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Solution of a problem of plane theory of elasticity for a square domain with a partially unknown boundary
Author(s) -
Odishelidze Nana,
CriadoAldeanueva Francisco,
Sanchez Jose Maria
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600072
Subject(s) - mathematics , mathematical analysis , boundary (topology) , boundary value problem , elasticity (physics) , square (algebra) , plane (geometry) , domain (mathematical analysis) , arch , geometry , physics , structural engineering , engineering , thermodynamics
In this article we consider a problem of the plane theory of elasticity for a finite doubly‐connected domain whose external boundary is a square whose vertices vicinities are cut with the equal smooth unknown full‐strength arches and whose internal boundary is the unknown full‐strength hole. Absolutely smooth rigid punches with rectilinear bases, which are under the action of the force that applies to their middle points are attached to each component of the broken line of the outer boundary of the plate. Unknown part of the boundary is free from external forces. Using the methods of complex analysis, the unknown part of the boundary is found under the condition that the tangential normal stress on that takes a constant value. Numerical analysis is performed and the corresponding graphs are constructed.