Static and Buckling Analysis of a Three-Dimensional  (3-D) Rectangular Thick Plates Using Exact Polynomial Displacement Function

Onyeka, F. C.; Okeke, T. E.; Nwa-David, Chidobere

doi:10.24018/ejeng.2022.7.2.2725

Cited by 4 publications

(8 citation statements)

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“…In the validation of the result of the present study, a comparative analysis is performed to show the degree of divergence between the result of the present study with those of classical plate theory (CPT) and refined plate theory (RPT) as presented in Table 1&2 and Figure 13. The average percentage difference between the present study and those of authors in [18], [20], [21] and [27] is about 6.33%, 6.37%, 6.47 and 2.59% respectively. Moreover, the result of the result of percentage difference being lower is quite expected because 3-D theory predict more closeform answer to the problem and prudent to use compared to the CPT and RPT.…”

Section: Resultscontrasting

confidence: 71%

Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory

Onyeka¹,

Edozie²,

Chidobere³

2022

J. Engg. Res. & Sci.

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In this study, exact trigonometric displacement function was used to solve the buckling problem of a three-dimensional (3-D) rectangular plate that is clamped at the first-three edges and the other remaining edge simply supported (CCCS) under uniaxial compressive load. Employing 3-D constitutive relations which consist of entire components, the functional for total potential energy was obtained. After that, the rotation and deflection at x-axis and y-axis were formulated from the established compatibility equations to get an exact trigonometric deflection function. The characteristics equation was obtained by differentiating energy equation with respect to deflect to obtain the relations between deflection and rotation. The equation of the total potential energy is minimized with respect to the deflection coefficient after incorporating the deflection and rotation function, the critical buckling load formula was established. The solution for the buckling problem gotten shown that the structure of the plate is safe when the plate thickness is increased as the outcome of the study showed that the critical buckling load increased as the span-thickness ratio increased. The overall difference in form of percent between the present work and previous studies recorded is 5.4%. This shows that at about 95% certainty, the present work is perfect. The comparison of this study with the results of previous similar studies revealed the uniformity 3-D plate theory and the variations of CPT and RPT theories in the exact buckling analysis of a rectangular plate. However, this approach which includes all the six stress elements of the plate material in the analysis produced an exact deflection function unlike the previous studies which used assumed functions. Furthermore, the theoretical analysis of this study demonstrates a novel approach to solve the buckling problem rectangular plate which is capable of analyzing rectangular plates of any thickness configuration.

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Section: Resultscontrasting

confidence: 71%

Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory

Onyeka¹,

Edozie²,

Chidobere³

2022

J. Engg. Res. & Sci.

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“…Authors in [64][65][66][67][68] have used the trigonometric and hyperbolic displacement potential functions for a 3-D analysis thick rectangular plates subjected to in-plane either uniaxial or biaxial static loads. Their functions which are presented in the form of trigonometric and hyperbolic was used to develop the governing differential equations which was solved using separation of variables method and satisfying the exact boundary conditions, to obtain the analytical solution for linear elastic buckling of simply supported rectangular thick plates.…”

Section: Elastic Buckling Of An Isotropic and Orthotropic Thick Platesmentioning

confidence: 99%

“…They did not obtain an exact displacement function from the compatibility equation. In addition, only the author in [64,67] consider the use of polynomial displacement function which can be easily applied, nor solve for order boundary condition.…”

Section: Elastic Buckling Of An Isotropic and Orthotropic Thick Platesmentioning

confidence: 99%

Stability analysis of three-dimensional thick rectangular plate using direct variational energy method

Onyeka

2022

J. Adv. Sci. Eng.

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This study investigated the elastic static stability analysis of homogeneous and isotropic thick rectangular plates with twelve boundary conditions and carrying uniformly distributed uniaxial compressive load using the direct variational method. In the analysis, a thick plate energy expression was developed from the three-dimensional (3-D) constitutive relations and kinematic deformation; thereafter the compatibility equations used to resolve the rotations and deflection relationship were obtained. Likewise, the governing equations were derived by minimizing the equation for the potential energy with respect to deflection. The governing equation is solved to obtain an exact deflection function which is produced by the trigonometric and polynomial displacement shape function. The degree of rotation was obtained from the equation of compatibility which when equated to the deflection function and put into the potential energy equation formulas for the analysis were obtained after differentiating the outcome with respect to the deflection coefficients. The result obtained shows that the non-dimensional values of critical buckling load decrease as the length-width ratio increases (square plate being the highest value), this continues until failure occurs. This implies that an increase in plate width increases the probability of failure in a plate. Hence, it can be deduced that as the in-plane load on the plate increase and approaches the critical buckling, the failure in a plate structure is abound to occur. Meanwhile, the values of critical buckling load increase as the span-thickness ratio increases for all aspect ratios. This means that, as the span-thickness ratio increases an increase in the thickness increases the safety in the plate. It also indicates that the capacity of the plate to resist buckling decreases as the span-depth ratio increases. To establish the credibility of the present study, classical plate theory (CPT), refined plate theory (RPT) and exact solution models from different studies were employed to validate the results. The present works critical buckling load varied with those of CPT and RPT with 7.70% signifying the coarseness of the classical and refined plate theories. This amount of difference cannot be overlooked. The average total percentage differences between the exact 3-D study (Moslemi et al., 2016), and the present model using polynomial and trigonometric displacement functions is less than 1.0%. These differences being so small and negligible indicates that the present model using trigonometric and polynomial produces an exact solution. Thus, confirming the efficacy and reliability of the model for the 3-D stability analysis of rectangular plates.

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“…Plates can be classified according to shapes such as; quadrilateral, square, circular, or rectangular; they can be classified based on the integral constituents as homogeneous, non -homogeneous, orthotropic, anisotropic, or isotropic [6][7]. Considering boundary status, plates are fixed, free, or simply supported, and they can be thin, moderately thick, or thick based on the spanto-thickness ratio of the plate [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Stress Analysis of Transversely Loaded Isotropic Three-Dimensional Plates Using a Polynomial Shear Deformation Theory

Onyeka¹,

Mama²,

Nwa-David³

2023

ETJ

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 A 3-D total potential energy was developed.  A derived shape function of the plate was obtained.  An expression for stress and moment of the plate was formulated.An exact solution for the bending attributes of a thick rectangular plate under transverse loading is modeled herein using three-dimensional (3-D) elasticity plate theory and fourth-order polynomial shear deformation function. Precluding coefficients of shear correction, this model captured the effect of shear deformation along with the transverse normal strain stress. The expression for total potential energy was derived from a 3-D kinematic and constitutive relation the equilibrium equation was developed and employed from the energy functional transformation to get the relationship between slope and deflection. Exact polynomial functions were obtained from the outcome of the equilibrium equation and with the aid of the direct variation approach, the coefficient of deflection of the plate was generated from the governing equation. The expression for computing the displacement, bending moments, and stress components along the three axes of the plate was established from these solutions for the assessment of the bending characteristics of a rectangular plate. The result of a simply supported at one edge, free at one edge and clamped at the two outer edges (SCFC) was evaluated using the obtained functions in this study. The report of this study confirms the exactness and consistency of the 3-D model unlike the refined plate theories applied by previous authors in the available literature. The value of 8.05% is the comprehensive average percentage variation of the values for center deflection obtained by Onyeka and Okeke (2020) and Gwarah (2019). It is established that at the 92 % confidence level, this model is worthy of adoption for safe, cost-effective and accurate bending analysis of thick plates of any support condition.

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Static and Buckling Analysis of a Three-Dimensional (3-D) Rectangular Thick Plates Using Exact Polynomial Displacement Function

Cited by 4 publications

References 0 publications

Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory

Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory

Stability analysis of three-dimensional thick rectangular plate using direct variational energy method

Stress Analysis of Transversely Loaded Isotropic Three-Dimensional Plates Using a Polynomial Shear Deformation Theory

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