Critical Lateral Load Analysis of Rectangular Plate Considering Shear Deformation Effect

Abstract

This work present flexural analysis of rectangular plate subjected to uniform distributed transverse loads using displacement and third-order shear deformation theory. The aim of this study is to establish the formula’s for calculation of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit q𝑖𝑤 and critical lateral imposed load before plate reaches an elastic yield point q𝑖𝑝. The essence is to ensure that deflection does not exceed specified maximum limit and the plate shear not exceeding the elastic yielding point. Furthermore, this approach overcomes the challenges of the conventional practice in the structural analysis/design which involves checking of deflection and shear; the process which is proved unreliable. Total potential energy equation of a thick plate was formulated from the static elastic theory of the plate. The formulated potential energy was in the same way used by the method of direct variation to obtain the coefficient of deflection and shear deformation. This expression was applied to solve bending problem of two different types of rectangular thick plates. The plates has one edge clamped and other three edges simply supported (CSSS). From the result obtained in this work among the two types of plate, it is observed that the value of q𝑖𝑝 if greater than that of q𝑖𝑤. It can be said that the failure of plate in q𝑖𝑤 is like a warning requesting maintenance whereas failure in q𝑖𝑝 means total failure and cannot be maintained. Hence, failure in deflection (q𝑖𝑤) is seen in the plate into consideration. The numerical analysis obtained, it is found that if the value of critical lateral imposed load (q𝑖𝑤 and q𝑖𝑝) increase as the specified thickness (t) of plate increases and decrease as the length to width ratio increases. This implies that as we increase the thickness and allowable deflection improve the safety in the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure. Furthermore, effects of aspect ratio of the critical lateral load of isotropic plates are investigated and discussed. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the thickness of plate variation and satisfied the transverse flexibility of the condition of the plate while predicting the be characteristics for the CSSS isotropic rectangular thin or thick plate.

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

“…Critical buckling load becomes the greatest load which causes an axially loaded plate to lose its stability [6]. To avoid failure of the plate due to buckling of the plate structure, relatively more accurate and practical studies on stability analysis of plate is required.…”

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

“…The classical plate theory (CPT) [14] cannot address the bending of thick plates due to its inability to consider the effect of shear deformation [15]. The refined plate theories (RPT) consist of the first order shear deformation plate theory (FSDT), exponential shear deformation theory (ESDT) [16], the trigonometric shear deformation theory (TSDT) [17], polynomial shear deformation theory (PSDT) [18] and the higher-order shear deformation plate theories (HSDT). RPT is employed to analyze thick plates as the limitation of CPT is handled in FSDT using the shear correction factor [19,20], while in HSDT, varying functions are used to the changes in transversal shear stress at the plate surfaces [21].…”

An Analytical 3-D Modeling Technique of Non-Linear Buckling Behavior of an Axially Compressed Rectangular Plate

“…Considering the insufficient ability of plates towards withstanding compressive forces in structures carrying inplane compressive loads, the necessity of stability analysis is undeniable. Buckling of plates can be analyzed using numeric, equilibrium or energy methods [11,12].…”