A Continuation Problem for Computing Solutions of Discretised Evolution Problems with Application to Plane Quasi-Static Contact Problems with FrictionReport as inadecuate




A Continuation Problem for Computing Solutions of Discretised Evolution Problems with Application to Plane Quasi-Static Contact Problems with Friction - Download this document for free, or read online. Document in PDF available to download.

* Corresponding author 1 DMAaAM PrF UP - Department of Mathematical Analysis and Applications of Mathematics 2 ICJ - Institut Camille Jordan Villeurbanne

Abstract : A continuation problem for finding successive solutions of discretised abstract first-order evolution problems is proposed and a general piecewise $C^{1}$ continuation problem is studied.
A condition ensuring local existence and uniqueness of its solution curves is given.
An analogy of the first-order system of smooth problems is derived and results of existence and uniqueness of its solutions are stated.
Possibility of continuation of a solution curve along directions solving the first-order system is discussed.
A technique for numerical continuation of the solution curves is developed.
Furthermore, an application of the abstract continuation problem is presented for plane quasi-static contact problems with friction.
Various formulations of the first-order system are derived for this case so that the analysis from the abstract frame can be developed and supplemented.
Finally, the proposed numerical continuation is tested.


Keywords : continuation piecewise-smooth system first-order system predictor-corrector contact problem Coulomb friction





Author: Tomas Ligursky - Yves Renard -

Source: https://hal.archives-ouvertes.fr/



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