64 citations · 146 across the 27 of their papers we have counts for
24 papers · 1 filter
Korn and Poincaré-Korn inequalities for thin domains in
Davit Harutyunyan
We prove Korn's first inequalities with and without boundary conditions in () in -regular thin domains with Lipschitz thickness boundaries with a cons…
On weighted rigidity estimates for bulk and thin domains
Davit Harutyunyan, Andre. M. Rodrigues
This work is concerned with weighted Geometric Rigidity Estimates and Korn's first inequalities in bulk and thin domains. We consider weights, that are a nonnegative power of the d…
On the fractional Korn inequality in bounded domains: Counterexamples to the case
Davit Harutyunyan, Hayk Mikayelyan
The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in…
The buckling load of cylindrical shells under axial compression depends on the cross-section curvature
Davit Harutyunyan, Andre Martins Rodrigues
It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimen…
A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells
Davit Harutyunyan
The general theory of slender structure buckling by Grabovsky and Truskinovsky [\textit{Cont. Mech. Thermodyn.,} 19(3-4):211-243, 2007], (later extended in [\textit{Journal of Nonl…
The sharp Korn interpolation and second inequalities in thin domains
Davit Harutyunyan
In the present paper we extend the Korn interpolation and second inequalities in thin domains, proven in [\ref{bib:Harutyunyan.4}], to the space for any A…
A note on the extreme points of the cone of quasiconvex quadratic forms with orthotropic symmetry
Davit Harutyunyan
We study the extreme points of the cone of quasiconvex quadratic forms with linear elastic orthotropic symmetry. We prove that if the determinant of the acoustic matrix of the asso…
The asymptotically sharp Korn interpolation and second inequalities for shells
Davit Harutyunyan
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequ…
Weighted asymptotic Korn and interpolation Korn inequalities with singular weights
Davit Harutyunyan, Hayk Mikayelyan
In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants (K…
On the Korn interpolation and second inequalities in thin domains
Davit Harutyunyan
We consider shells of non-constant thickness in three dimensional Euclidean space around surfaces which have bounded principal curvatures. We derive Korn's interpolation (or the so…
On the maximization of the solution of Poisson's equation: Brezis-Gallouet-Wainger type inequalities and applications
Davit Harutyunyan, Hayk Mikayelyan
For the solution of the Poisson problem with an right hand side \begin{equation*} \begin{cases} -Δu(x) = f (x) & \mbox{in } D, u=0 & \mbox{on } \partial D, \end{cases} \…
Gaussian curvature as an identifier of shell rigidity
Davit Harutyunyan
In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shells…
Korn inequalities for shells with zero Gaussian curvature
Yury Grabovsky, Davit Harutyunyan
We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that…
High frequency homogenization for travelling waves in periodic media
Davit Harutyunyan, Richard V. Craster, Graeme W. Milton
We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wa…
Sharp weighted Korn and Korn-like inequalities and an application to washers
Davit Harutyunyan
In this paper we prove asymptotically sharp weighted "first-and-a-half" Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change o…
On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials
Davit Harutyunyan, Graeme Walter Milton
We prove that an elasticity tensor with orthotropic symmetry is extremal if the determinant of its acoustic tensor is an extremal polynomial that is not a perfect square.
Rigorous derivation of the formula for the buckling load in axially compressed circular cylindrical shells
Yury Grabovsky, Davit Harutyunyan
The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed ci…
Scaling instability of the buckling load in axially compressed circular cylindrical shells
Yury Grabovsky, Davit Harutyunyan
In this paper we initiate a program of rigorous analytical investigation of the paradoxical buckling behavior of circular cylindrical shells under axial compression. This is done b…
Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex
Davit Harutyunyan, Graeme Walter Milton
We prove that if the associated fourth order tensor of a quadratic form has a linear elastic cubic symmetry then it is quasiconvex if and only if it is polyconvex, i.e. a sum of co…
Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells
Yury Grabovsky, Davit Harutyunyan
Understanding asymptotics of gradient components in relation to the symmetrized gradient is im- portant for the analysis of buckling of slender structures. For circular cylindrical…
Scaling laws and the rate of convergence in thin magnetic films
Davit Harutyunyan
We study static 180 degree domain walls in thin infinite magnetic films. We establish the scaling of the minimal energy by Γ-convergence and the energy minimizer pro-file, which tu…
New asymptotically sharp Korn and Korn-like inequalities in thin domains
Davit Harutyunyan
It is well known that Korn inequality plays a central role in the theory of linear elasticity. In the present work we prove new asymptotically sharp Korn and Korn-like inequalities…
Rigorous asymptotic analysis of buckling of thin-walled cylinders under axial compression
Yury Grabovsky, Davit Harutyunyan
Using rigorous constitutive linearization of second variation introduced in [6] we study weak stability of homogeneous deformation of the axially compressed circular cylindrical sh…
Existence and the stability of minimizers in ferromagnetic nanowires
Davit Harutyunyan
We study static 180 degree domain walls in infinite magnetic wires with bounded, and rotationally symmetric cross sections. We prove an existence of global minimizers for the…