eversvd,+5 (11)

In this paper, a three-dimensional (3-D) stability analysis of a rectangular deformable plate was performed to find the solution to the buckling problem of a uniaxially compressed plate with two adjacent loaded edges clamped and the other simply supported (CSCS). A three-dimensional kinematics and constitutive relations were employed to derive the equation of the total energy functional. The general and direct variation of the total potential energy function was executed to arrive at the governing equation of the plate while considering shear deformation effects. The solution to the governing equation yielded the deflection of the plate, expressed in terms of the coefficient of deflection and the shape function derived using polynomial and trigonometric functions. The critical buckling load and relevant formulae were obtained by minimizing the total potential energy equation, taking into account deflection and shear deformation rotation functions. Varying the span-to-thickness ratio and aspect ratios allowed an assessment of the buckling behavior of different plate types under uniformly distributed loads. The results indicated an increase in the critical buckling load with the span-thickness ratio, affirming the safety of plate structures with increased thickness. The study demonstrated that the critical buckling loads from both polynomial and trigonometric theories yielded similar outcomes, with an overall average percentage difference of 2.4%, thus validating the reliability of the derived relationships.