Analysis of Simply Supported Rectangular Kirchhoff Plates by the Finite Fourier Sine Transform Method

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

doi:10.22161/ijaers.4.3.44

Cited by 7 publications

(3 citation statements)

References 18 publications

(14 reference statements)

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“…The classical plate theory (CPT) is mainly used in the analysis of thin plates and has also been used by [12 -14] in the analysis of solutions involving plates and shells, respectively. But it has been found to be inadequate by [15] for the analysis of thick plates as its neglects the effect of shear deformationa gap that led to the development of refined plate theory by researchers.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

Onyeka¹,

Okeke²

2021

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

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In this paper, a new polynomial shear deformation theory for the static flexural analysis of anisotropic rectangular thick plate was developed. The plate which carries a uniformly distributed load is clamped on the three edges, and free of support on the other edge (CCFC), is analyzed to determine the in-plane displacement, vertical displacement, bending moment, and shear force, bending and transverse shear stress. The General variation approach was used to obtain the general governing equation and its associated boundary conditions, thereafter the coefficient of deflection and shear deformation along the direction of x and y coordinate was determined by minimizing the energy equation obtained using the new established theory. The study revealed that: (i) as the displacement and stress decrease, the plate's span-thickness ratio increases (ii) as the length to breadth ratio of the plate increases, the value of displacement and stresses increase. To validate the theory, the numerical results are obtained and compared with an available solution in the literature. The result showed good agreement with those in the literature.

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Section: Introductionmentioning

confidence: 99%

Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

Onyeka¹,

Okeke²

2021

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

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“…Integral transform methods were used for determining problems of thin plates under bending deformations by authors in [10] and [26].…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

“…Plates are applied extensively in the varied fields of engineering and used in civil, mechanical, aeronautical, naval, spacecraft and structural components. This has resulted in the extensive studies done by many previous scholars on the subject matter [1][2][3][4][5][6][7][8][9][10]. Plates are subject to loads that produce dynamic ASTESJ ISSN: 2415-6698 This work considers rectangular thin plates made with isotropic, homogeneous, linear elastic materials.…”

Section: Introductionmentioning

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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Generalized Finite Continuous Ridgelet Transform

Gupta

Gorty

2022

Trends in Mathematics

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Analysis of Simply Supported Rectangular Kirchhoff Plates by the Finite Fourier Sine Transform Method

Abstract: Abstract-In

Cited by 7 publications

References 18 publications

Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

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

Generalized Finite Continuous Ridgelet Transform

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