正交各向异性板带有一般孔形时应力分析

Stress Analysis for an Orthotropic Plate with a General Shaped Hole

摘要:

采用复变函数方法研究面内均布荷载作用下带孔正交各向异性板的应力解析解.对含一个正六角形孔或不规则孔的无限平板进行分析，得到不同工况下（纤维角度、外荷载方向）孔边及部分孔外域的应力分布规律.结果表明，当单向荷载作用方向与孔边尖点指向垂直时，若正交各向异性板的纤维按0°和-90.0°布置，最大切向应力发生在孔边，并且位于尖点位置，但随着纤维角度的旋转，孔边的最大应力点逐渐偏离尖点，并且最大应力值也逐渐降低；因此，正交各向异性板的应力集中可以通过调整材料的纤维方向来改善.除此之外，当单向均布荷载σ的作用方向与坐标轴平行时，该坐标轴与孔边界交点的切向应力均为-σ.

Abstract:

The complex variables function method was used for analyzing the stresses in an infinite orthotropic plate with a hole under uniform inplane loadings at infinity. When the hole was hexagonal or irregular shaped, the stress distributions along/near the hole boundary were obtained for different fiber angles and loading directions. The research shows that the maximum tangential stress occurs on the hole boundary and exactly in the sharp corner point, when the fiber orientation angles are 0° and -90.0° and the uniaxial loadings are perpendicular to the pointing direction of the sharp corner. However, the position of the maximum tangential stress will get farther from the sharp corner point with the rotating of the fiber orientation angles, and the magnitude of the maximum tangential stress decreases correspondingly. Therefore, the stress concentration of the orthotropic plate can be decreased by adjusting the fiber orientation angles. In addition, the tangential stresses at the intersections of the axis of the uniaxial loadings σ and the hole boundary are always exactly the same value -σ for the orthotropic plate.