Author(s)

K. Szuwalski & A. Ustrzycka

Abstract

The mixed rupture theory to the optimization problem for the complex stress state is used. The problem of optimal shape for the rotating full disk with respect to mixed rupture time is investigated. The mathematical model of mixed creep rupture is described by the system of five partial differential equations. Difficulty of the problem results from two types of nonlinearities: geometrical connected with the use of the finite strain theory and physical - the material is described by the Norton’s creep law, here generalized for true stresses and logarithmic strains. Additional time factor leads to subsequent complications. The parametric optimization describing the initial shape of the disk is applied. The obtained results are compared with the optimal disks with respect to ductile creep rupture time. Keywords: mixed creep rupture, structural optimization, full disk. 1 Introduction Structural elements working under creep conditions belong to the relatively new branches of structural optimisation, started in the seventieth years of the last century. The problem of time to rupture evaluation is of obvious relevance for various machine parts working under high temperature conditions. Theoretical modelling of long time strength appears to be important. A broad presentation of various objective functions with division on time-dependent and timeindependent, was given by Życzkowski [1]. To the latter group belong criteria connected with creep rupture. Most papers on optimal structural design are based on the brittle creep rupture theory proposed by Kachanov (small strain theory). It was due to its relative simplicity - possibility of rigidification theorem

Keywords

mixed creep rupture, structural optimization, full disk.