非径向对称带状载荷作用下有限长圆柱体的应力和位移解

Solutions for stress and displacement within finite long cylinder under non-radial symmetry strip loading

从微元体弹性力学基本方程组出发,求解有限长圆柱体在非径向对称面载荷、切向载荷和扭转载荷共同作用下任意点的应力和位移。采用分离变量法、有限Hankel变换和Fourier-Bessel级数,求得两个位移函数;将由位移函数表示的应力和位移通解代入边界条件中,求出应力和位移表达式中的未知常数。将应力和位移解析式应用于四辊轧机工作辊,得到其应力和位移沿轴向的分布情况,并对应力和位移曲线进行了分析。

Based on the essential equations of elastic mechanics for infinitesimal element, the stress and displacement at arbitrary point of finite long cylinder under non-radial symmetry area load, tangential load and torsion load were solved. Two displacement functions were obtained with the separation of variables, finite Hankel transform and Fourier Bessel series. Unknown constants in expressions of stress and displacement were solved by substituting general solutions of stress and displacement into boundary conditions of cylinder. Axial distributions of stress and displacement for work rolls were analyzed by using the analytical equations of stress and displacement.