Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation

Shao, Wenting; Wu, Xun

doi:10.1016/j.enganabound.2010.09.011

Cited by 13 publications

(10 citation statements)

References 18 publications

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“…Computational Modeling. According to the basic assumption of the Kirchhoff theory [19], in this paper, for homogeneous, isotropic, elastic plate, the standard governing equation form as modified Helmholtz equation can be obtained as The boundary conditions involve clamped edges, simply supported edges, and free edges, which can be denoted as Γ 1 , Γ 2 , and Γ 3 , respectively, and then the boundary of irregular domain Ω is Γ = Ω = Γ 1 ∪ Γ 2 ∪ Γ 3 , the boundary conditions are given as follows [1,20]:…”

Section: Computational Modeling and Formulations By Using Regular Dommentioning

confidence: 99%

“…Linear elastic thin plates bending problems involving complex geometries, loads, and boundary conditions have been widely studied. There are some traditional methods, such as the finite difference method (FDM), the finite element method (FEM), and the boundary element method (BEM) [1]. It is necessary to point out that these traditional methods not only take a large amount of work to divide elements, but also the precision is not very high.…”

Section: Introductionmentioning

confidence: 99%

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Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

Zhuang

Miao

2018

Mathematical Problems in Engineering

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Regular domain collocation method based on barycentric rational interpolation for solving irregular thin plate bending problems on Winkler foundation is presented in this article. Embedding the irregular plate into a regular domain, the barycentric rational interpolation is used to approximate the unknown function. The governing equation and the boundary conditions of thin plate bending problems on Winkler foundation in a rectangular region can be discretized by the differentiation matrices of barycentric rational interpolation. The additional method or the substitute method is used to impose the boundary conditions. The overconstraint equations can be solved by using the least square method. Numerical solutions of bending deflection for the irregular plate bending problems on Winkler foundation are obtained by interpolating the data on rectangular region. Numerical examples illuminate that the proposed method for irregular thin plate bending problems on Winkler foundation has the merits of simple formulations, efficiency, and relative error precision of 10−9 orders of magnitude.

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Section: Computational Modeling and Formulations By Using Regular Dommentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

Zhuang

Miao

2018

Mathematical Problems in Engineering

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“…But it is difficult to solve the problem with irregular region and it has instability to a large number of nodes by using differential quadrature method [6]. The computation of Fourier differential quadrature method is very large [7]. Based on the selected differential equations which have analytical solution, numerical solution can be obtained by HPM [8].…”

Section: Introductionmentioning

confidence: 99%

“…At present, there are many methods to obtain the numerical solution of bending of circular plate such as finite difference method [2], finite element method [3], boundary element method [4], meshless method [5], differential quadrature method [6], Fourier differential quadrature method [7], homotopy perturbation method (HPM) [8], etc.…”

Section: Introductionmentioning

confidence: 99%

Collocation Method for Axisymmetric Bending Problems of Circular Thin Plates Based on Barycentric Interpolation

Ge¹,

Zhuang²,

Miao³

2018

Proceedings of the 2018 2nd International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2018)

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Abstract-Collocation method based on barycentric rational interpolation (BRICM) is used in this article to study axisymetric bending problems of circular thin plates in polar coordinates. Unknown function is approximated by barycentric rational interpolation and the discrete algebraic equations of differential equations are obtained by forcing the differential equations to satisfy the value of the discrete nodes. The boundary conditions are imposed by substitution method and the numerical solution can be obtained by solving the differential equations. Numerical calculation example demonstrates that the proposed method for circular thin plates bending problems has the merits of higher computation accuracy, convenient program, simple calculation formulations.

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“…Therefore, some numerical methods have to be used to handle the problem, such as the finite difference method [1], the finite strip method [2], the finite element method (FEM) [3][4][5], the boundary element method [6][7][8][9][10][11][12], the Galerkin method [9][10][11] and the boundary integral equation method [12][13][14]. In recent years, there have been some new numerical methods for bending of plates on elastic foundations, such as the iterative method [15,16], the differential quadrature method [17], the discrete singular convolution method [18], the method of fundamental solutions [19], Illyushin's method [20] and the Fourier differential quadrature method [21]. Thus, numerical methods could be used to solve most plate bending problems.…”

Section: Introductionmentioning

confidence: 99%

Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

Zhong

2013

Proc. R. Soc. A.

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Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.

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Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation

Cited by 13 publications

References 18 publications

Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

Collocation Method for Axisymmetric Bending Problems of Circular Thin Plates Based on Barycentric Interpolation

Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

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