Applied Mathematics and Mechanics

, Volume 34, Issue 2, pp 239–248

# Contact problem for regular hexagon weakened with full-strength hole

• N. Odishelidze
• J. M. Sanchez
Article

## Abstract

A problem of the plane elasticity theory is addressed for a doubly connected body with an external boundary of the regular hexagon shape and with a 6-fold symmetric hole at the center. It is assumed that all the six sides of the hexagon are subjected to uniform normal displacements via smooth rigid stamps, while the uniformly distributed normal stress is applied to the internal hole boundary. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili’s complex potentials and the shape of the hole contour are determined from the condition that the circumferential normal stress is constant along the hole contour. Numerical results are given and shown in relevant graphs.

## Key words

plate elasticity theory complex variable theory stress state regular polygon

## Chinese Library Classification

O344.1 O174.5 O312

## 2010 Mathematics Subject Classification

74A10 74S70 74G70

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© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

## Authors and Affiliations

• N. Odishelidze
• 1