A meshless method for Kirchhoff plate bending problems

Leitão, Vitor M.A.

doi:10.1002/nme.244

Cited by 65 publications

(23 citation statements)

References 24 publications

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“…The analytical results given by Timoshenko [38] and numerical results given, respectively, by differential cubature DC method [39] and RBF collocation [28] are also listed for comparison. The analytical solution is solved by combining the solution for the uniformly loaded simply supported square plate and that of the same plate subjected to moments along the edges so that compatibility is enforced.…”

Section: Square Platementioning

confidence: 99%

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

Liu

Hon

Liew

2006

Int. J. Numer. Meth. Engng

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SUMMARYA meshfree computational method is proposed in this paper to solve Kirchhoff plate problems of various geometries. The deflection of the thin plate is approximated by using a Hermite-type radial basis function approximation technique. The standard Galerkin method is adopted to discretize the governing partial differential equations which were derived from using the Kirchhoff's plate theory. The degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions. Numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency, accuracy, and robustness of the method.

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Section: Square Platementioning

confidence: 99%

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

Liu

Hon

Liew

2006

Int. J. Numer. Meth. Engng

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“…In this context, we have developed a meshfree approach in order to capture the non-linear responses of shell-like structures in CNT. For general reviews on the meshfree and particle methods and application to shell and plate structures, we refer to the work described in [15][16][17][18][19][20][21][22][23][24][25][26]. Comparing with the standard continuum treatment of shell or plate, an important difference in the developed meshfree approach in this paper is the fact that the "thickness" of the single layer of CNT is considered to be zero.…”

Section: Introductionmentioning

confidence: 99%

Multiscale simulation of nanostructures based on spatial secant model: a discrete hyperelastic approach

2008

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The main objective of this paper is to present a coarse-grained material model for the simulation of threedimensional nanostructures. The developed model is motivated by the recent progress in establishing continuum models for nanomaterials and nanostructures. As there are conceptual differences between the continuum field defined in the classical sense and the nanomaterials consisting of discrete, space-filling atoms, existing continuum measures cannot be directly applied for mapping the nanostructures due to the discreteness at small length scale. In view of the fundamental difficulties associated with the direct application of the continuum approach, we introduce a unique discrete deformation measure called spatial secant and have developed a new hyperelastic model based on this measure. We show that the spatial secant-based model is consistently linked to the underlying atomistic model and provides a geometric exact mapping in the discrete sense. In addition, we outline the corresponding computational framework using the finite element and/or meshfree method. The implementation is within the context of finite deformation. Finally we illustrate the application of the model in studying the mechanics of low-dimensional carbon nanostructures such as carbon nanotubes (CNT). By comparing with full-scale molecular mechanics simulations, we show that the proposed coarsegrained model is robust in that it accurately captures the nonlinear mechanical responses of the CNT structures.

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“…Instead we construct the modified singular fundamental solution, which satisfies the homogeneous governing equation of Winkler plate and is employed in the BPM to calculate the homogeneous solution. The BPM solutions are compared with those of the Hermite collocation method [30] and the MFS-DRM.…”

Section: Introductionmentioning

confidence: 99%

Winkler plate bending problems by a truly boundary-only boundary particle method

Yang

2009

Comput Mech

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This paper makes the first attempt to use the boundary particle method (BPM) to solve the problems of Winkler plate under lateral loading. In this study, we find that the standard fundamental solution does not work well with the BPM. Instead we construct the modified singular fundamental solution, which satisfies the homogeneous governing equation of Winkler plate and is employed in the BPM to calculate the homogeneous solution. Unlike the other boundary discretization methods, the BPM does not require any inner nodes to evaluate the particular solution of inhomogeneous problems, since the method is a truly boundaryonly meshfree technique by using the recursive composite multiple reciprocity technique. Our numerical experiments demonstrate efficiency and high accuracy of the BPM in the solution of Winkler plate bending problems.

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A meshless method for Kirchhoff plate bending problems

Cited by 65 publications

References 24 publications

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

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

Multiscale simulation of nanostructures based on spatial secant model: a discrete hyperelastic approach

Winkler plate bending problems by a truly boundary-only boundary particle method

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