Layout optimization of disks by the use of rigid-plastic element model

Abstract

In the paper, the layout optimization of rigid-plastic disks is presented. The method is based on a model where a disk is subdivided into rectangular elements interconnected by normal and shear forces along their edges. Using this model statically admissible stress fields are constructed and the static theorem of limit analysis is applied. Following the concept of porous materials the design variables are the unknown densities of the elements with variable yield stress expressed in terms of the densities. Two complementary optimum design problems are presented. The load intensity is maximized at given intensity of the load and the total amount of material is minimized at prescribed amount of material, respectively. Both problems are expressed in the forms of nonlinear mathematical programming. The application is illustrated by two examples.