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Multiscale expansion and numerical approximation for surface defects⋆

V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, F. Hérau, S. Tordeux, G. Vial (2011)

ESAIM: Proceedings

This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...

Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Philippe Karamian, Jacqueline Sanchez-Hubert, Évariste Sanchez Palencia (2002)

International Journal of Applied Mathematics and Computer Science

We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.

Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type

Stanislav Sysala (2010)

Applications of Mathematics

A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...

Numerical study of acoustic multiperforated plates

Abderrahmane Bendali, M’Barek Fares, Sophie Laurens, Sébastien Tordeux (2012)

ESAIM: Proceedings

It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.

On a 3D-Hypersingular Equation of a Problem for a Crack

Samko, Stefan (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.

On a type of Signorini problem without friction in linear thermoelasticity

Jiří Nedoma (1983)

Aplikace matematiky

In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity as well as its finite element approximation is proved. It is known that...

On Asymptotic Theory of Beams, Plates and Shells

L.A. Aghalovyan, M.L. Aghalovyan (2016)

Curved and Layered Structures

Bases of asymptotic theory of beams, plates and shells are stated. The comparison with classic theory is conducted. New classes of thin bodies problems, for which hypotheses of classic theory are not applicable, are considered. By the asymptotic method effective solutions of these problems are obtained. The effectiveness of the asymptotic method for finding solutions of as static, as well as dynamic problems of beams, plates and shells is shown.

On finite element uniqueness studies for Coulombs frictional contact model

Patrick Hild (2002)

International Journal of Applied Mathematics and Computer Science

We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known...

On identification of critical curves

Jaroslav Haslinger, Václav Horák (1990)

Aplikace matematiky

The paper deals with the problem of finding a curve, going through the interior of the domain Ω , accross which the flux ∂ u / ∂ n , where u is the solution of a mixed elliptic boundary value problem solved in Ω , attains its maximum.

On quasistatic inelastic models of gradient type with convex composite constitutive equations

Krzysztof Chełmiński (2003)

Open Mathematics

This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.

On semiconvexity properties of rotationally invariant functions in two dimensions

Miroslav Šilhavý (2004)

Czechoslovak Mathematical Journal

Let f be a function defined on the set 𝐌 2 × 2 of all 2 by 2 matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function f can be represented as a function f ˜ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of f in terms of its representation f ˜ .

On the accuracy of Reissner–Mindlin plate model for stress boundary conditions

Sheng Zhang (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...

On the Asymptotic Analys of a Non-Symmetric Bar

Abderrazzak Majd (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.

Currently displaying 161 – 180 of 298