Search results for "Boundary Condition"

Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches.

2012

The object of the paper concerns a consistent formulation of the classical Signorini’s theory regarding the frictionless contact problem between two elastic bodies in the hypothesis of small displacements and strains. The employment of the symmetric Galerkin boundary element method, based on boundary discrete quantities, makes it possible to distinguish two different boundary types, one in contact as the zone of potential detachment, called the real boundary, the other detached as the zone of potential contact, called the virtual boundary. The contact-detachment problem is decomposed into two sub-problems: one is purely elastic, the other regards the contact condition. Following this method…

An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials

2015

An enhanced three-dimensional (3D) framework for computational homogenization and intergranular cracking of polycrystalline materials is presented. The framework is aimed at reducing the computational cost of polycrystalline micro simulations, with an aim towards effective multiscale modelling. The scheme is based on a recently developed Voronoi cohesive-frictional grain-boundary formulation. A regularization scheme is used to avoid excessive mesh refinements often induced by the presence of small edges and surfaces in mathematically exact 3D Voronoi morphologies. For homogenization purposes, periodic boundary conditions are enforced on non-prismatic periodic micro representative volume ele…

Electronic and optical properties of carbon nanotubes under pure bending

2010

The high aspect ratio of carbon nanotubes makes them prone to bending. To know how bending affects the tubes is therefore crucial for tube identification and for electrical component design. Very few studies, however, have investigated tubes under small bending well below the buckling limit, because of technical problems due to broken translational symmetry. In this Brief Report a cost-effective and exact modeling of singe-walled nanotubes under such small bending is enabled by revised periodic boundary conditions, combined with density-functional tight-binding. The resulting, bending-induced changes in electronic and optical properties fall in clear chirality-dependent trend families. Whil…

Density-Functional Tight-Binding Simulations of Curvature-Controlled Layer Decoupling and Band-Gap Tuning in BilayerMoS2

2014

Monolayer transition-metal dichalcogenides (TMDCs) display valley-selective circular dichroism due to the presence of time-reversal symmetry and the absence of inversion symmetry, making them promising candidates for valleytronics. In contrast, in bilayer TMDCs both symmetries are present and these desirable valley-selective properties are lost. Here, by using density-functional tight-binding electronic structure simulations and revised periodic boundary conditions, we show that bending of bilayer MoS2 sheets breaks band degeneracies and localizes states on separate layers due to bending-induced strain gradients across the sheets. We propose a strategy for employing bending deformations in …

A Multiscale Approach to Polycrystalline Materials Damage and Failure

2014

A two-scale three-dimensional approach for degradation and failure in polycrystalline materials is presented. The method involves the component level and the grain scale. The damage-induced softening at the macroscale is modelled employing an initial stress boundary element approach. The microscopic degradation is explicitly modelled associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a cohesive-frictional 3D grain-boundary formulation to simulate intergranular degradation and failure in the Voronoi morphology. Macro-strains are downscaled as RVEs' periodic boundary conditions, while overall macro-stresses are obtained upscaling the micr…

Regularization and finite element approximation of the wave equation with Dirichlet boundary data

1990

Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem

2015

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.

Nonlocal Third Order Boundary Value Problems with Solutions that Change Sign

2014

We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.

A multi-sphere particle numerical model for non-invasive investigations of neuronal human brain activity

2013

In this paper, a multi-sphere particle method is built- up in order to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain activity. The partial difierential equations governing the relationships between neural current sources and the data produced by neuroimaging technique, are able to compute the scalp potential and magnetic fleld distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the computation by avoiding the mesh construction. The current dipoles are into an homogeneous spherical domain modeling the head and the computational approach i…

A Boundary Control Approach to an Optimal Shape Design Problem

1989

Abstract We consider the problem of controlling the coincidence set in connection with an obstacle problem. We shall transform the obtained optimal shape design problem into a boundary control problem with Dirichlet boundary conditions.