A Collapse Surface for a Perforated Plate With an Equilateral Triangular Array of Penetrations

Abstract

A collapse surface is developed for use in limit-load analysis of plates containing a large number of small circular penetrations arranged in an equilateral triangular array of holes with a ligament efficiency of 0.31733. The collapse surface is obtained by calculating the limit load for a unit cell model of the penetration pattern using a three-dimensional elastic-perfectly plastic [EPP] finite element analysis [FEA] computer program. The EPP response from incipient yielding to plastic collapse for the unit cell is obtained for a sufficient number of load cases to define the complete collapse surface. The collapse surface is expressed analytically by using a fourth-order function that incorporates the periodicity dictated by the triangular hole pattern. The coefficients of the fourth-order function were obtained by statistically fitting the collapse surface generated by the EPP-FEA results. The resulting collapse surface was shown to be appropriate for development of an EPP-EQS theory for perforated plates. The analytic surface agrees to within 7 percent of the actual collapse surface obtained by EPP-FEA of the unit cell representing the penetration.

Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading

“…III provides homogenized elastic material properties for perforated plates (ASME 2007). For the homogenized plastic properties of perforated plates, several studies have been devoted to investigating macro-yield surfaces and conditions in plane stress states (O'Donnell and Porowski 1973;Porowski and O'Donnell 1974;Reinhardt 2001;Gordon et al 2002;Khatam et al 2009;Khatam and Pindera 2011). The operating temperatures of perforated plates are considerably high in fast breeder reactors and high temperature gas cooled reactors.…”

Novel Method of Carbon Precursor Masking to Generate Controlled Perforations in a Carbon Film

“…Two plates of PTFE were machined with the intended patterning geometry, which consists of small pillars with circular tops arranged in an equilateral array, as seen in Figure 1. This geometrical distribution is based on the work of Gordon et al [32] and Jones and Gordon [33], resulting in an isotropic structure and relatively high toughness for a brittle material. The clamps were used to cover the film from both sides in the disk areas using additional pressure to prohibit the acid from reaching the masked areas, as shown in Figure 1.…”

An Elastic-Perfectly Plastic Flow Model for Finite Element Analysis of Perforated Materials

“…Pitch means that we seek the relationship between the total stress and the total strain of the form T = ilq /i@ where T is the consistent tangent modulus matrix.This surface is shown inFigure 1 in (oXX, crw)stress space. The constants P, Q, R, T, Y, Z1, and Z2 which define this surface were obtained byGordon, et al (1999) for a Triangular Penetration Pattern…”