Related papers: Symmetry and rigidity for the hinged composite pla…
In this paper we deal with the composite plate problem, namely the following optimization eigenvalue problem $$ \inf_{\rho \in \mathrm{P}} \inf_{u \in \mathcal{W}\setminus\{0\}} \frac{\int_{\Omega}(\Delta u)^2}{\int_{\Omega} \rho u^2}, $$…
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…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
In this article we give a brief overview of some known results in the theory of obstacle-type problems associated with a class of fourth-order elliptic operators, and we highlight our recent work with collaborators in this direction.…
A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. By using methods of the theory…
We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are…
We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered…
The inverse problem of special geometry (Seiberg-Witten geometry of 4d N=2 SCFT) asks for a recursive construction of all such geometries in rank $r$ by assembling together known lower-rank ``strata''. This leads to a program to…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…
We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff-Love plates, including the biharmonic equation as a particular case. The…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
We consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eingenvalue problem. In order to improve the stability of the plate, it seems…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
This paper addresses the challenging issue of symmetry in mixed-integer convex optimization problems, which frequently arise in real-world applications such as the unit commitment problem. Although variable aggregation techniques have been…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
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…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
The homogenized stiffnesses of a corrugated plate are calculated by solving the periodicity cell problem of the homogenization theory by using two-steps dimension reduction procedure. The three-dimensional periodicity cell problem first…