Parallel Solution Of Contact Shape Optimization
Problems With Coulomb Friction Based On
Domain Decomposition
Author(s)
P. Beremlijski, T. Brzobohatý, T. Kozubek, A. Markopoulos
& J. V. Outrata
Abstract
We shall first briefly review the FETI based domain decomposition methodology
adapted to the solution of multibody contact problems in 3D with Coulomb
friction. These problems play a role of the state problem in contact shape
optimization problems with Coulomb friction.We use a modification of FETI that
we call Total FETI, which imposes not only the compatibility of a solution across
the subdomain interfaces, but also the prescribed displacements. For solving a state
problem we use the method of successive approximations. Each iterative step of
the method requires us to solve the contact problem with Tresca friction.
The discretized problem with Coulomb friction has a unique solution for small
coefficients of friction. The uniqueness of the equilibria for fixed controls enables
us to apply the so-called implicit programming approach. Its main idea consists in
minimization of a nonsmooth composite function generated by the objective and
the control-state mapping. The implicit programming approach combined with the
differential calculus of Clarke was used for a discretized problem of 2D shape
optimization. There is no possibility to extend the same approach to the 3D case.
The main problem is the nonpolyhedral character of the second-order cone, arising
in the 3D model. To get subgradient information needed in the used numerical
method we use the differential calculus of Mordukhovich. Application of the
Keywords
total FETI, contact problems, Coulomb friction, shape optimization, nonsmooth optimization
Related Book
Other papers in this volume
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