| Chairman : Jaroslav Haslinger |
| 14:00 |
Part I - Opening |
|
| 14:15 |
Prof. Dr. Barbara Wohlmuth
(University of Stuttgart, Germany) |
Stabilized semi-smooth Newton algorithms for variational
inequalities
Numerical simulation for partial differential equations plays an important
role in many fields. Although efficient solution strategies are well
known for simple settings, more complex models involving non-smooth
nonlinearities are still quite challenging. In this talk we present some
applications from structural mechanics and finance where variational
inequalities play an important role. Surprisingly frictional contact
problems
with plasticity fit into the same mathematical framework as American
options.
We propose fast and robust numerical approaches based on the concept of
domain
decomposition, adaptivity and stabilized time integration. |
| 15:15 | Coffee |
| Chairman : Jiri Jarusek |
| 15:40 |
Part II - Opening |
|
| 15:50 |
Prof. Dr. Christof Eck
(University of Stuttgart, Germany) |
Existence results for contact problems with friction
Contact problems in elasticity belong to the classical topics of applied
mathematics, but there are still many questions unsolved, in particular if
friction is taken into account. The main difficulty is the combination of
the unilateral contact condition with the Coulomb friction law that leads to a
non-monotone and non-compact formulation. This requires special approaches to
prove the existence of solutions.
The most successful approach to analyze contact problems with Coulomb
friction was established by Jindrich Necas together with Jiri Jarusek and
Jaroslav Haslinger in a seminal paper "On the solution of the variational
inequality to the Signorini problem with small friction." (Boll. Un. Mat.
Ital. B 5(17), pp. 943-958). It consists in the approximation of the problem
by some convex problem, the proof of some addition regularity of the solution
by a certain translation technique and the application of a fixed point
argument. This approach was first applied to static contact problems with
Coulomb friction. It was later extended to many other types of frictional
contact problems, as e.g. quasistatic contact problems and dynamic problems
for viscoelastic and viscoplastic materials. Some results also include the
transport of heat generated by friction. In the lecture we present this
approach and give a survey on the available existence results for static,
quasistatic and dynamic frictional contact problems. |
| 16:50 |
Prof. RNDr. Igor Bock, PhD
(Slovak University of Technology Bratislava, Slovakia). |
Dynamic Contact Problems for von Karman Plates
We deal with systems consisting of a nonlinear hyperbolic
variational inequality for a deflection and a nonlinear elliptic
equation for the Airy stress function. The systems describe
moderately large deflections of thin elastic and viscoelastic
plates with an inner obstacle and in a dynamic action. The dynamic
contact problems are not frequently solved in the framework of
variational inequalities. Mainly for the elastic problems there is
only limited amount of results available. The aim of the
presentation is to extend these results to von K\'arm\'an plates. We
neglect the rotational inertia member in the elastic case. We will
consider the short memory and the
long memory material in the case of a viscoelastic plate. The fist
one is expressed by a pseudo-hyperbolic unilateral problem. The long
memory material will be considered as an integro-differential
variational inequality with a singular kernel.
|
| 17:15 | Wine and Cheese |