Application of alternative II theory to vibration and stability analysis of thick rectangular plates  (Isotropic and orthotropic)

Ibearugbulem, O. M.; Ebirim, Stanley I; Anya, U. C.; Ettu, L. O.

doi:10.4314/njt.v39i1.6

Cited by 5 publications

(10 citation statements)

References 7 publications

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“…The credibility of the relationship is given in the percentage difference calculation presented in the Table 2. The average percentage difference between the present study (𝑎𝑡 a/t = 5) using trigonometric function and those of [14,19,17,23] is about 12.4% while the average percentage difference between the present study using the polynomial function and those of [14,19,17,23] is 12.5%. This means that at the 87% confidence level, the values from the present study are the same with those from of previous studies.…”

Section: Resultscontrasting

confidence: 55%

“…Meanwhile, Reissner (1979), Ibearugbulem (2016), Onyeka et al (2021) and Senjanović et al (2013) [15][16][17][18] did not consider the effect of the in-plane load on the stability of the structure. The HSDT or moderately thick plate theory developed by previous scholars is an improvement of the FSDT, due to its avoidance of shear correction factor and has been applied successfully by different researchers in the stability analysis of thick plates [19][20][21][22][23][24][25]. Reddy and Phan (1985) [19] studied the stability and vibration of isotropic, orthotropic and laminated plates.…”

Section: Introductionmentioning

confidence: 99%

“…Another study was carried out by Gunjal et al (2015) [22] using refined trigonometric theory (TSDT) to obtain the buckling load of thick isotropic rectangular plates. Ibearugbulem et al (2020) [23] used orthogonal polynomial displacement functions (OPDF) and a polynomial shear deformation function f (z) in the buckling analysis of isotropic thick rectangular plate subjected to uniaxial inplane compressive loading, Nx. The same type of function (polynomial displacement shape function) was also applied by Ezeh et al (2018) [24], in their work, the free vibration and stability analysis of thick isotropic and orthotropic plates with SSSS and SSFS support conditions were performed by applying the alternative II theory.…”

Section: Introductionmentioning

confidence: 99%

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Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

2022

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In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF

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Section: Resultscontrasting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

2022

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“…Total energy expression being the algebraic summation of strain energy (M) and external work (V) is expressed mathematically as [39][40][41]:…”

Section: Potential Energy Expressionsmentioning

confidence: 99%

Non-linear bending and stress analysis of a transversely loaded isotropic plates material using 3-D plate theory

2022

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This paper presents the bending stress analysis of anisotropic plate material under transverse loading using a three-dimensional (3-D) plate theory. The static elastic theory was used to formulate the total energy expression of the plate thereafter, transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of equations of the equilibrium gave rise to the exact polynomial deflection function while the coefficient of deflection and shear deformation of the plate was gotten from the governing equation through the direct variation method. These solutions were used to obtain the characteristic expression for analyzing the displacement and stresses of the rectangular plate. This formula was used for the solution of the bending problem of the rectangular plate that is clamped at the first-two edge and the other edges simply supported (CCSS). The result of the deflection and stresses decrease as the span-thickness ratio increases. More so, the aspect ratio effect of the shear stress of isotropic plates is investigated and discussed after a comparative analysis between the present work and previous studies. The result shows that the present study differs from that refined plate theory (RPT) of assumed deflection by 5.5% whereas exact 2-D RPT by 5.3%. This shows the efficacy of the exact 3-D plate theory for flexural characteristics of CCSS isotropic rectangular thick plate.

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“…[16] used Navier's method to compare the results obtained from plate analysis using Kirchhoff's concept and Ressiner's concept. [17] applied 'Alternative II' approach in stability and dynamic study of isotropic and orthotropic thick plates by making use of polynomial deflection expression. Galerkin-Vlasov approach was used by [18] to carry out bending analysis of rectangular plates that are carrying uniformly distributed loads.…”

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confidence: 99%

Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

Onyechere¹,

Anya²,

Ibearugbulem³

et al. 2021

Nig. J. Tech.

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This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.

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Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)

Cited by 5 publications

References 7 publications

Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

Non-linear bending and stress analysis of a transversely loaded isotropic plates material using 3-D plate theory

Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

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