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We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.
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.
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...
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...
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 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...
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...
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...
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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