Effective Elastic Constants for Thick Perforated Plates With Square and Triangular Penetration Patterns

Abstract

An exact formulation is presented of the relationship between the effective elastic constants for thick perforated plates (generalized plane strain) and thin perforated plates (plane stress). Extensive numerical results covering a wide range of ligament efficiencies and Poisson’s ratios are given for plates with square and triangular penetration patterns.

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

“…The work of Slot (1972) and Slot and O'Donnell (1971 ) are typical of the fundamental works in this area. The technology for use of elastic methods in design is summarized by Paliwal and Saxena, (1993) and Ukadgaonker, et al (1996).…”

“…By calculating the EQS stress that brings the highest stressed point in the perforated material to yield for a sufficient number of load cases, the constants P, Q, R, and T solutions can be obtained. Calling these points the incipient yield stress points and using a unit cell representation for a pattern, incipient yield stresses for the cell loaded in the xdirection (Sm),y-direction (Sw), the equibiaxial case (SJ, and the pure-shear case (SJ can be obtained by elastic analysis such as available in Slot and O'Donnell (1971 Table 1. The inplane loading cases were run as generalized plane strain problems making the solutions independent of the plate thickness.…”

Application and experimental qualification of the equivalent solid plate method to the analysis of perforated plates with square penetration patterns

“…As shown in [I] and [23, the material properties turn out to be a function of h ligament efficiency (p = -), elastic constants of the base material P (E and v ) , and ligament orientation. As given in [ 2 ] , for the square penetration patterns, the constitutive equations are…”

“…However, even though the displacements may not depend strongly on 8, the stresses do. Given the &independent displacements and hence strains, the equivalent solid plate stresses may be calculated as a function of 0 through equation (2).…”

“…(1) The BESTRAN f i n i t e element s o l u t i o n s u s i n g t h e c i r c u m f e r e n t i a l l y averaged e q u i v a l e n t s o l i d p l a t e p r o p e r t i e s ; (2) The t h i n -p l a t e t h e o r e t i c a l s o l u t i o n using t h e circumf e r e n t i a l l y averaged e q u i v a l e n t s o l i d p l a t e p r o p e r t i e s and s o l i d s t i f f e n i n g r i n g model; and (3) The ASAAS f i n i t e element s o l u t i o n which i n c l u d e s t h e p,eriodic v a r i a t i o n of t h e e q u i v a l e n t s o l i d p l a t e p r o p e r t i e s e x p l i c i t l y . Given t h a t t h e p l a t e s t e s t e d q u a l i f y a s moderately-thick t o t h i n , good agreement i s expected between t h e t h e o r e t i c a l t h i n p l a t e s o l u t i o n and t h e BESTRAN r e s u l t s .…”