Related papers: Junction between a plate and a rod of comparable t…
This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
The aim of this work is to study the asymptotic behavior of a structure made of plates of thickness $2\delta$ when $\delta\to 0$. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2\delta when \delta rightarrow 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour…
We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…
In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a…
We consider the linearized elasticity system in a multidomain of the three dimensional space. This multidomain is the union of a horizontal plate, with fixed cross section and small thickness "h", and of a vertical beam with fixed height…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the…
In this paper, we study an interaction problem between an elastic plate and a compressible viscous fluid located between the rigid bottom $z=0$ and the plate. First, by utilizing the vertical fluid dissipation, we show that $\ln\eta(t) \in…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the…
The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…
The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal…
This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary…
Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…