Plastic Buckling Analysis of an Isotropic C-SS-SS-SS Plate under In-plane Loading using Taylor’s Series Displacement Function

摘要

Solutions to numerous plate buckling problems have been found using trigonometric series. However, the use of trigonometric series in formulating the displacement function of plates with certain boundary conditions may be rigorous. This paper presents a technique for the plastic buckling analysis of a thin, rectangular, isotropic plate under uniform in-plane compression in the longitudinal direction. The plate was bounded by two simply supported loaded edges, one simply supported unloaded edge and one clamped unloaded edge. The deformation theory of plasticity based on Stowell’s approach was applied in deriving the governing equation. The study involved a theoretical derivation based on Taylor’s series and application of a work principle. The approximate displacement function formulated from the Taylor’s series was truncated at the fifth term which resulted to a peculiar displacement function for the boundary conditions. The displacement function was substituted in the governing equation and results for the plate buckling coefficient were obtained for aspect ratios ranging from 0.1 to 2.0 at intervals of 0.1, with values for the ratio of the tangent modulus to the secant modulus (Et/Es) equal to 0.5, 0.6, 0.7, 0.8 and 0.9. The results for Et/Es equal to 0.9 compared favourably with the elastic buckling values with an average percentage difference of -2.274%. This difference shows that the technique from the present study can be used to analyze the plastic buckling of thin isotropic plates with C-SS-SS-SS boundary conditions.