非均布载荷作用下厚壁筒平面问题的应力解析解

Analytic stress solution for plane problem of a thick-walled cylinder under a non-uniform loading

采用复变函数法,求出表面受一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、内外应力比例系数的增大,圆筒内某些区域的周向应力和径向应力由压应力变为拉应力,且拉应力区域范围随之改变;对圆筒内部存在应力极值的问题进行分析,得到应力极值出现位置、应力极值随载荷非均匀系数、内外应力之比的变化规律及应力极值区域的变化规律;采用数值方法验证了理论分析的正确性。

The analytic solution of stress for plane problem of a thick-walled cylinder under a non-uniform radial pressure is ob-tained based on complex function method .The results show that ,with the increase of non-uniform lateral pressure coefficient and stress ratio coefficient ,circumferential stresses and radial stresses change into tensile stresses from compressive stresses ,and the scopes of tensile stress zone correspondingly change . On the premise of existence of maximum stresses , the variations of the po-sition and values of maximum stresses are obtained with different non-uniform lateral pressure coefficients and stress ratio coeffi-cient . Therefore , the variation of maximum stress zone is obtained . The theoretical analytical results are verified by the numeri-cal method .