Search results for "Boundary value problem"

A unifying variational framework for stress gradient and strain gradient elasticity theories

2015

Abstract Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int…

Nonlinear Nonhomogeneous Elliptic Problems

2019

We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…

Numerical assessment of the thermomechanical behaviour of the DEMO Water-Cooled Lithium Lead inboard blanket equatorial module

2018

Abstract Within the framework of EUROfusion R&D activity, a research campaign has been carried out at the University of Palermo, in close cooperation with ENEA labs, in order to assess the thermo-mechanical performances of the DEMO Water-Cooled Lithium Lead (WCLL) inboard blanket equatorial module, whether properly integrated within its whole inboard segment. In particular, a detailed 3D model of this segment, including all the other modules, the back-supporting structure and the attachment system, has been considered in order to realistically simulate the boundary conditions affecting the equatorial module behaviour. The study has been focused on the investigation of the module thermo-mech…

Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions

2019

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.

Thermomechanical Phenomena in Extended Thermodynamics of an Ideal Monoatomic Superfluid

1992

Monotony Based Imaging in EIT

2010

We consider the problem of determining conductivity anomalies inside a body from voltage‐current measurements on its surface. By combining the monotonicity method of Tamburrino and Rubinacci with the concept of localized potentials, we derive a new imaging method that is capable of reconstructing the exact (outer) shape of the anomalies. We furthermore show that the method can be implemented without solving any non‐homogeneous forward problems and show a first numerical result.

Stefan-Boltzmann Radiation on Non-convex Surfaces

1997

We consider the stationary heat equation for a non-convex body with Stefan–Boltzmann radiation condition on the surface. The main virtue of the resulting problem is non-locality of the boundary condition. Moreover, the problem is non-linear and in the general case also non-coercive and non-monotone. We show that the boundary value problem has a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. In the two dimensional case or when a part of the radiation can escape the system we obtain coercivity and stronger existence result. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

2014

The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is…

Thixotropy of Highly Viscous Sodium (Carboxymethyl)cellulose Hydrogels

1997

A general method to quantify the thixotropic behavior of systems with very low thixotropy is proposed. The areas enclosed by the rheograms τ=fγ. must be fitted to functions with well-determined boundary conditions. From these equations the corresponding thixotropic areas are obtained, together with the theoretical area enclosed by the rheogram corresponding to the maximum rheodestruction. The proposed method is applied to high viscosity sodium (carboxymethyl)cellulose gels.

Variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models

2016

Abstract The principle of minimum total potential energy and the primary principle of virtual power for stress gradient elasticity are presented as kinematic type constructs dual of analogous static type principles from the literature (Polizzotto, 2014; Polizzotto, 2015a). The extra gradient-induced boundary conditions are formulated as “boundary congruence conditions” on the microstructure’s deformation relative to the continuum, which ultimately require that the normal derivative of the stresses must vanish at the boundary surface. Two forms of the governing PDEs for the relevant boundary-value problem are presented and their computational aspects are discussed. The Timoshenko beam and th…