Boundaries of optimally designed elastoplastic structures

Abstract

This study investigates the boundaries of optimally designed elastoplastic bodies. It reviews the problem of the optimum shape selection of a closed surface when the limit load factor is known. The case wherein the limit load factor for feasible bodies is quite large while the acceptable holes in the plate are not too small is presented. The assumption is that under these conditions, the optimum structure is a Maxwell or Michell beam system. It is shown that the Michell structure cannot have large internal holes; however, the Maxwell beam system can include significant holes. Sufficient conditions are presented when the holes can be designed for a solid plate of optimum weight. The results can be spread over three-dimensional elastoplastic structures.