Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory

Sayyad, Atteshamuddin S.; Shinde, Bharti M.; Ghugal, Yuwaraj M.

doi:10.1590/1679-78252241

Cited by 11 publications

(5 citation statements)

References 32 publications

(55 reference statements)

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“…Those values of load at the middle plane at which deflection tend to grow indefinitely are the critical value [16]. If the in-plane compressive load applied to the plate are further increased beyond their critical values, very large deflections and bending stresses will occur which will eventually lead to complete failure of the plate [22][23][24][25]. To avoid failure of the plate, relatively more accurate and practical studies on stability analysis of plate are required.…”

Section: Definition Of Notationsmentioning

confidence: 99%

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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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Section: Definition Of Notationsmentioning

confidence: 99%

“…24 Percentage difference of buckling load on the CSCS rectangular plate between polynomial and trigonometric approach.…”

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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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“…Isotropic plates are widely used in structures under heavy transverse loading which generates large stresses [10][11][12]. The actual stress induced in such a plate is analyzed using one of the shear deformation theories [13][14][15] of different shape functions [16][17][18]. A Series of theories have been developed and applied to analyze ---This paper presents the bending stress analysis of anisotropic plate material under transverse loading using a three-dimensional (3-D) plate theory.…”

Section: Introductionmentioning

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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“…Sayyad et al [10][11][12] has done the detailed analytical study of buckling and vibration on anti-symmetric laminated plates by using novel trigonometric theory which includes shear deformation effect, to understand the effects of slender ratio, modular ratio and fibre angle of the composite plate. Ferreira et al [13] numerically analysed the vibration and instability of composite plates under irregular geometries by considering the radial basis function on FSDT.…”

Section: Introductionmentioning

confidence: 99%

Free vibration and inherent material damping characteristics of boron-FRP plate: influence of non-uniform uniaxial edge loads

Gunasekaran

Pitchaimani

Chinnapandi

2021

Int. J. Simul. Multidisci. Des. Optim.

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The current investigation presents the analytical investigation on free vibration and inherent material damping of boron-FRP plate, subjected to non-uniform uniaxial edge loads. Initially critical buckling load (Pcr) is obtained, then followed by free vibration response and inherent material damping values for corresponding modal indices of the FRP plate is calculated for different load fraction of non-uniform uniaxial edge loads. The buckling load and free vibration response are obtained by using strain energy method and Reddy's TSDT respectively. It is observed that the nature of load and aspect ratio influence the bucking, free vibration and inherent material damping behaviour of the fibre reinforced polymer plate significantly.

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Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory

Cited by 11 publications

References 32 publications

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

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

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

Free vibration and inherent material damping characteristics of boron-FRP plate: influence of non-uniform uniaxial edge loads

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