A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed finite element...
A general setting is proposed for the mixed finite element approximations of
elliptic differential problems involving a unilateral boundary condition. The
treatment covers the Signorini problem as well as the unilateral contact
problem with or without friction. Existence, uniqueness for both the
continuous and the discrete problem as well as error estimates are established
in a general framework. As an application, the approximation of the Signorini
problem by the lowest order mixed finite element...
The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately,...
In this work, we consider the quasistatic frictionless contact problem between a
viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic
constitutive law is employed to model the piezoelectric material and the normal compliance
condition is used to model the contact. The variational formulation is derived in a form
of a coupled system for the displacement and electric potential fields. An existence and
uniqueness result is recalled. Then, a fully discrete scheme...
Wilkins' method has been successfully used since early 60s for numerical
simulation of high velocity contact elastic-plastic flows. The present work
proposes some effective modifications of this method including more
sophisticated material model including the Baushinger effect; modification of
the algorithm based on correction of the initial configuration of a solid; a
contact algorithm based on the idea of a mild contact.
The analysis of dynamic contacts/impacts of several deformable bodies belongs to both theoretically and computationally complicated problems, because of the presence of unpleasant nonlinearities and of the need of effective contact detection. This paper sketches how such difficulties can be overcome, at least for a model problem with several elastic bodies, using i) the explicit time-discretization scheme and ii) the finite element technique adopted to contact evaluations together with iii) the...
Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous generalizations including 3-dimensional ones, and supplied by numerical examples obtained from...