一类非均布荷载作用下厚壁圆筒平面问题的应力解析解

STRESS ANALYTICAL SOLUTION FOR PLANE PROBLEM OF A THICK-WALLED CYLINDER SUBJECTED TO A TYPE OF NON-UNIFORM DISTRIBUTED PRESSURES

采用复变函数法给出了表面受有一类非均布径向压力作用下厚壁圆筒平面问题的应力解析解,发现随着非均布侧压系数的增大,圆筒内某些区域的切向应力和(或)径向应力会由压应力变为拉应力,并且切向拉应力远大于径向拉应力。在不存在拉应力区的前提下,反算出非均布侧压系数的范围,并给出了不同非均布侧压系数所对应的拉应力区。最后用数值方法验证了理论分析的正确性。

The stress analytical solution for plane problem of a thick-walled cylinder subjected to a type of non-uniform distributed pressures is given by the complex variable function method.The results show that tangential stresses and/or radial stresses change into tensile stresses from compressive stresses with the increase of non-uniform lateral pressure coefficient.And the value of tangential tensile stress is much larger than that of radial tensile stress.On the premise of non-existence of tensile stress zones,the range of non-uniform lateral pressure coefficients is back-calculated and the tensile stress zones corresponding to different non-uniform lateral pressure coefficients are given.Theoretical analysis results are verified by numerical method.