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Structural Engineering and Mechanics
  Volume 34, Number 2, January30 2010, pages 143-157

Stress concentrations around a circular hole in an infinite plate of arbitrary thickness
Longchao Dai, Xinwei Wang and Feng Liu

    This paper presents theoretical solutions for the three-dimensional (3D) stress field in an infinite isotropic elastic plate containing a through-the-thickness circular hole subjected to far-field inplane loads by using Kane and Mindlin\'s assumption. The dangerous position, where the premature fracture or failure of the plate will take place, the expressions of the tangential stress at the surface of the hole and the out-of-plane stress constraint factor are found in a concise, explicit form. Based on the present theoretical solutions, a comprehensive analysis is performed on the deviated degree of the in-plane stresses from the related plane stress solutions, stress concentration and out-of-plane constraint, and the emphasis has been placed on the effects of the plate thickness, Poisson\'s ratio and the far-field in-plane loads on the stress field. The analytical solution shows that the effects of the plate thickness and Poisson\'s ratio on the deviation of the 3D in-plane stress components is obvious and could not be ignored, although their effects on distributions of the in-plane stress components are slight, and that the effect of the farfield in-plane loads is just on the contrary of that of the above two. When only the shear stress is loaded at far field, the stress concentration factor reach its peak value about 8.9% higher than that of the plane stress solutions, and the out-of-plane stress constraint factor can reach 1 at the surface of the hole and is the biggest among all cases considered.
Key Words
    three-dimensional stress field; through-the-thickness circular hole; thickness effect; stress concentration; out-of-plane constraint.
Longchao Dai and Xinwei Wang: Institute of Structure and Strength, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
Feng Liu: College of Aviation Engineering, Civil Aviation Flight University of China, Guanghan, 618307, P.R. China

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