AN IMPROVED FORMULATION OF NONLINEAR STRAIN-DISPLACEMENT RELATIONS AND SPECIFIC MATHEMATICAL MODELS FOR STABILITY ANALYSIS OF THIN RECTANGULAR PLATES
Abstract
ABSTRACT: The present work is aimed at deriving from the first principle the strain-displacement relations, and to develop specific stability equations for five (5) plate types using polynomial displacement shape functions for large deflection analysis of thin rectangular plates. This was done by looking at the deformation of a cube and formulating the new nonlinear strain-displacement relations, and substituting the new relations together with stress-strain relations into the total potential energy functional equation to arrive at the general stress parameter equation. From this equation, the general mathematical model for stability analysis of thin rectangular plates was formulated. The polynomial displacement shape function for each of the five plate types considered here was evaluated to obtain the individual stiffness. The obtained stiffnesses were substituted into the general stability model and evaluated to obtain specific mathematical models for the five plate types. The observed numerical values indicate that the frequency increases as the displacement increases and decreases as the aspect ratio increases. This conforms with existing works in literature and the behavior of plates. Therefore, the conclusion is that these newly formulated mathematical models are adequate for these analyses.
KEYWORDS: Strain-displacement relations, Stress parameter, Buckling and Postbuckling loads, Stability, Large deflection, Specific Models
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