Korn's inequalities for junctions of elastic bodies with thin plates.
Korn's inequality for an arbitrary system of distorted thin rods.
La méthode de Kikuchi appliquée aux équations de von Karman.
La trave in parete sottile a sezione aperta e variabile: formulazione teorica e risultati sperimentali
Theoretical and experimental results concerning the shear-center of a bent beam with variable section are carried out. The matrix methods of structural analysis for the static linear elastic problem is extended; the stiffness and load matrix are formulated starting from the sectorial areas theory in order to interpret the effect of non-uniform torsion. The formulation may be used through the general matrix displacement method of structural analysis.
Laplace transform of distribution-valued functions and its applications
Limiting behavior of global attractors for singularly perturbed beam equations with strong damping
The limiting behavior of global attractors for singularly perturbed beam equations is investigated. It is shown that for any neighborhood of the set is included in for small.
Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity
The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of Γ-convergence, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order ε2α−2, with α ≥ 3. According to the value of α, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized...
Liouville integrability of geometric variational problems.
Local Parameterization and the Asymptotic Numerical Method
The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problems
Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point
In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.
Locking free matching of different three dimensional models in structural mechanics
The present paper proposes and analyzes a general locking free mixed strategy for computing the deformation of incompressible three dimensional structures placed inside flexible membranes. The model involves as in Chapelle and Ferent [Math. Models Methods Appl. Sci.13 (2003) 573–595] a bending dominated shell envelope and a quasi incompressible elastic body. The present work extends an earlier work of Arnold and Brezzi [Math Comp.66 (1997) 1–14] treating the shell part and proposes a global...
Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping
We are concerned with a transmission problem for the Kirchhoff plate equation where one small part of the domain is made of a viscoelastic material with the Kelvin-Voigt constitutive relation. We obtain the logarithmic stabilization result (explicit energy decay rate), as well as the wellposedness, for the transmission system. The method is based on a new Carleman estimate to obtain information on the resolvent for high frequency. The main ingredient of the proof is some careful analysis for the...
Long-term damped dynamics of the extensible suspension bridge.
Love and Rayleigh correction terms and Padé approximants.
Material constraints in continuum mechanics
Si dimostra che ci sono valide ragioni per considerare la teoria standard dei vincoli interni, nella meccanica dei continui, insufficientemente generale. In particolare, con l’unica eccezione dell’iperelasticità, l’extra-stress dovrebbe dipendere anche dai moltiplicatori di Lagrange, cioè, dallo stress che non effettua lavoro (virtuale).
Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device
The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear...
Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device
The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear...
Mathematical modeling and simulation of flow in domains separated by leaky semipermeable membrane including osmotic effect
In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect. The model is solved...
Mathematical modelling for keyhole surgery simulations: Spleen capsule as an elastic membrane.
Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...