Search results for "Boundary value problem"

Shakedown analysis for a class of strengthening materials within the framework of gradient plasticity

2010

Abstract The classical shakedown theory is extended to a class of perfectly plastic materials with strengthening effects (Hall–Petch effects). To this aim, a strain gradient plasticity model previously advanced by Polizzotto (2010) is used, whereby a featuring strengthening law provides the strengthening stress, i.e. the increase of the yield strength produced by plastic deformation, as a degree-zero homogeneous second-order differential form in the accumulated plastic strain with associated higher order boundary conditions. The extended static (Melan) and kinematic (Koiter) shakedown theorems are proved together with the related lower bound and upper bound theorems. The shakedown limit loa…

Shakedown of elastic—plastic solids with frictionless unilateral contact boundary conditions

1997

Abstract Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d -stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discus…

Large-eddy simulations of turbulent flow with heat transfer in simple and complex geometries using Harwell-FLOW3D

1996

Abstract Large-eddy simulation (LES) results are presented and discussed for the turbulent flow with heat transfer in different geometrical configurations, including a plane channel, a channel bearing transverse square ribs on one of the walls, and a crossed-corrugated air heater. They were obtained using the computational fluid dynamics (CFD) code Harwell-FLOW3D (Release 2), finite-volume grids having up to 423 nodes, and the Smagorinsky subgrid model with several variants regarding near-wall damping and wall boundary conditions. The first problem (plane turbulent Poiseuille flow with heat transfer) was mainly used as a benchmark to investigate the influence of numerical methods (pressure-…

Experimental Investigations and Numerical Analysis for Improving Knowledge of Incremental Sheet Forming Process for Sheet Metal Parts

2009

The paper is related to the analysis of shape distortions and springback effects arising in Single Point Incremental Forming. An experimental set up has been designed and manufactured to carry single point incremental forming on small size sheet metal parts. The experimental set up is mounted on 3-axes CNC milling machine tool and the forming tool is attached and move with the spindle. Experiments have been carried out on sheet metal parts to obtain tronconical shapes. The forming strategy associated to the movement of the forming tool has been also investigated. The experiments indicate that shape distortions arising in the corners of the tronconical shape are clearly related to forming st…

Helical Shift Mechanics of Rubber V-Belt Variators

2011

A very common configuration of V-belt variators for motorcycles considers the correction of the belt tensioning depending on the resistant torque by means of suitable helical-shaped tracks allowing the driven half-pulleys to close/open. The theoretical model for belt-pulley coupling is rather complex for this configuration, where one half-pulley may run in advance and the other one behind with respect to the belt, and requires the repeated numerical solution of a strongly nonlinear differential system by a sort of shooting technique, until all the operating conditions are fulfilled (angular contact extent, torque, and axial force). After solving the full equations, the present study develop…

Confinement-induced screening of hydrodynamic interactions and spinodal decomposition: Multiscale simulations of colloid-polymer mixtures

2012

Phase separation kinetics of a colloid-polymer mixture confined between two planar repulsive walls is studied by a multiscale simulation approach. Colloids and polymers are described by particles interacting with continuous potentials suitable for molecular-dynamics simulation, while hydrodynamic interactions mediated by solvent particles are accounted for by the multiparticle collision dynamics method. Varying the distance D between the walls and the character of the boundary conditions, the interplay of structure formation parallel and perpendicular to the walls is studied, and the effect of hydrodynamics on the growth of domain size ld(t) with time t is elucidated. Only for slip boundary…

Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: A multiparticle collision dynamics study

2013

A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent flui…

Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities

2013

Strictly convergent algorithm for an elliptic equation with nonlocal and nonlinear boundary conditions

2012

The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.

Age-Structured Human Population Dynamics

2006

ABSTRACT A von Foerster-McKendrick model to study age-structured human population dynamics is presented in this paper. Forecasts of population density (population per age unit) depending on ages are possible using this model. The model consists of a quasi-linear first order partial differential equation for the dynamics of population density per age-unit (except for the zero-age), a boundary condition for the births flow at zero-age, and an initial condition for the population density at the initial instant. A general solution independent of the particular human-system under study is obtained based on some hypotheses about the mathematical structure of its input variables. The model has bee…