Computational study of the step size parameter of the subgradient optimization method

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.

Minimization of stock weight during close-die forging of a spindle

In this paper, Finite Element method and full-scale experiments have been used to study a hot forging method for fabri-cation of a spindle using reduced initial stock size. The forging sequence is carried out in two stages. In the first stage, the hot rolled cylindrical billet is pre-formed and pierced in a closed die using a spherical nosed punch to within 20 mm of its base. This process of piercing or impact extrusion leads to high strains within the work piece but requires high press loads. In the second stage, the resulting cylinder is placed in a die with a flange chamber and upset forged to form a flange. The stock mass is optimized for complete die filling. Process parameters such as effective strain distribution, material flow and forging load in different stages of the process are analyzed. It is concluded from the simulations that minor modifications of piercing punch geometry to reduce contact between the punch and emerging vertical walls of the cylinder appreciably reduces the piercing load. In the flange chamber, a die surfaces angle of 52° instead of 45° is pro-posed to ensure effective material flow and exert sufficient tool pressure to achieve complete cavity filling. In order to achieve better compression, it is also proposed to shorten both the length of the inserted punch and the die “tongues” by a few mm.

A dislocation based theory for the deformation hardening behavior of DP steels : Impact of martensite content and ferrite grain size

A dislocation model, accurately describing the uniaxial plastic stress-strain behavior of dual phase (DP) steels, is proposed and the impact of martensite content and ferrite grain size in four commercially produced DP steels is analyzed. It is assumed that the plastic deformation process is localized to the ferrite. This is taken into account by introducing a non-homogeneity parameter, f(e), that specifies the volume fraction of ferrite taking active part in the plastic deformation process. It is found that the larger the martensite content the smaller the initial volume fraction of active ferrite which yields a higher initial deformation hardening rate. This explains the high energy absorbing capacity of DP steels with high volume fractions of martensite. Further, the effect of ferrite grain size strengthening in DP steels is important. The flow stress grain size sensitivity for DP steels is observed to be 7 times larger than that for single phase ferrite.