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Symmetrized semi-smooth Newton method for solving 3D contact problems

Kucera R., Haslinger J., Motycková K., Markopoulos A.

Systemy Wspomagania w Inżynierii Produkcji

2017

Vol. 6, iss. 4

286--293

The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).

V práci je analyzována nehladká Newtonova metoda pro rešení diskretizovaných kontaktních úloh s Trescovým trením ve trech prostorových dimenzích. Slanting funkce je aproximována za úcelem získání symetrických vnitrních lineárních úloh. Pro použití metody sdružených gradientu je primárne-duální algoritmus preveden na duální. R-lineární rychlost konvergence je dokázána pro nepresnou globálne konvergentní variantu metody. Záverem jsou uvedeny numerické experimenty. Kontaktní úlohy mají radu významných aplikací, napr. biologické procesy, design stroju a prepravních systému, tvárení kovu nebo medicína (modelování kostních náhrad).

Improvement of design technique of track machines bodies bearing structures

Tovt B.

Transport Problems

2012

T. 7, z. 3

95-107

The paper is devoted to improvement of design technique of track machines bodies bearing structures. The review and analysis of state-of-the-art of the mathematical programming theory and the optimal designing are done. The numerical optimization procedure for track machines bodies bearing structures is proposed. The approbation of the proposed procedure is taken on structural optimization problems. Mathematical aspects of proposed procedure implementation are investigated, particularly the algorithm convergence and the sensitivity analysis of initial designs. Deflected mode of the ballast leveling machine SPZ-5/UA body bearing structure was investigated analytically (FEM study) and experimentally (trial running inspection on durability). The necessity of optimization implementation for bodies bearing structures is substantiated. The rational design of track machine SPZ-5/UA bearing structure was obtained with the numerical optimization procedure proposed in the paper. The deflected mode of the body rational bearing structure was investigated.