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### 3D-2D asymptotic analysis for micromagnetic thin films

ESAIM: Control, Optimisation and Calculus of Variations

$\Gamma$-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness $\epsilon$ approaches zero of a ferromagnetic thin structure ${\Omega }_{\epsilon }=\omega ×\left(-\epsilon ,\epsilon \right)$, $\omega \subset {ℝ}^{2}$, whose energy is given by${ℰ}_{\epsilon }\left(\overline{m}\right)=\frac{1}{\epsilon }{\int }_{{\Omega }_{\epsilon }}\left(W\left(\overline{m},\nabla \overline{m}\right)+\frac{1}{2}\nabla \overline{u}·\overline{m}\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$subject to$\text{div}\left(-\nabla \overline{u}+\overline{m}{\chi }_{{\Omega }_{\epsilon }}\right)=0\phantom{\rule{1.0em}{0ex}}\text{on}{ℝ}^{3},$and to the constraint$|\overline{m}|=1\text{on}{\Omega }_{\epsilon },$where $W$ is any continuous function satisfying $p$-growth assumptions with $p>1$. Partial results are also obtained in the case $p=1$, under an additional assumption on $W$.

### 3D-2D Asymptotic Analysis for Micromagnetic Thin Films

ESAIM: Control, Optimisation and Calculus of Variations

Γ-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure ${\Omega }_{\epsilon }=\omega ×\left(-\epsilon ,\epsilon \right)$, $\omega \subset {ℝ}^{2}$, whose energy is given by ${ℰ}_{\epsilon }\left(\overline{m}\right)=\frac{1}{\epsilon }{\int }_{{\Omega }_{\epsilon }}\left(W\left(\overline{m},\nabla \overline{m}\right)+\frac{1}{2}\nabla \overline{u}·\overline{m}\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$ subject to $\text{div}\left(-\nabla \overline{u}+\overline{m}{\chi }_{{\Omega }_{\epsilon }}\right)=0\phantom{\rule{1.0em}{0ex}}\phantom{\rule{4.0pt}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}{ℝ}^{3},$ and to the constraint $|\overline{m}|=1\phantom{\rule{4.0pt}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}{\Omega }_{\epsilon },$ where W is any continuous function satisfying p-growth assumptions with p> 1. Partial results are also obtained in the case p=1, under an additional assumption on W.

### A contact problem of the interaction of a semi-finite inclusion with a plate.

Georgian Mathematical Journal

### A discretization method for the problem of a membrane constrained by elastic obstacle

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

In questo lavoro sono dati alcuni modelli matematici per il problema di contatto tra una membrana ed un suolo od ostacolo elastico. Viene costruita una approssimazione lineare a tratti della soluzione e, tramite una disequazione variazionale discreta, se ne dà il corrispondente teorema di convergenza.

### A Finite Element Lumped Mass Scheme for Solving Eigenvalue Problems of Circular Arches.

Numerische Mathematik

### A finite element method for stiffened plates

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

The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...

### A finite element method for stiffened plates

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...

### A finite element scheme for the evolution of orientational order in fluid membranes

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, J. Phys. II7 (1997) 1509–1520; N. Uchida, Phys. Rev. E66 (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce...

### A Finite-Difference Approximation for the Eigenvalue of the Clamped Plate.

Numerische Mathematik

### A free boundary problem with a volume penalization

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A Galerkin spectral approximation in linearized beam theory

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

### A Galerkin-parameterization method for the optimal control of smart microbeams.

Mathematical Problems in Engineering

### A general asymptotic dynamic model for Lipschitzian elastic curved rods.

Journal of Applied Mathematics

### A general scheme of equations covering rectilinearly drawn shell structures

Applicationes Mathematicae

### A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory

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

A shear deformation theory is developed to analyse the geometrically nonlinear behaviour of layered composite plates under transverse loads. The theory accounts for the transverse shear (as in the Reissner Mindlin plate theory) and large rotations (in the sense of the von Karman theory) suitable for simulating the behaviour of moderately thick plates. Square and rectangular plates are considered: the numerical results are obtained by a finite element computational procedure and are given for various...

### A hybrid finite element method to compute the free vibration frequencies of a clamped plate

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

### A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

International Journal of Applied Mathematics and Computer Science

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into...

### A Landesman-Lazer type condition and the long time behaviour of floating plates

Acta Mathematica et Informatica Universitatis Ostraviensis

### A linear and weakly nonlinear equation of a beam: the boundary-value problem for free extremities and its periodic solutions

Czechoslovak Mathematical Journal

### A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to develop a finite element method which allows computing the buckling coefficients and modes of a non-homogeneous Timoshenko beam. Studying the spectral properties of a non-compact operator, we show that the relevant buckling coefficients correspond to isolated eigenvalues of finite multiplicity. Optimal order error estimates are proved for the eigenfunctions as well as a double order of convergence for the eigenvalues using classical abstract spectral approximation theory...

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