The work deals with an iteration method for numerical solving the equilibrium problem of two-dimensional elastic body with a crack under the nonpenetration condition. The method is based on the domain decomposition and Uzawa’s algorithm. To construct an algorithm, the domain is partitioned into two subdomains whose common boundary contains the crack. In each subdomain the linear problems are solved. We use Lagrangian multipliers to couple the solutions and provide the nonpenetration condition on the crack.

DOI: 10.1051/m2an/2015064

Keywords: Crack, nonpenetration condition, domain decomposition method, Lagrange multipliers, Uzawa’s algorithm

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@article{M2AN_2016__50_4_995_0, author = {Rudoy, Evgeny}, title = {Domain decomposition method for crack problems with nonpenetration condition}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {995--1009}, publisher = {EDP-Sciences}, volume = {50}, number = {4}, year = {2016}, doi = {10.1051/m2an/2015064}, zbl = {1457.65242}, mrnumber = {3521709}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015064/} }

TY - JOUR AU - Rudoy, Evgeny TI - Domain decomposition method for crack problems with nonpenetration condition JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 995 EP - 1009 VL - 50 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015064/ DO - 10.1051/m2an/2015064 LA - en ID - M2AN_2016__50_4_995_0 ER -

%0 Journal Article %A Rudoy, Evgeny %T Domain decomposition method for crack problems with nonpenetration condition %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 995-1009 %V 50 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015064/ %R 10.1051/m2an/2015064 %G en %F M2AN_2016__50_4_995_0

Rudoy, Evgeny. Domain decomposition method for crack problems with nonpenetration condition. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 4, pp. 995-1009. doi : 10.1051/m2an/2015064. http://www.numdam.org/articles/10.1051/m2an/2015064/

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