广义导数在材料力学中的应用

APPLICATION OF GENERALIZED DERIVATIVES TO MECHANICS OF MATERIALS

介绍了利用广义导数导出材料力学中拉（压）变形、扭转变形及弯曲变形时的广义平衡微分方程。着重讨论了弯曲变形时的平衡微分方程。从而推广了杆件基本变形时的平衡微分方程．该方程更深刻、更精确、更全面地反映了杆件基本变形这些物理现象。作者把其称为杆件基本变形时的广义平衡微分方程。计入问题的边界条件，求解这些广义的平衡微分方程，能得到这几种基本变形统一的内力、变形表达式，将给力学中的其它计算带来很大的方便。

This paper presents generaled equilibrium differential equations of the defonnation for elongation (compression), torsion and bending in mechanics of materials by use of generaed derivative. The discussion emphasis the equilibrium differential equatinns of bending deformation, then, the equilibrium differential equations for the basic defonnation of a shaft are extended. These equations more deeply,more precisely and more comprehensively represent the physical phenomena of the basic deformation of a shaft. We call these equations of the basic deformation for a shaft. The boundary conditions of these questions are considered, the generalized equilibrium differcntial equations are solved, the unified internal force and the deformation expression of several kinds of basic deformation can be obtained. Except the calculations rneationed above, other calculations of mechanics will be more convenient.