Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT

Liew, K.M.; Wang, J.; Tan, Ming Jen; Rajendran, S.

doi:10.1016/j.cma.2004.03.013

Cited by 53 publications

(21 citation statements)

References 17 publications

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“…Zhao et al [31] employed the reproducing kernel particle estimation in hybridized form with harmonic functions to study the frequency characteristics of cylindrical panels. Liew et al [32] presented a meshfree kernel particle Ritz method (kp-Ritz) for the geometrically nonlinear analysis of laminated composite plates with large deformations, which is based on the FSDT and the total Lagrangian formulation. Liew et al [33] adopted a moving least squares differential quadrature (MLSDQ) method for predicting the free vibration behaviour of square, circular and skew plates with various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

Ngo-Cong

Mai‐Duy

Karunasena

et al. 2011

Computers & Structures

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This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, onedimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

Ngo-Cong

Mai‐Duy

Karunasena

et al. 2011

Computers & Structures

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“…Comparison of the analytical [34] and numerical solutions by the kp-Ritz method for 12 t  is illustrated in Fig. 1.…”

Section: Examplementioning

confidence: 99%

“…Using the element-free kp-Ritz method, geometrically nonlinear analyses of functionally graded plates and shells were reported by Zhao and Liew [29,30]. More related achievements in this meshfree method can be found in [25,[31][32][33][34][35][36][37]. It is worth mentioning that the discrete singular convolution (DSC) algorithm for the sine-Gordon equation and the Fokker-Planck equations was investigated by Wei [38,39].…”

Section: Introductionmentioning

confidence: 94%

Numerical solution of nonlinear Klein–Gordon equation using the element-free kp-Ritz method

Guo

Liew

Zhu

2015

Applied Mathematical Modelling

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This paper presents a numerical analysis of the one-dimensional Klein-Gordon equation with quadratic and cubic nonlinearity, using the element-free reproducing kernel particle Ritz method (kp-Ritz method). Approximation of the wave displacement is expressed according to a set of meshfree kernel particle functions. Based on the established functional corresponding to the nonlinear Klein-Gordon equation, a system of nonlinear discrete equations can be obtained by applying the Ritz minimization procedure. The Newmark integration scheme combined with an iterative technique is applied to the resulting nonlinear system equations.Numerical examples are tested to validate the proposition that the presented numerical solutions are in good agreement with analytical results available in extant literature.

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“…As an alternative to mesh-based methods, meshless methods [4][5][6][7][8][9][10][11][12][13][14] have attracted much attention in recent years due to: (1) the lack of dependence on mesh and avoiding meshing;…”

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confidence: 99%

A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems

Chen

Liew

2010

Comput Mech

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A meshless Local Petrov-Galerkin approach based on the moving Kriging interpolation (Local Kriging method; LoKriging hereafter) is employed for solving partial different equations that govern the heat flow in two-and three-dimensional spaces. The method is developed based on the moving Kriging interpolation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for domain integral in symmetric weak form. As the shape functions possess the Kronecker delta function property, essential boundary conditions can be implemented without any difficulties. The traditional two-point difference method is selected for the time discretization scheme. For computation of 3D problems, a novel local sub-domain from the polyhedrons is used for evaluating the integrals. Several selected numerical examples are presented to illustrate the performance of the LoKriging method.

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Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT

Cited by 53 publications

References 17 publications

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

Numerical solution of nonlinear Klein–Gordon equation using the element-free kp-Ritz method

A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems

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