Optimal Design of Bars Under Nonuniform Tension with Respect to Ductile Creep Rupture*

Abstract

Abstract In this paper, the first attempt of applying ductile rupture theory to the problem of optimal design in creep conditions is made. A bar is subject to tension due to the presence of body forces. The bar is made of material that is described by the generalized Norton creep law. The problem addressed is optimal distribution of the cross-sectional area along the axis of the bar, with a given volume V, to maximize the ductile rupture time, consistent with finite strain theory. Two cases are distinguished: body forces connected with material (Lagrangian) coordinates and with spatial (Eulerian) coordinates. For the former problem, an analytical solution is found. The latter problem is restricted to parametric optimization and is solved numerically.