Kantorovich-Vlasov Method for the Flexural Analysis of Kirchhoff Plates with Opposite Edges Clamped, and Simply Supported (CSCS Plates)

H.N, Onah; B.O, Mama; -, Ike; C.Ce, -; Nwoji, -; -, C.U

doi:10.21817/ijet/2017/v9i6/170906073

Cited by 4 publications

(1 citation statement)

References 3 publications

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“…In [29], the authors used the Kantorovich method to perform natural transverse vibrational analysis of rectangular Kirchhoff plates, thus obtaining the natural frequencies of transverse vibration. In [30], the authors used the Kantorovich-Vlasov methodology for solving the flexural problems of rectangular Kirchhoff plates with opposite sides fixed, and the other two sides simply supported; with the plate subject to distributed uniform loading. In [31], the authors used the Kantorovich method to solve flexural problems of Kirchhoff-Love plates having two sides fixed and the other sides on simple supports.…”

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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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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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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Computing static behavior of flexible rectangular von Kármán plates in fast and reliable way

Awrejcewicz

Kalutsky²,

Кrysko³

2022

International Journal of Non-Linear Mechanics

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Kantorovich variational method for the flexural analysis of CSCS Kirchhoff-Love plates

Ike¹,

Mama²

2018

Math. models, eng.

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Abstract. The Kantorovich variational method was used in this study to solve the flexural problem of Kirchhoff-Love plates with two opposite edges = ± 2 ⁄ clamped and the other two edges = ± 2 ⁄ simply supported, for the case of uniformly distributed transverse load over the entire plate domain. The plate considered was assumed homogeneous, and isotropic. The total potential energy functional for the Kirchhoff-Love plate was found as the sum of the potential energy of the applied distributed load and the strain energy functional of the plate. The symmetrical nature of the plate and the load was used to choose the deflection function as a single series of infinite terms involving the cosine function of the y coordinate variable with the unknown function being dependent on the coordinate variable. Integration with respect to the coordinate variable simplified the total potential energy functional to be dependent on the unknown function of , and its derivatives. Euler-Lagrange differential equations were used to find the differential equations of equilibrium of the plate as a system of homogeneous fourth order ordinary differential equations (ODE) in the unknown function. The system of fourth order ODE was solved using the method of differential D operators, or the method of trial functions to obtain the general solution as the linear superposition of the homogeneous and particular solutions. The demands of symmetry of unknown function about the point = 0, and the boundary conditions at the clamped edges were used to obtain all the four integration constants; thus, completely determining the deflection. Bending moment distributions were determined using the bending moment deflection relations. The deflection was determined at the centre of the plate. The bending moment values were also determined at the centre of the plate, and at the middle of the clamped edges. Expressions obtained for the deflection at the centre, and bending moment values were found to be single series of infinite terms with highly converging properties. The solutions obtained converged to the exact solutions with the use of only four terms of the series.

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Kantorovich-Vlasov Method for the Flexural Analysis of Kirchhoff Plates with Opposite Edges Clamped, and Simply Supported (CSCS Plates)

Cited by 4 publications

References 3 publications

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

Computing static behavior of flexible rectangular von Kármán plates in fast and reliable way

Kantorovich variational method for the flexural analysis of CSCS Kirchhoff-Love plates

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