Some axially symmetric problems of the theory of plane elasticity with partially unknown boundaries

Odishelidze, Nana; Criado-Aldeanueva, Francisco

doi:10.1007/s00707-007-0554-5

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…To assess the stability and strengthening of the structure, it is crucial to compute the stresses on the edges of the holes precisely. Odishelidze and Criado-Aldeanueva [1] studied axially symmetric problems of the plane theory of elasticity with partially unknown limits, where these problems were studied for a rhombus weakened by one or two holes. Manickam et al [2] attempted to study the nonlinear thermo-elastic buckling characteristics of composite variable stiffness beams with layers using curvilinear fibers under a thermal environment.…”

Section: Introductionmentioning

confidence: 99%

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

Alharbi,

Alhendi

2024

Symmetry

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In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

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Section: Introductionmentioning

confidence: 99%

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

Alharbi,

Alhendi

2024

Symmetry

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“…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%

“…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. In , the outer and inner boundaries of the doubly connected domain are a rhombus boundary and the required full‐strength hole, respectively. A uniformly distributed normal stress is applied to the hole boundary.…”

Section: Introductionmentioning

confidence: 99%

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

Odishelidze

Criado-Aldeanueva

Sánchez

2016

Z. Angew. Math. Mech.

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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.

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“…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

Criado-Aldeanueva

Criado³

et al. 2014

Mathematics and Mechanics of Solids

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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.

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Some axially symmetric problems of the theory of plane elasticity with partially unknown boundaries

Cited by 9 publications

References 4 publications

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

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

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

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