Analytical Solution for the Static Bending Elastic Analysis of Thick Rectangular Plate Structures Using 3-D Plate Theory

Onyeka, F. C.; Nwa-David, Chidobere; Edozie, Thompsom

doi:10.30684/etj.2022.134687.1244

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Onyeka and Okeke [22] studied thick plates using refined shear deformation theory and energy method. Onyeka et al, [23][24][25] have used energy methods for thick plate problems under buckling and bending. Recent studies by Onyeka et al, [26][27][28] considered thick rectangular plates with various edge support conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Onyeka et al, [23][24][25] have used energy methods for thick plate problems under buckling and bending. Recent studies by Onyeka et al, [26][27][28] considered thick rectangular plates with various edge support conditions. Onah et al, [29] used the stress function method to derive elastostatic solutions to thick circular plate bending problems.…”

Section: Introductionmentioning

confidence: 99%

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Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Ike

2023

ETJ

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The double finite sine transform method was utilized to obtain exact buckling solutions for thick plate problems • The method simplified the problem to algebraic ones since the sinusoidal function satisfies the boundary conditions • The buckling solutions aligned with exact solutions for thick plates This paper derives buckling solutions for single variable thick plate buckling problems using the double finite sine transform method (DFSTM). The problem governing partial differential equation (GPDE), originally formulated by Shimpi and others, uses a refined plate theory (RPT) and accounts for transverse shear deformations, rendering it applicable to thick plates. The thick plate is simply supported and subjected to (i) uniform uniaxial compressive load in the x direction. (ii) uniform biaxial compressive load in the x and y axes. The DFSTM was applied to the GPDE, and the problem transformed into an algebraic equation, which was simpler in this case due to the Dirichlet boundary conditions satisfied by the sinusoidal kernel of the DFSTM. Analytical buckling solutions were determined for the two considered cases of uniaxial and biaxial compressive loads in terms of the buckling modes, Poisson's ratio (µ), and thickness (h) to least dimension (a) ratio. Critical buckling loads (Pcr) determined at the first buckling modes agreed with previously obtained Navier solutions for Mindlin, Reddy, and Refined plates. Pcr calculated for ratios of h/a equal to 0.01 converged to the solutions obtained using Kirchhoff-Love plate theory (KLPT), illustrating the applicability of the GPDE to thin and thin plate buckling.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Ike

2023

ETJ

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A third-order shear deformation plate bending formulation for thick plates: first principles derivation and applications

Ike

2023

Math. models, eng.

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A third-order shear deformation plate bending formulation is presented in this study from the first principles. The derivation assumed a displacement field constructed using third-order polynomial function of the transverse (z) coordinate; and made to apriori satisfy the linear three-dimensional (3D) kinematics relations as well as the transverse shear stress free boundary conditions at the top and bottom plate surfaces. The formulation thus has no need for shear stress correction factors of the first-order shear deformation plate theories. The domain equations of equilibrium are obtained as a set of three coupled differential equations in terms of three unknown displacements. The system of coupled equations is solved for simply supported rectangular and square plates subjected to four cases of loading distributions: sinusoidal loading, uniformly distributed loading, linearly distributed loading and point load at the plate center. Navier’s double trigonometric series method is used to construct trial solutions for the three displacement functions such that the boundary conditions are satisfied identically. The integration problem is thus reduced to an algebraic problem and is solved for each considered loading. It is found that the present formulation gives exact results for the normal stresses σxx for sinusoidal and uniformly distributed loads. The study further showed that the results for deflection and stresses agreed with Krishna Murty’s higher order shear deformation plate theory results. The present formulation gave accurate results because of the inclusion of transverse normal strain effects in the formulation. The formulation gives a quadratic variation of the transverse shear stresses across the thickness in consonance with the theory of elasticity method.

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Analytical Solution for the Static Bending Elastic Analysis of Thick Rectangular Plate Structures Using 3-D Plate Theory

Cited by 2 publications

References 15 publications

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

A third-order shear deformation plate bending formulation for thick plates: first principles derivation and applications

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