有限长厚壁圆筒康托洛维奇应力变分解端部偏差的修正

THE CORRECTION OF THE STRESSES NEAR THE BOTTOM OF THICK-WALLED CYLINDER OF FINITE LENGTH SOLVED BY THE KANTOROVICH STRESS VARIATION METHOD

本文指出文献[4]、[5]在用康托洛维奇应力变分法解有限长厚壁圆筒轴对称问题时存在的端部应力偏差；提出一个消除该偏差的反向端部效应的问题；通过简单计算推导出满足其全部应力边界条件与平衡微分方程的应力表达式，并用应力变分法求得其解答；数值计算结果表明，该解答较好地修正了文献[4]中端部附近应力的偏差。

In this paper, the bottom stress deviations are highlighted about the axisymmetric solution of the thick-walled cylinder of finite length by the Kantorovich stress variation method. A problem about the inverse bottom effect is proposed to eliminate these deviations. Through a simple manipulation, the stress expressions are presented and the differential equilibrium equations and all stress boundary conditions are satisfied. The solutions for these stresses are obtained by the stress variation method. Numerical results show that the stress deviations near the bottom of the cylinder are corrected satisfactorily well by the present method.