Acta Mechanica Solida Sinica

, Volume 30, Issue 3, pp 318–326 | Cite as

Minimizing stress concentrations around an elliptical hole by concentrated forces acting on the uniaxially loaded plate

  • Aizhong Lu
  • Ning Zhang
  • Guisen Zeng


When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy’s integral formula. And then, based on the superposition principle, the analytical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concentrated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the optimized concentrated forces are applied.


Elliptical hole Closed-form solution for stress Cauchy’s integral method Minimum stress concentration Optimization 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.Institute of Hydroelectric and Geotechnical EngineeringNorth China Electric Power UniversityBeijingChina

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