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

Georgian Mathematical Journal

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-Difference Approximation for the Eigenvalue of the Clamped Plate.

Numerische Mathematik

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

Acta Mathematica et Informatica Universitatis Ostraviensis

A mixed finite element method for plate bending with a unilateral inner obstacle

Applications of Mathematics

A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.

A mixed finite element method for the biharmonic problem

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

A multigrid method for Reissner-Mindlin plates.

Numerische Mathematik

A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

ESAIM: Control, Optimisation and Calculus of Variations

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when $S\subset {ℝ}^{2}$. The convergence holds provided...

A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

ESAIM: Control, Optimisation and Calculus of Variations

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when $S\subset {ℝ}^{2}$. The convergence holds provided...

A Potential Method for the Biharmonic Equation.

Numerische Mathematik

Kybernetika

A study of an operator arising in the theory of circular plates

Aplikace matematiky

The operator ${L}_{0}:{D}_{{L}_{0}}\subset H\to H$, ${L}_{0}u=\frac{1}{r}\frac{d}{dr}\left\{r\frac{d}{dr}\left[\frac{1}{r}\frac{d}{dr}\left(r\frac{du}{dr}\right)\right]\right\}$, ${D}_{{L}_{0}}=\left\{u\in {C}^{4}\left(\left[0,R\right]\right),{u}^{\text{'}}\left(0\right)={u}^{\text{'}\text{'}\text{'}\text{'}}\left(0\right)=0,u\left(R\right)={u}^{\text{'}}\left(R\right)=0\right\}$, $H={L}_{2,r}\left(0,R\right)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on ${L}_{0}$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types ${L}_{0}u=g$ and ${u}_{tt}+{L}_{0}u=g$, respectively.

A study of bending waves in infinite and anisotropic plates

Applications of Mathematics

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.

A system of semilinear evolution equations with homogeneous boundary conditions for thin plates coupled with membranes.

Electronic Journal of Differential Equations (EJDE) [electronic only]

A theoretical approach to the problem of the most dangerous initial deflection shape in stability type structural problems

Aplikace matematiky

The author introduces a global measure of initial deflection given by the energy norm. Solving the formulated minimization problem with a subsidiary condition the most dangerous initial deflection shape is obtained. The theoretical results include a wide range of stability type structural problems.

A transmission problem for beams on nonlinear supports.

Boundary Value Problems [electronic only]

A variational model for nonlinear elastic plates.

Journal of Convex Analysis

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