boundary

A method of fundamental solution without fictitious boundary

Investigation of regularized techniques for boundary knot method

Mathematical analysis and treatment for the true and spurious eigenequations of circular plates by the meshless method using radial basis function

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