arXiv subjects

Elisa Davoli

Publications and source records attributed to Elisa Davoli.

58 records · Page 4Linked to original sources

arXiv2013

Quasistatic evolution models for thin plates arising as low energy Gamma-limits of finite plasticity

In this paper we deduce by Γ-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we study the case where the scaling factor of the elasto- plastic energy is of order ε^ (2α-2), with α>=3. We show that solutions to the three- dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on α.

math.AP↗

arXiv2013

Linearized plastic plate models as Gamma-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 is of order ε^(2α-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 Karman plate theory and the linearized plate theory.

math.AP↗

arXiv2011

Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity

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 δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

math.AP↗

arXiv2010

Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density

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 physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.

math.AP↗