Elastic buckling analysis of uniaxially compressed CCSS Kirchhoff plate using single finite Fourier sine integral transform method

Onah, Hyginus; Nwoji, CU; Ike, Charles Chinwuba; Mama, Benjamin

doi:10.18280/mmc_b.870208

Cited by 7 publications

(7 citation statements)

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“…Elastic stability problems involving rectangular Kirchhoff plates subjected to inplane compressive loads were investigated by authors in [32][33][34][35][36].…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

“…In [32], the authors used the two-dimensional finite Fourier sine integral transformation technique for solving the elastic buckling problems of simply supported rectangular thin plates. In [33], the authors used the one-dimensional (single) finite Fourier sine integral transform method for the elastic stability solutions of thin plates simply supported at two opposite sides and fixed along the remaining two sides for uniaxial uniform compression. In [34], the authors used the Galerkin-Kantorovich technique for the elastic buckling analysis of thin rectangular shaped plates with two opposite sides simply supported and the other two sides fixed (SCSC plates).…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

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Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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This paper presents the generalized integral transform method for solving flexural and elastic stability problems of rectangular thin plates clamped along /2 yb = and simply supported along remaining boundaries (x = 0, x = a) (CSCS plate). The considered plate is homogeneous, isotropic and carrying uniformly distributed transversely applied loading causing bending. Also studied, is a plate subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments expressions are double series with infinite terms which are rapidly convergent. Maximum deflections and bending moments values occur at the plate centre in agreement with symmetry. The present results gave double series solutions with good convergent properties in closed form for bending problems. The resulting bending solutions were exact. Solving the resulting eigenvalue equation gave closed analytical equation for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution. The use of more terms in the eigenfunction expansion could give more acceptable results for the eigenvalue problem of buckling of CSCS plates.

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“…Elastic stability problems involving rectangular Kirchhoff plates subjected to inplane compressive loads were investigated by authors in [32][33][34][35][36].…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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“…Onah et al [36] solved the elastic buckling problem of thin rectangular plates with two opposite simply supported edges under uniform compressive loads and two clamped edges. They used the single finite Fourier sine integral transform method which they found suitable for the problem since the Dirichlet boundary conditions are identically satisfied by the integral kernel.…”

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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“…Finite Fourier sine transform methods have been used to solve plate problems by Ike [34], Nwoji et al [35], Mama et al [36], Mama et al [37], Mama et al [38], Onah et al [39], Ike [40], Oguaghamba and Ike [41], and Onyia et al [42].…”

Section: Introductionmentioning

confidence: 99%

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

Mama¹,

Oguaghamba²,

Ike³

2020

International Journal of Engineering Research and Technology

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This paper presents the single finite Fourier sine integral transform method for the flexural analysis of rectangular Kirchhoff plate with opposite edges simply supported, and the other edges clamped for the case of triangular load distribution on the plate domain. The finite sine transform method is adopted because the sinusoidal integral kernel function satisfies all the Dirichlet boundary conditions along the simply supported edges. The governing domain equation which is a nonhomogeneous biharmonic equation is converted by the transformation to an integral equation over the solution domain. The integral equation is reduced by the linearity properties of the transformation, Leibnitz rule and boundary conditions along the simply supported edges to ordinary differential equations (ODEs). Classical methods of solving ODEs in closed-form were used to obtain the solutions that satisfy the boundary conditions along the clamped edges. Thus exact solutions to the boundary value problem that satisfy the governing equation at all points in the solution domain as well as at all points along the four edges are obtained. The resulting expression for the deflection is a single infinite series with demonstrated rapidly convergent properties. The bending moments Mxx, Myy expressions were obtained using the bending moment-deflection relations as infinite series with demonstrated rapid convergence. The converged values of the maximum deflection and bending moments Mxx, Myy evaluated at the plate centre are in excellent agreement with the previous exact results to the problem obtained by researchers who used the Kantorovich-Vlasov method; Levy's method; and the superposition method.

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Elastic buckling analysis of uniaxially compressed CCSS Kirchhoff plate using single finite Fourier sine integral transform method

Cited by 7 publications

References 1 publication

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

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

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

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