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Master Thesis Year : 2021

Numerical optimization for rolling frictional contact problems

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Abstract

The scope of this report is to study the optimal solution of a model for the problem of unilateral contact between solid bodies with rolling friction, by means of an interior-point algorithm. The model is based on the second-order cone programming (also SOCP) but with a conical constraint given by the rolling friction cone that is not a standard cone in convex optimization as the Lorentz cone, for instance. The difficulties are that the KKT system related to this model is not square (the number of variables and equations are not equal) and the rolling friction cone is not symmet- ric. That means it is necessary to find out the way that transforms the KKT system into a square version, and as well as symmetrizes the conical constraint in order to be able to apply the solving techniques for the standard SOCP. Some prerequisites will be firstly known in annex, then one of the best possibility is proposed to solve the model in this report, along with difficulties and their solutions. In the last section, more than 200 experiments are introduced to apply this proposed approach and then present the results and observations of exceptional phenomena.
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Dates and versions

hal-03483150 , version 1 (16-12-2021)

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  • HAL Id : hal-03483150 , version 1

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Minh Hoang Nguyen. Numerical optimization for rolling frictional contact problems. Mathematics [math]. 2021. ⟨hal-03483150⟩
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