Effect of Plane Strain, Plane Stress and Bending on Equivalent Solid Collapse Predictions for Perforated Plates

An equivalent solid based method of predicting the plastic (limit) collapse of perforated plates has been developed in the recent literature. Higher order collapse surfaces with suitable symmetry properties are used for the analysis. The equation for the collapse surface contains a number of constants that are determined by comparison to a Finite Element analysis of an actual perforated periodic cell subject to selected membrane states of stress. Using a typical triangular perforation pattern, the present paper investigates the effect of simplifying assumptions that were made during the periodic cell analysis on the predicted collapse load of the actual cell geometry. For a finite thickness cell subjected to a membrane state of stress, the collapse load is expected to lie between that of the bounding cases of plane stress and generalised plane strain, which are compared here. The connection between the collapse of a cell subjected to a membrane state of stress and a cell of large thickness in bending is established.