A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the mesh-based adaptive finite element method.

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“…Local weak form methods relying on shape functions resulting from RBF interpolation have been proposed e.g. in [25,26].…”

Section: Introductionmentioning

confidence: 99%

Adaptive meshless centres and RBF stencils for Poisson equation

Davydov

Oanh

2011

Journal of Computational Physics

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“…Therefore, it enables us to treat this problem with the present statement of the interpolation formulation. However, a Hermite-type technique developed in the RPIM [31,32] might be applicable where both deflection and its derivatives are defined as variables field in the interpolation. The MK approach may have a similar manner which is thus needed such a development.…”

Section: Numerical Examplesmentioning

confidence: 99%

Buckling analysis of simply supported composite laminates subjected to an in-plane compression load by a novel mesh-free method

Bui

2011

Vietnam J. Mech.

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Abstract. Buckling analysis of composite laminates under an in-plane compression load based on the mesh -free Galerkin Kriging method is presented. The moving Kriging interpolation (MK) technique possessing the delta property is employed to construct the shape functions, and thus no special techniques for imposing the essential boundary conditions are required. The present formulation is based on the Krichhoff plate theory. The applicability, the accuracy and the effectiveness of the method are illustrated through a number of numerical examples. The results calculated by the proposed method are compared with those of existing reference solutions available in the literature and very good agreements are observed. It can be said that the proposed method can be considered as an alternative numerical technique in terms of meshfree methods.

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“…Liu et al [23][24][25][26][27] systematically presented a reproducing kernel element method in which the nodal rotations are included in the defelctional approximation. A Hermitetype radial point interpolation method was also proposed by Liu et al [28] for thin plate problems.…”

Section: Introductionmentioning

confidence: 97%

Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures

Wang

Lin

2011

Comput Mech

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A dispersion analysis is carried out to study the dynamic behavior of the Hermite reproducing kernel (HRK) Galerkin meshfree formulation for thin beam and plate problems. The HRK approximation utilizes both the nodal deflectional and rotational variables to construct the meshfree approximation of the deflection field within the reproducing kernel framework. The discrete Galerkin formulation is fulfilled with the method of sub-domain stabilized conforming integration. In the dispersion analysis following the HRK Galerkin meshfree semi-discretization, both the deflectional and rotational nodal variables are expressed by harmonic functions and then substituted into the semi-discretized equation to yield the characteristic equation. Subsequently the numerical frequency and phase speed can be obtained. The transient analysis with full-discretization is performed by using the central difference time integration scheme. The results of dispersion analysis of thin beams and plates show that compared to the conventional Gauss integration-based meshfree formulation, the proposed method has more favorable dispersion performance. Thereafter the superior performance of the present method is also further demonstrated by several transient analysis examples.Keywords Hermite reproducing kernel approximation · Meshfree method · Thin beam and plate · Sub-domain stabilized conforming integration · Dispersion analysis · Transient analysis

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A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems

Cited by 67 publications

References 35 publications

Adaptive meshless centres and RBF stencils for Poisson equation

Adaptive meshless centres and RBF stencils for Poisson equation

Buckling analysis of simply supported composite laminates subjected to an in-plane compression load by a novel mesh-free method

Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures

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