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

Abstract

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.

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

“…It can be deduced that, thinner the plate more failure tendency results. Comparing the result of the present study with those of CPT, FSDT and HSDT as presented in Table 2, it was discovered that as the span-thickness ratio increases, the results of the present study become closer to those obtained using the CPT [16], FSDT [14] and closest to those using other refined plate theory [19,17,21,22,24]. Then, it can be said that the values obtained are in agreement with those obtained in the literature.…”

“…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.…”

“…Saffron, and M. Eisenberger (2005) [14] used both first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) in their analysis of isotropic plate while Reissner (1979) [15] applied the same to anisotropic plate material. Onyeka et al (2021) and Senjanović et al (2013) [17,18] utilized the analytical approach to get the exact polynomial displacement function from the governing equation. They did not apply trigonometric function which gives closer form solution than polynomial whose exact function tends to infinity.…”

“…They did not apply trigonometric function which gives closer form solution than polynomial whose exact function tends to infinity. 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].…”

Static Elastic Bending Analysis of a Three-Dimensional Clamped Thick Rectangular Plate using Energy Method

“…Even though the result of their displacements and stresses, a 3-D theory was not applied. Onyeka & Edozie (2021) [29] analyzed the displacements and stresses of thick rectangular CCFC plate applying the higher order polynomial which was derived from the governing equation using the general variation method. The results of their study agreed well with those of refined plate theory, but varied more with the value of the classical plate theory.…”