On numerical solving a rigid inclusions problem in 2D elasticity

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10 Citations (Scopus)

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 languageEnglish
Article number19
Number of pages18
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume68
Issue number1
DOIs
Publication statusPublished - 1 Feb 2017

Keywords

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

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