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

This paper is devoted to study the buckling response of axially compressed rectangular thick plate based on the exact polynomial potential functional. The governing and equilibrium equation of an isotropic plate was derived based on the three-dimensional (3-D) static theory of elasticity, to get the relations between the rotations and deflection. These equations are solved in the form of polynomial analytically to obtain the exact displacements and stresses that are induced due to uniaxial compressive load action on the plate. By incorporating deflection and rotation function into the fundamental equation and minimized with respect to deflection coefficient, a new expression of the determination of the critical buckling load was established. This expression was applied to solve the buckling problem of a clamped thick rectangular plate which was simply supported at the first and freely supported at the third edge (SCFC). A graphic representation of results showed that, as the aspect ratio of the plate increases, the value of critical buckling load decreases while as critical buckling load increases as the length to breadth ratio increases. This implies that an increase in plate width increases the chance of failure in a plate structure. This theory obviates the numerical approximations in the thickness direction thereby guaranteeing accuracy in the solution of the displacement along the direction of thickness axis of the plate, hence, a significant lessening of the cost of computation.