Junction of elastic plates and beams
TLDR
In this paper, the linearized elasticity system in a multidomain of R 3 is considered, where the lateral boundary of the plate and the top of the beam are assumed to be clamped.Abstract:
We consider the linearized elasticity system in a multidomain of R 3 . This multidomain is the union of a horizontal plate with fixed cross section and small thickness e, and of a vertical beam with fixed height and small cross section of radius r e . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When e and r e tend to zero simultaneously, with r e e 2 , we identify the limit problem. This limit problem involves six junction conditions.read more
Citations
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Junction of a periodic family of elastic rods with a 3d plate. Part I
TL;DR: In this article, a set of elastic rods periodically distributed over an elastic plate whose thickness tends here to 0 was considered, and the homogenization process for the junction of the rods and a thin plate was described.
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Junction in a thin multidomain for a fourth order problem
Antonio Gaudiello,Elvira Zappale +1 more
TL;DR: In this paper, the authors consider a thin multidomain of ℝN, N ≥ 2, consisting of a vertical rod upon a horizontal disk and derive the equilibrium configuration of two joint beams, T-shaped, clamped at the three endpoints and subject to transverse loads.
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Influence of non degenerated joint on the global and local behavior of joined rods
Antonio Gaudiello,A.G. Kolpakov +1 more
TL;DR: Gaudiello and Kolpakov as discussed by the authors considered a three-dimensional transport problem (thermoconductivity, diffusion, etc.) in joined thin plates under condition that the characteristic dimension of the joint is comparable with the thickness of the plates.
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Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S 2
Antonio Gaudiello,Rejeb Hadiji +1 more
TL;DR: In this article, the authors consider a thin multidomain of R 3 consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section.
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Equilibrium problem for elastic body with delaminated T-shape inclusion
TL;DR: An asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero is provided and an existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters.
References
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Book
Function Spaces and Potential Theory
David R. Adams,Lars Inge Hedberg +1 more
TL;DR: In this paper, the interplay between function space theory and potential theory is discussed. And a surprisingly large part of classical potential theory has been extended to this nonlinear setting, sometimes surprising, usually they are nontrivial and have required new methods.
Book
Mathematical Problems in Elasticity and Homogenization
TL;DR: In this paper, the authors present an extension of the Dirichlet problem for the case of Perforated Domains with a Non-Periodic Structure, where the boundary value problem is solved with Neumann conditions on the outer part of the boundary and on the surface of the Cavities.
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A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity
TL;DR: The energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by G. Kirchhoff in 1850 as mentioned in this paper, and it arises as a 0-limit of three-dimensional nonlinear elasticity theory as the thickness of a plate goes to zero.
the derivation of nonlinear plate theory from three dimensional elasticity
Gero Friesecke,Richard D. James +1 more
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A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence
TL;DR: In this paper, a hierarchy of plate models from three-dimensional nonlinear elasticity by Γ-convergence is derived, where the scaling of the elastic energy per unit volume is related to the strength of the applied force, where h is the thickness of the plate.