An Exact Boundary Technique for Improved Accuracy in the Finite Element Method

Discretization procedures such as the finite difference andfinite element methods for the solution of elliptic equationswith Dirichlet boundary conditions suffer in general from thedefect that for a given grid size, the solution is influencedonly by a limited amount of the boundary data. Here blendingfunction interpolants (Gordon, 1971) are used to construct anoverall interpolant for a closed region which matches all theboundary information on the perimeter of the region for anyvalue of the grid spacing. This overall interpolant is incorporatedinto the Ritz Galerkin version of the finite element methodand error estimates obtained for this improved procedure. Twonumerical examples are given which demonstrate the increasedaccuracy of the exact boundary scheme as compared with the discretizedboundary scheme, and as expected, the improvement is particularlynoticeable when the number of elements is small.     

The Compaction of Granular Materials by Rolling II. The Effect of Material Compressibility

In an earlier paper a theory for the compaction of an incompressiblegranular material into a cohesive strip by rolling was developed.The present paper deals with the extension of this theory tothe case of a compressible material. The investigation is basedon the model of the plane-strain deformation of an isotropiccontinuum satisfying the Coulomb-Mohr flow criterion in whichthe material density is related to the pressure by a power law.General equations for the determination of the roll pressureare derived and are used to compute the roll force and torquefactors for a particular physical process. The results of thesecomputations are compared with values obtained experimentally.     

A coupled mathematical model for the rollgap and interstand regions in a hot strip mill

In this paper we consider the process of hot-rolling steel strip.The thickness is reduced by passing the strip through a sequenceof rollers with reductions varying from 40% at the first rollpair to about 10% at the last pair. Between the roll pairs,the strip deflection curve is controlled by a looper roll. Amathematical model of the coupled roll gap and interstand regionis required to assist in the initial setup so as to spread theloads and torques evenly through the roll stands. The modelis of potential value in monitoring the transient behaviourof the rolling process. A review of the various models for eachregion and a coupled complete rolling model is described.     

Effect of pH on lipid oxidation of red onion skin extracts treated with washed tilapia (Oreochromis niloticus) muscle model systems

The aim of the study was to investigate the effect of pH on the lipid oxidation of red onion skin extracts (ROSEs) treated with washed tilapia muscle model systems (WTMS). Minced and buffered washed samples were prepared at pH 6.3 and 6.8. The WTMS were treated with2 different concentrations of red onion skin prior to storage for 5 days. Lipid oxidation was investigated via peroxide values (PVs), thiobarbituric acid reactive substances (TBARS), and the formation of volatile compounds. Fatty acid profiles of the samples were also identified. The ROSEs were able to significantly suppress the PV (~71%) and TBARS (~42%) formation. Hexanal and octanal formations in the WTMS were relatively less in the ROSE-treated samples. The WTMS samples prepared at pH 6.3 were more vulnerable to lipid oxidation than those prepared at pH 6.8. Red onion skin polyphenols may increase the lag phase of lipid oxidation, depending on pH levels, resulting in the shelf life extension of raw fish.     

A Theory for the Compaction of Incompressible Granular Materials by Rolling

A theory for the compaction of incompressible granular materialsinto cohesive strip by rolling is developed, from which rollpressure distributions and rolling loads and torques can becalculated. The analysis is based on the model of the plane-straindeformation of an isotropic, frictional, cohesive continuumwhich satisfies the Coulomb-Mohr criterion of yielding. Generalequations for the determination of the roll pressure are obtainedand a computational solution is given for a particular set ofphysical parameters. This is compared with an approximate analyticalsolution of the general equations.     

The Dynamic Plane Deformation of a Rigid, Perfectly-Plastic Slab

A perturbation method is used to investigate the problem ofthe dynamic plane deformation of a rigid, perfectly-plasticslab by a pair of rough, rigid parallel plates. Perturbationsolutions for the stress and velocity fields are given whichare correct to first-order quantities in the non-dimensionalparameter pc²/2k. These solutions are used to examine a situationwhich occurs in forging practice where a slab is deformed bythe sudden application of constant forces in excess of the initialquasi-static yield load.