Thickness effects on the plastic collapse of perforated plates with triangular penetration patterns

This paper investigates the effects of plate thickness on the accuracy of limit load solutions obtained using an elastic-perfectly plastic [EPP] equivalent solid [EQS] procedure for flat perforated plates with a triangular array of penetrations. The EQS approach for limit loads is based on an EQS collapse surface that is valid for generalized plane strain. This assumption is applicable for very thick plates but is known to be less reasonable for very thin plates where plane stress may be a better assumption. The limits of applicability of the generalized plane strain assumption are investigated by obtaining limit load solutions for perforated plates of various thicknesses that are subjected to in-plane and bending loads. Plastic limit load solutions obtained using three-dimensional EPP finite element analysis [FEA] of models which include each penetration explicitly are compared with solutions obtained using the EQS approximation. The penetration pattern chosen for this study has a ligament efficiency (ligament width-to-pitch ratio, h/P) of 0.32. For plates thicker than the pitch, the limit load calculated using the EQS method for both in-plane and bending loads is shown to be very accurate (within 4%) of the limit load calculated for the explicit model. On the other hand, for thin plates (t/P< 2), the EQS limit load is 5% greater than the explicit limit load for bending and 8% greater than the explicit limit load for in-plane loads. For thinner plates, the collapse surface is tied to the local geometry deformation and, hence, an equivalent solid plate representation of plastic collapse is a function of deformation mode and thickness