Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité
Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders
Mathematics Subject Classification: 74D05, 26A33In this paper, a comparative analysis of the models involving fractional derivatives of di®erent orders is given. Such models of viscoelastic materials are widely used in various problems of mechanics and rheology. Rabotnov's hereditarily elastic rheological model is considered in detail. It is shown that this model is equivalent to the rheological model involving fractional derivatives in the stress and strain with the orders proportional to a certain positive...
Comparative Study of a Solid Film Dewetting in an Attractive Substrate Potentials with the Exponential and the Algebraic Decay
We compare dewetting characteristics of a thin nonwetting solid film in the absence of stress, for two models of a wetting potential: the exponential and the algebraic. The exponential model is a one-parameter (r) model, and the algebraic model is a two-parameter (r, m) model, where r is the ratio of the characteristic wetting length to the height of the unperturbed film, and m is the exponent of h (film height) in a smooth function that interpolates the system's surface energy above and below...
Comparison of crack propagation criteria in linear elastic fracture mechanics
In linear fracture mechanics, it is common to use the local Irwin criterion or the equivalent global Griffith criterion for decision whether the crack is propagating or not. In both cases, a quantity called the stress intensity factor can be used. In this paper, four methods are compared to calculate the stress intensity factor numerically; namely by using the stress values, the shape of a crack, nodal reactions and the global energetic method. The most accurate global energetic method is used to...
Comparison results between minimal barriers and viscosity solutions for geometric evolutions
Compatibility conditions for discrete elastic structures.
Compensated compactness and one-dimensional elastodynamics
Complément à une étude de 1871 sur la théorie de l'équilibre et du mouvement des solides élastiques dont certaines dimensions sont très-petites par rapport à d'autres.
Complément à une étude de 1871 sur la théorie de l'équilibre et du mouvement des solides élastiques dont certaines dimensions sont très-petites par rapport à d'autres.
Comportamiento asintótico de las ecuaciones de la termoelasticidad generalizada.
In this paper it is first shown that the linear evolution equations for a generalized thermoelastic solid generate a C0 semigroup. Next an analysis of the long time evolution behaviour yields the some results known for classical thermoelasticity: generically, the natural state is asymptotically stable.
Comportement d'une plaque élastique dont une petite région est rigide et animée d'un mouvement vibratoire. Étude asymptotique de la matrice d'impédance
Computation of 3D vertex singularities for linear elasticity : error estimates for a finite element method on graded meshes
This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...
Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes
This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...
Computation of displacements for nonlinear elastic beam models using monotone iterations.
Computation of generalized stress intensity factors for bonded elastic structures
COMPUTATION of generalized stress intensity factors for bonded elastic structures
We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities....
Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators.
Computation of the drag force on a sphere close to a wall
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
Computation of the drag force on a sphere close to a wall
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
Computation of the drag force on a sphere close to a wall
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.