TY - JOUR

T1 - On numerical solving a rigid inclusions problem in 2D elasticity

AU - Rudoy, Evgeny

PY - 2017/2/1

Y1 - 2017/2/1

N2 - A 2D elastic problem for a body containing a set of bulk and thin rigid inclusions of arbitrary shapes is considered. It is assumed that rigid inclusions are bonded into elastic matrix. To state the equilibrium problem, a variational approach is used. The problem is formulated as a problem of minimization of the energy functional over the set of admissible displacements. Moreover, it is equivalent to a variational equality which holds for test functions belonging to the subspace of functions with the prescribed rigid displacement structure on the inclusions. We propose a novel algorithm of solving the equilibrium problem. The algorithm is based on reducing the original problem to a system of the Dirichlet and Neumann problems. A numerical examination is carried out to demonstrate the efficiency of the proposed technique.

AB - A 2D elastic problem for a body containing a set of bulk and thin rigid inclusions of arbitrary shapes is considered. It is assumed that rigid inclusions are bonded into elastic matrix. To state the equilibrium problem, a variational approach is used. The problem is formulated as a problem of minimization of the energy functional over the set of admissible displacements. Moreover, it is equivalent to a variational equality which holds for test functions belonging to the subspace of functions with the prescribed rigid displacement structure on the inclusions. We propose a novel algorithm of solving the equilibrium problem. The algorithm is based on reducing the original problem to a system of the Dirichlet and Neumann problems. A numerical examination is carried out to demonstrate the efficiency of the proposed technique.

KW - Bulk rigid inclusion

KW - FEM

KW - Numerical algorithm

KW - Thin rigid inclusion

KW - Variational approach

KW - STRESS-CONCENTRATION

KW - CAVITIES

KW - FIELD

KW - CRACK

KW - LINE INCLUSION

UR - http://www.scopus.com/inward/record.url?scp=85008616084&partnerID=8YFLogxK

U2 - 10.1007/s00033-016-0764-6

DO - 10.1007/s00033-016-0764-6

M3 - Article

AN - SCOPUS:85008616084

VL - 68

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 1

M1 - 19

ER -