An inverse transient thermoelastic problem of a thin annular disc.
An two-well Liouville theorem.
An optimal algorithm with Barzilai-Borwein steplength and superrelaxation for QPQC problem
We propose a modification of MPGP algorithm for solving minimizing problem of strictly convex quadratic function subject to separable spherical constraints. This active set based algorithm explores the faces by the conjugate gradients and changes the active sets and active variables by the gradient projection with the Barzilai-Borwein steplength. We show how to use the algorithm for the solution of separable and equality constraints. The power of our modification is demonstrated on the solution...
An optimal control problem for a fourth-order variational inequality
An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem...
An optimal control problem for a pseudoparabolic variational inequality
We deal with an optimal control problem governed by a pseudoparabolic variational inequality with controls in coefficients and in convex sets of admissible states. The existence theorem for an optimal control parameter will be proved. We apply the theory to the original design problem for a deffection of a viscoelastic plate with an obstacle, where the variable thickness of the plate appears as a control variable.
An optimal dimension of submerged parallel bars as a wave reflector.
An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.
An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.
An XFEM/DG approach for fluid-structure interaction problems with contact
In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on...
Analisi generale delle vibrazioni libere trasversali dei gusci sferici ortotropi ribassati
Si risolve nella sua generalità il problema delle vibrazioni libere trasversali dei gusci sferici ortotropi ribassati, che in un precedente Lavoro era stato affrontato limitatamente al campo delle vibrazioni assialsimmetriche. L'integrazione delle equazioni del moto è conseguita per serie mediante particolari sviluppi, generabili grazie ad un'opportuna sostituzione di una delle variabili indipendenti.
Analogues of the Kolosov-Muskhelishvili general representation formulas and Cauchy-Riemann conditions in the theory of elastic mixtures.
Analyse numérique d'un modèle de coques de Koiter discrétisé en base cartésienne par éléments finis DKT
Analysis and numerical approximation of an elastic frictional contact problem with normal compliance
We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous...
Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem
We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error...
Analysis of a contact adhesive problem with normal compliance and nonlocal friction
The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence...
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....
Analysis of a discrete model for the contact problem between a membrane and an elastic obstacle
In questo lavoro viene risolto il problema del contatto tra una membrana ed un suolo od ostacolo elastico con una approssimazione lineare a tratti della soluzione. Sono date alcune formulazioni equivalenti del problema discreto e se ne discutono le corrispondenti proprietà computazionali.
Analysis of a force-based quasicontinuum approximation
We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation can be derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical “ghost” forces that occur in the atomistic to continuum interface during constant strain. The algorithmic simplicity and consistency with the purely atomistic model at...
Analysis of a frictional contact problem with adhesion.