应力集中圆孔附近的形变场

Deformation in rectangular plates with a stress-concentrating circular hole

具小圆孔薄板受均匀拉伸荷载的作用为弹性力学第一类边值问题,此类问题由于给定的是面力边界条件,因而位移解不是唯一的。本文依据几何参数和荷载条件的对称性,采用形变对称性,获得了圆孔附近的形变场的解析解。算例分析和有限元分析表明变形之后的圆孔为一椭圆形,且在远离圆孔处,回归到无圆孔时单向拉伸的位移解。结果显示解析解和有限元解非常一致。

Rectangular plates with a small, circular hole located at its center subjected to the uniform tension/compression are the boundary value problem of the first kind. The displacements are indeter- minate for such kind of problem since boundary conditions of simple surface force are provided. This paper presents analytical solutions of the deformation in such plates by assuming symmetric displace- ments in view of the geometrical and loading conditions. Parametric and finite element analyses show that the circular hole is transformed into an ellipse. At the place far from the hole, the displacements are exactly the same as those without a hole. It shows that the analytical solutions are in good agree- ment with finite element results.