挤压应力对圆柱壳轴对称弯曲变形的影响

The Influence of the Compressive Stress on the Deformation of Axisymmetrically Bended Cylindrical Shell

以柱面为中面的薄壳,称为柱形薄壳,简称为柱壳.因为这种薄壳在纵向(柱面的母线方向)没有曲率,在计算、设计、制造、施工方面都比较简单,所以得到广泛的使用.在壳体理论中,通常采用如下的计算假定:(1)垂直于中面方向的线应变可以不计;(2)中面的法线保持为直线,而且垂直于变形后的中面;(3)与中面平行的截面上的正应力σ_3(即挤压应力),远小于其垂直面上的正应力,因而它对形变的影响可以不计;(4)体力及面力均可化为作用于中面的荷载.本文在放弃计算假定(3)的情况下计算了圆柱壳在轴对称弯曲时的变形和应力,得到的最大应力比传统理论得到的最大应力更大,最大挠度更小,更接近有限元分析的结果.计算结果对高压容器的设计有一定参考价值.

The shell whose middle surface is cylindrical surface is called cylindrical shell. This kind of shell does not have curvature in longitudinal direction（the direction of generatrix of the cylindrical surface）, so it is convenient for computation, design, manufacture and installation. As a result, cylindrical shells are used extensively. The shell theory usually adopt the following computational assumptions：（1） the linear strain perpendicular to the middle surface can be neglected;（2） the normal line of the middle surface keeps straight and perpendicular to the deformed middle surface;（3） the normal stress σ_3 on the surface parallel to the middle surface（namely the compressive stress） is far smaller than the normal stress on the surface perpendicular to the middle surface, so its influence on the deformation can be neglected;（4） the body force and the surface force can be considered as the load executed on the middle surface. In this paper, the deformation and stress of axisymmetrically bended cylindrical shell was computed without the computational assumption（3）. The maximum stress is bigger while the maximum deflection is smaller. Both the stress and deflection are closer to the results of finite element analysis compared with the traditional theory. The results may be useful for the designing of high pressure vessel.