Modeling shot peening process is very complex as it involves the interaction of metallic surfaces with a large number of shots of very small diameter. Conventionally such problems are solved using the finite element software (such as ABAQUS) to predict the stresses and strains. However, the number of shots involved and the number of elements required in a real-life components for a 100% coverag...

In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ∈ CN×N is a singular and in general non-hermitian matrix that has an arbitrary index. One of these methods, modeled after the generalized conjugate residual method (GCR) and denoted DGCR,...

Control by eddy current is one of techniques that’s very used in nondestructive evaluation of materials .These processes find an application significant in the determination of the mechanical and metallurgical parameters of materials. The object of this work is to carry out an analysis of the residual stresses in the material created by external solicitations and analysed by eddy currents as a ...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...

A problem of thermally-induced residual stress under plane strain constraint is considered based on a Body Force Method (BFM). As a numerical example, a simple problem of limited plasticity due to a uniform strength of transient line heat source of finite width, which is applied to a surface of a semi-infinite solid for a short duration of time, was considered. Although the out-of-plane compone...

A novel iteration scheme, using boundary integral equations, is developed for error estimation in the boundary element method. The iteration scheme consists of using the boundary integral equation for solving the boundary value problem and iterating this solution with the hypersingular boundary integral equation to obtain a new solution. The hypersingular residual r is consistently defined as t...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...

Consider applying the Conjugate Residual (CR) method, which is a Krylov subspace type iterative solver, to systems of linear equations Ax = b or least squares problems min x∈Rn ‖b −Ax‖2, where A is singular and nonsymmetric. We will show that when R(A)⊥ = kerA, the CR method can be decomposed into the R(A) and kerA components, and the necessary and sufficient condition for the CR method to conv...

Thermodynamic analysis of a steady state flow and heat transfer of an Oldroyd 8-constant fluid with effect of heat source, velocity slip and buoyancy force under tranverse a magnetic field is is carried out in this paper. The model for momentum and energy balance is tackled numerically using Method of Weighted Residual (MWR). Partition method is used to minimize the associated residuals. The re...