Abstract

Based on the Tresca yield criterion, an analytical method is proposed to determine the elastoplastic interface around a circular hole in an infinite plate subjected to biaxial tension-compression loads at infinity. Comparing with the plastic region formed under the action of biaxial tension-tension or biaxial compression- compression loads, the characteristic of the plastic regions is that they cannot completely surround the hole and there may be two or four nonintersecting plastic regions around the hole. In both cases, the conformal mapping is employed to map the elastic region in the physical plane onto the outer region of a unit circle in the image plane, which transforms this kind of plane elastoplastic problem into a problem of mapping. According to the stress continuity conditions on the elastoplastic interface and the stress boundary conditions on the elastic part of the circular hole, a set of nonlinear equations containing the mapping function coefficients is established. The problem can be further transformed into an optimization problem determined by the differential-evolution algorithm. The correctness of the presented method is verified by numerical method. The influence of loads and material constant on the size and shape of the plastic regions is discussed in detail.

摘要

基于Tresca屈服准则，提出了一种在无限远处承受双轴拉压载荷的无限板圆孔周围弹塑性界面的解析方法。与在双轴拉-拉或双轴压-压载荷作用下形成的塑性区相比，塑性区的特点是不能完全包围孔，孔周围可能有两个或四个不相交的塑性区。在这两种情况下，共形映射都用于将物理平面中的弹性区域映射到图像平面中单位圆的外部区域，从而将这种平面弹塑性问题转化为映射问题。根据弹塑性界面上的应力连续条件和圆孔弹性部分的应力边界条件，建立了一组包含映射函数系数的非线性方程组。该问题可以进一步转化为由微分进化算法确定的优化问题。通过数值方法验证了所提方法的正确性。详细讨论了载荷和材料常数对塑性区域大小和形状的影响。通过数值方法验证了所提方法的正确性。详细讨论了载荷和材料常数对塑性区域大小和形状的影响。通过数值方法验证了所提方法的正确性。详细讨论了载荷和材料常数对塑性区域大小和形状的影响。