Related papers: Junction of elastic plates and beams (Preliminary …
We address a moving boundary problem that consists of a system of equations modeling an inviscid fluid interacting with a two-dimensional nonlinear Koiter plate at the boundary. We derive a priori estimates needed to prove the local-in-time…
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…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
The paper describes the first exact results in optimal design of three-phase elastic structures. Two isotropic materials, the "strong" and the "weak" one, are laid out with void in a given two-dimensional domain so that the compliance plus…
We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A…
The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…
Dualities have been known to map space trusses and plate structures to each other since the 1980-s. Yet the computational similarity of the two has not been used to solve the unfamiliar plate structure with the methods of the well known…
The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h,…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic (EHD)…
We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the…
I study how the contact area and the work of adhesion, between two elastic solids with randomly rough surfaces, depend on the relative humidity. The surfaces are assumed to be hydrophilic, and capillary bridges form at the interface between…
Based on the mathematical-physical model of pavement mechanics, a multilayer elastic system with interlayer friction conditions is constructed. Given the complex boundary conditions, the corresponding variational inequalities of the partial…
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises…
In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a…
We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…
A (bar-and-joint) framework is a set of points in a normed space with a set of fixed distance constraints between them. Determining whether a framework is locally rigid - i.e. whether every other suitably close framework with the same…
We describe theoretically ``electrolubrication'' in liquid mixtures, the phenomenon where an electric field applied transverse to the confining surfaces leads to concentration gradients that alter the flow profile significantly. When the…