Buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp-cloud method

Jafari, Nasrin; Azhari, Mojtaba

doi:10.1016/j.amc.2017.05.079

Cited by 18 publications

(4 citation statements)

References 19 publications

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“…Current analytical solutions for the buckling phenomenon in rectangular plates are primarily restricted to scenarios featuring uncomplicated boundary conditions with two opposite sides simply supported, commonly referred to as Lévy type plates. As for rectangular plates with non-opposite side simple supported, most research has relied on similar/numerical methods [3][4][5][6][7][8][9][10][11][12]. For rectangular plates under corner support conditions, finite difference method [13], differential quadrature method [14,15], discrete singular convolution method [16,17], meshless method [18], generalized Galerkin method [19,20], etc., have been used to obtain the similar/numerical solution of the buckling problem of such plates.…”

Section: Introductionmentioning

confidence: 99%

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Yang,

Xu,

Chu

et al. 2024

Mathematics

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The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing equations present a formidable obstacle to the attainment of analytical solutions for these problems. Despite the availability of various approximate/numerical methods for addressing these challenges, the literature lacks accurate analytic solutions. In this study, we employ the symplectic superposition method, a recently developed method, to effectively analyze the buckling problem of rectangular thin plates analytically. These plates have four supported corners and four free edges. To achieve this, the problem is divided into two sub-problems and solve them separately using variable separation and symplectic eigen expansion, leading to analytical solutions. Finally, we obtain the resolution to the initial issue by superposing the sub-problems. The current solution method can be regarded as a logical, analytical, and rational approach as it begins with the basic governing equation and is systematically derived without assuming the forms of the solutions. To examine various aspect ratios and in-plane load ratios of rectangular thin plates, which are supported at their four corner points with four edges free, we provide numerical examples that demonstrate the buckling loads and typical buckling mode shapes.

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Section: Introductionmentioning

confidence: 99%

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Yang,

Xu,

Chu

et al. 2024

Mathematics

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“…An increasing number of the meshless methods with different approximation methods and discretization schemes have been proposed and demonstrated during the past decades. Among them, the mature meshless methods include the smoothed particle hydrodynamics (Liu et al, 2019), element-free Galerkin method (Li and Dong, 2019), hp-cloud approach (Jafari and Azhari, 2017), reproducing kernel particle approach (Wang and Li, 2020), natural element approach (Somireddy and Rajagopal, 2015), local Petrov-Galerkin method (Abbaszadeh and Dehghan, 2020), finite point approach (Shojaei et al, 2017), element-free manifold approach (Gao and Wei, 2017), radial point interpolation approach (Zhou et al, 2020c), etc.…”

Section: Introductionmentioning

confidence: 99%

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Zhou

Xue

2022

Journal of Intelligent Material Systems and Structures

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Piezoelectric materials have played an important role in industry due to a number of beneficial properties. However, most numerical methods for the piezoelectric materials need mesh, in which the mesh generation and remeshing are prominent difficulties. This paper proposes a Hermite interpolation element-free Galerkin method (HIEFGM) for piezoelectric materials, where the Hermite approximate approach and interpolation element-free Galerkin method (IEFGM) are combined. Based on the constitutive equation, geometric equation, and Galerkin integral weak form, the HIEFGM formulation for piezoelectric materials is established. In the proposed method, the problem domain is discretized by many nodes rather than the meshes, so the pre-processing of numerical computation is simplified. Furthermore, a new approximation technique based on the moving least squares method and Hermite approximate approach is used to derive the approximation function of field quantities. The derived approximation function has the Kronecker delta property and considers the field quantity normal derivatives of boundary nodes, which avoids the problem of imposing the essential boundary conditions and improves the accuracy of meshless approximation. The effects of the scaling factor, node density, and node arrangement on the accuracy of the proposed method are investigated. Numerical examples are given for assessing the proposed method and the results uniformly demonstrate the proposed method has excellent performance in analyzing piezoelectric materials.

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“…Some significant contributions to the research on plate stability are reported by: Gambhir [2], Bulson [3], Chajes [4], Timoshenko and Gere [5], Shi [8], Shi and Bezine [9], Ullah et al [10,11,12,13], Wang et al [14], Abodi [15], Yu [16], Abolghasemi et al [17], Xiang et al [18] and Bouazza et al [19] Contemporary research work on the plate stability problems have used various numerical methods such as the differential quadrature method (DQM), discrete singular convolution (DSC) method, harmonic differential quadrature method, ordinary finite difference method (FDM), meshfree method, generalized Galerkin method, finite strip method, B-spline finite strip method, exact finite strip method, hp-cloud method, modified Ishlinskii's solution method, meshless analog equation method, finite element method (FEM), extended Kantorovich method (EKM) and pb2-Ritz method. Very recent research work on the subject of plate stability using various numerical and analytical techniques have been reported by Lopatin and Morozov [20], Ghannadpour et al [21], Jafari and Azhari [22], Zureick [23], Seifi et al [24], Li et al [25], Wang et al [26], Mandal and Mishra [27], Shama [28], and Yao and Fujikubo [29].…”

Section: Introductionmentioning

confidence: 99%

Elastic Buckling Analysis of SSCF and SSSS Rectangular Thin Plates using the Single Finite Fourier Sine Integral Transform Method

Onyia¹,

Rowland-Lato²,

Ike³

2020

International Journal of Engineering Research and Technology

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The analysis of the stability problem of plate subjected to inplane compressive load is important due to the relatively poor capacity of plates in resisting compressive forces compared to tensile forces. It is also significant due to the nonlinear, sudden nature of buckling failures. This study presents the elastic buckling analysis of SSCF and SSSS rectangular thin plates using the single finite Fourier sine integral transform method. The considered plate problems are (i) rectangular thin plate simply supported on two opposite edges, clamped on one edge and free on the fourth edge; (ii) rectangular thin plate simply supported on all edges. The plates are subject to uniaxial uniform compressive loads on the two simply supported edges. The governing domain equation is a fourth order partial differential equation (PDE). The problem solved is a boundary value problem (BVP) since the domain PDE is subject to the boundary conditions at the four edges. The single finite sine transform adopted automatically satisfies the Dirichlet boundary conditions along the simply supported edges. The transform converts the BVP to an integral equation, which simplifies upon use of the linearity properties and integration by parts to a system of homogeneous ordinary differential equations (ODEs) in terms of the transform of the unknown buckling deflection. The general solution of the system of ODEs is obtained using trial function methods. Enforcement of boundary conditions along the y = 0, and y = b edges (for the SSCF and SSSS plates considered) results in a system of four sets of homogeneous equations in terms of the integration constants. The characteristic buckling equation in each case considered is found for nontrivial solutions as a transcendental equation, whose roots are used to obtain the buckling loads for various values of the aspect ratio and for any buckling modes. In each considered case, the obtained buckling equation is exact and identical with exact expressions previously obtained in the literature using other solution methods. The buckling loads obtained by the present method are validated by the observed agreement with results obtained by previous researchers who used other methods.

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Buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp-cloud method

Cited by 18 publications

References 19 publications

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Elastic Buckling Analysis of SSCF and SSSS Rectangular Thin Plates using the Single Finite Fourier Sine Integral Transform Method

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