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A new finite element approach for problems containing small geometric details

Wolfgang Hackbusch, Stefan A. Sauter (1998)

Archivum Mathematicum

In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization...

An adaptive finite element method for solving a double well problem describing crystalline microstructure

Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

Simulation and design of extraction and separation fluidic devices

Bijan Mohammadi, Juan G. Santiago (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.

Simulation and design of extraction and separation fluidic devices

Bijan Mohammadi, Juan G. Santiago (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.

Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

Janusz Dyszlewicz (1997)

Applicationes Mathematicae

A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms u ̲ = ( 0 , u θ , 0 ) , φ ̲ = ( φ r , 0 , φ z ) ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how u ̲ and φ ̲ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated...

Sull’estensione di un teorema di Menabrea al caso di una microstruttura a deformazioni finite

Antonio Claudio Grioli (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.

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