## Abstract

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.

Original language | English |
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Article number | 19 |

Number of pages | 18 |

Journal | Zeitschrift fur Angewandte Mathematik und Physik |

Volume | 68 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Feb 2017 |

## Keywords

- Bulk rigid inclusion
- FEM
- Numerical algorithm
- Thin rigid inclusion
- Variational approach
- STRESS-CONCENTRATION
- CAVITIES
- FIELD
- CRACK
- LINE INCLUSION