Search results for "Boundary value problem"
showing 10 items of 551 documents
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Fractional visco-elastic Euler–Bernoulli beam
2013
Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…
On numerical simulation of the continuous casting process
1988
In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.
Thermodynamically consistent residual-based gradient plasticity theory and comparison
2006
A gradient plasticity theory for small deformations is presented within the framework of nonlocal continuum thermodynamics. The second principle (Clausius–Duhem inequality), enriched by an additional term named energy residual, is employed in conjunction with the concepts of insulation condition and locality recovery condition, in order to derive all the pertinent restrictions upon the constitutive equations. These include the expressions of the energy residual and of the plastic dissipation density, as well as the PDEs governing the gradient kinematic and isotropic hardening of the material, together with the related higher-order boundary conditions for both the fixed and the moving bounda…
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects
2017
In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.
On the numerical solution of some finite-dimensional bifurcation problems
1981
We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.
Controllability-type properties for elliptic systems and applications
1991
We consider approximate and exact controllability results for elliptic problems. These results enable one to formulate optimal shape design problems in a fixed domain with certain boundary conditions.
Time-dependent simulation of Czochralski silicon crystal growth
1997
We have developed a detailed mathematical model and numerical simulation tools based on the streamline upwind/Petrov-Galerkin (SUPG) finite element formulation for the Czochralski silicon crystal growth. In this paper we consider the mathematical modeling and numerical simulation of the time-dependent melt flow and temperature field in a rotationally symmetric crystal growth environment. Heat inside the Czochralski furnace is transferred by conduction, convection and radiation, Radiating surfaces are assumed to be opaque, diffuse and gray. Hence the radiative heat exchange can be modeled with a non-local boundary condition on the radiating part of the surface. The position of the crystal-me…
Onset of convection in a porous rectangular channel with external heat transfer to upper and lower fluid environments
2012
Published version of an article in the journal: Transport in Porous Media. Also available from the publisher at: http://dx.doi.org/10.1007/s11242-012-0018-9 The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead…