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### 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 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 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 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...

### 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...

### A mathematical model of suspension bridges

Applications of Mathematics

We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.

### A model of neck formation on a rod under tension.

Revista Colombiana de Matemáticas

### A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.

Numerische Mathematik

### A new approach of Timoshenko's beam theory by asymptotic expansion method

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

### A new mixed finite element method for the Timoshenko beam problem

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

### A nonlinear boundary value problem associated with the static equilibrium of an elastic beam supported by sliding clamps.

International Journal of Mathematics and Mathematical Sciences

### A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity

Annales de l'I.H.P. Analyse non linéaire

### A semianalytical method for nonlinear vibration of Euler-Bernoulli beams with general boundary conditions.

Mathematical Problems in Engineering

### A seminalytical approach to large deflections in compliant beams under point load.

Mathematical Problems in Engineering

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