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<p>The paper addresses the problem of plane elasticity theory for a square weakened with five unknown holes, four of which are identical, equidistant from the center of the square, symmetric with respect to the square diagonals, and intersect them. The fifth hole contains the center <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(z=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> of the square, symmetric with respect to the diagonals, and to the segments connecting the midpoints of the opposite sides of the square. Absolutely smooth rigid punches with rectilinear bases, which are under the action of the force that applies at their middle points are attached to each component of the broken line of the outer boundary of plate. The boundaries of the holes are free from external loads. Taking into account the symmetry, the problem is reduced to the problem of a doubly connected domain. Using the methods of the theory of analytic functions, an effective solution to the problem is constructed.</p>

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Complex analysis solution of a plane elasticity problem for a square weakened with unknown full-strength holes

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  • 发表日期：

    2026年7月20日

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  • Nana Odishelidze,
  • Francisco Criado-Aldeanueva

摘要

The paper addresses the problem of plane elasticity theory for a square weakened with five unknown holes, four of which are identical, equidistant from the center of the square, symmetric with respect to the square diagonals, and intersect them. The fifth hole contains the center \(z=0\) z = 0 of the square, symmetric with respect to the diagonals, and to the segments connecting the midpoints of the opposite sides of the square. Absolutely smooth rigid punches with rectilinear bases, which are under the action of the force that applies at their middle points are attached to each component of the broken line of the outer boundary of plate. The boundaries of the holes are free from external loads. Taking into account the symmetry, the problem is reduced to the problem of a doubly connected domain. Using the methods of the theory of analytic functions, an effective solution to the problem is constructed.