On some contact problems for bodies with elastic inclusions.
On the analysis of boundary value problems in nonsmooth domains [Book]
On the approximation of the Signorini problem with friction
On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.
In questo lavoro viene studiato il comportamento dinamico di una piastra vincolata monolateralmente su una fondazione elastica alla Winkler. Si presentano alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti. Tali risultati mettono in luce l'influenza di alcuni fattori tipici come le funzioni di forma, il parametro di mesh e l'ampiezza dell'intervallo con cui si realizza l'integrazione nel tempo delle equazioni del moto. Si istituiscono infine dei confronti con risultati...
On the frictionless unilateral contact of two viscoelastic bodies.
On the numerical treatment of the contact problem.
On the Signorini problem with friction in linear thermoelasticity: The quasi-coupled 2D-case
The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary of a polygonal domain is given. The rate of convergence is proved if the exact solution is sufficiently regular.
On the solution of a finite element approximation of a linear obstacle plate problem
In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably...
On the thermal aspect of dynamic contact problems
A short survey of available existence results for dynamic contact problems including heat generation and heat transfer is presented.
On the two-step iterative method of solving frictional contact problems in elasticity
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem...
On three-dimensional dynamical problems of the generalized theory of elastothermodiffusion.
Optimization of the domain in elliptic unilateral boundary value problems by finite element method
Quadratic finite elements with non-matching grids for the unilateral boundary contact
We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...
Quasistatic problems in contact mechanics
We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved...
Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact.
Regularity for Signorini's Problem in linear eleasticity.
Remarks about Signorini's problem in linear elasticity
Residual a posteriori error estimators for contact problems in elasticity
This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.
Sensitivity analysis of a nonlinear obstacle plate problem
We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9, 10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...