线性分布压力作用下开口厚壁圆筒空间轴对称问题的解析解

构造了一个新应力函数,使其满足双调和函数和对应的边界条件。应用所构造的应力函数推导出厚壁圆筒内外壁在线性分布压力作用下的解析解。通过对解析解分析,当厚壁圆筒长l→∞时可得到著名的Lam e公式。所得结果不仅能够适用于厚壁圆筒受均匀压力的情况,也适用于线性分布压力的情况。

Analytical Solution for Spatially Axisymmetric Problem of an Open-Ended Thick-Walled Cylinder Subjected to Different Linearly Varying Pressures

Aim.To our best knowledge,in the open literature,there is no stress-function solution of thick-walled cylinder subjected to different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis.We now present such a solution.After repeated trials,we finally succeeded in finding the necessary Airy stress function,which is given by eq.(5) in the full paper;the coefficients A_1 through A_8 in eq.(5) are found with the correspondence boundary conditions and are given in eq.(9) in the full paper.Finally we give a numerical example to compare our exact method with the approximate method of Ref.7.The dimensions of the thick walled cylinder in our example are: inner diameter 2r_1,thickness r_1,length 10r_1.Pressure on inner surface is zero and pressure on outer surface is hydrostatic,varying from zero at the top(z=10r_1) and to a maximum at the bottom(z=0).We computed the circumferential stresses at a cross-section 3r_1 from the bottom.The non-dimensional circumferential stresses at the inner surface are respectively-1.866 7(exact) and-1.732 0(approximate);those at the outer surface are-1.166 7(exact) and-1.348 7(approximate).Our exact method gives not only more accurate results but also it is simpler and faster.