A mixed problem of plane elasticity for a domain with partially unknown boundary

Odishelidze²,

Sánchez³

2017

Scientia Iranica

Abstract. This paper addresses the problem of plane elasticity theory for a doubly connected body whose external boundary is a rhombus with its diagonals lying at the coordinate axes OX and OY . The internal boundary is the required full-strength hole and the symmetric axes are the rhombus diagonals. Smooth stamps with rectilinear bases are applied to the linear parts of the boundary and the middle points of these stamps are under the action of concentrated forces; thus, there are no friction forces between the stamps and the elastic body. The hole boundary is free from external load and the tangential stresses are zero along the entire boundary of the rhombus. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili's complex potentials (characterizing an elastic equilibrium of the body) and the equation of an unknown part of the boundary are determined under the condition that the tangential normal stress arising at it takes a constant value. Such holes are called full-strength holes. Numerical analyses are performed and the corresponding graphs are constructed.

Section: Introductionmentioning

confidence: 99%

On the solution of a contact problem for a rhombus weakened with a full-strength hole

Odishelidze²,

Sánchez³

2017

Scientia Iranica

“…Boundary‐value problems for a finite doubly connected domain with a part of its boundary being unknown full‐strength and the other part being a polygonal line are solved in . The axis‐symmetric and cycle‐symmetric problems of the plane theory of elasticity and plate bending with partially unknown boundaries are studied in .…”

Section: Introductionmentioning

confidence: 99%

“…Although the type of problem of this article is the same as that of , , and , boundary conditions are different and are worth to be examined separately: in , the outer and inner boundaries of the doubly connected domain are regular polygons and neighborhoods of the vertices of the inner polygon are full‐strength arcs. Absolutely smooth rigid punches with rectilinear bases are pressed by a force into all the rectilinear sections of the inner boundary, whereas the unknown arcs are free from external forces.…”

Section: Introductionmentioning

confidence: 99%

Solution of a problem of plane theory of elasticity for a square domain with a partially unknown boundary

Odishelidze

Sánchez

2016

Z. Angew. Math. Mech.

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.

“…The axis-symmetric and cycle-symmetric problems of the plane theory of elasticity and plate bending with partially unknown boundaries are studied in [9–19].…”

Section: Introductionmentioning

confidence: 99%

Stress concentration in an elastic square plate with a full-strength hole

Odishelidze

Mathematics and Mechanics of Solids

Criado³

et al. 2014

This paper addresses the problem of plate bending for a square weakened with a full-strength hole including the origin of coordinates. The vertices of the square lie on the coordinate axes and its neighbourhoods are cut by the same smooth full-strength arcs which are symmetric with respect to the coordinate axes. Rigid bars are attached to each component of the broken line of the outer boundary of the plate. The plate bends under the action of concentrated moments applied to the middle points of the bars. The 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 moment takes a constant value. Numerical analysis is performed and the corresponding graphs are constructed.