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We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic…

Analysis of PDEs · Mathematics 2024-08-27 G. Alessandrini , A. Morassi , E. Rosset , E. Sincich , S. Vessella

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the…

Mathematical Physics · Physics 2017-06-16 Giulio G. Giusteri , Luca Lussardi , Eliot Fried

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…

Numerical Analysis · Mathematics 2018-10-23 Javier Videla , Sundararajan Natarajan , Stephane PA Bordas

This work presents a generalized Kirchhoff-Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for…

Materials Science · Physics 2023-06-06 Thang Xuan Duong , Vu Ngoc Khiêm , Mikhail Itskov , Roger Andrew Sauer

The dynamics of a (nonlinear) Berger plate in the absence of rotational inertia are considered with inhomogenous boundary conditions. In our analysis, we consider boundary damping in two scenarios: (i) free plate boundary conditions, or…

Analysis of PDEs · Mathematics 2016-02-02 Pelin G. Geredeli , Justin T. Webster

We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…

Dynamical Systems · Mathematics 2010-10-26 Igor Chueshov , Stanislav Kolbasin

We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity…

Analysis of PDEs · Mathematics 2022-02-23 Robert Denk , Jürgen Saal

In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong…

Analysis of PDEs · Mathematics 2014-10-23 Anna Marciniak-Czochra , Andro Mikelic

We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…

Analysis of PDEs · Mathematics 2018-07-17 Virginia Agostiniani , Alessandro Lucantonio , Danka Lučić

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…

Analysis of PDEs · Mathematics 2024-11-05 Dominic Breit , Arnab Roy

A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…

Differential Geometry · Mathematics 2013-04-04 Hongliang Shao

A thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base is considered; the diameter of $\theta_{h}$ is of the same order as the plate relative thickness $h\ll1$. In…

Mathematical Physics · Physics 2017-04-20 G. Buttazzo , G. Cardone , S. A. Nazarov

This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…

Numerical Analysis · Mathematics 2025-09-16 Jun Hu , Zhen Liu , Rui Ma

A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled…

Optimization and Control · Mathematics 2019-02-08 Alexander Zuyev , Julia Novikova

In this paper, we consider the following Kirchhoff type equation $$ -\left(a+ b\int_{\R^3}|\nabla u|^2\right)\triangle {u}+V(x)u=f(u),\,\,x\in\R^3, $$ where $a,b>0$ and $f\in C(\R,\R)$, and the potential $V\in C^1(\R^3,\R)$ is positive,…

Analysis of PDEs · Mathematics 2021-03-01 Zhisu Liu , Haijun Luo , Jianjun Zhang

We use Hamiltonian Floer theory to recover and generalize a classic rigidity theorem of Ekelend and Lasry. That theorem can be rephrased as an assertion about the existence of multiple closed Reeb orbits for certain tight contact forms on…

Symplectic Geometry · Mathematics 2019-02-20 Ely Kerman

In this paper we address some questions about symmetry, radial monotonicity, and uniqueness for a semilinear fourth-order boundary value problem in the ball of $\mathbb R^2$ deriving from the Kirchhoff-Love model of deformations of thin…

Analysis of PDEs · Mathematics 2025-03-19 Giulio Romani

We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat…

Analysis of PDEs · Mathematics 2018-11-06 Irena Lasiecka , Michael Pokojovy , Xiang Wan

In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo's law. In the absense of any additional mechanical dissipations, the system is often not…

Analysis of PDEs · Mathematics 2015-06-18 Michael Pokojovy

We consider a conservative system consisting of an elastic plate interacting with a gas filling a semi-infinite tube. The plate is placed on the bottom of the tube. The dynamics of the gas velocity potential is governed by the linear wave…

Analysis of PDEs · Mathematics 2016-01-19 Igor Chueshov