拉压超静定问题中变形协调方程的讨论

Discussion on the Deformation Coordination Equation in the Hyperstatically Indeterminate Problem

在材料力学中利用小变形放大法得到变形协调方程是求解杆件拉压静不定问题的重难点。在教学实践中发现,学生往往对杆件拉压受力的定性判断不够准确,导致对杆件力的方向假定不一致以及假设变形长度不同,所得到的变形协调方程也是不同的。现就教科书上针对杆件拉压问题所讲授的变形协调方程的几种形式进行了探讨,在此基础上提出了利用投影法形成变形协调方程简单易于理解,特别是在不易进行拉压定性判断的复杂杆系中更显优势。

In the mechanics of materials, the small deformation magnification method is used to obtain the deformation compatibility equation. In the teaching practice, it is found that the qualitative judgment of the tension and compression of the rod is not accurate, which leads to the difference of the assumption that the direction of the rod is not consistent and the length of the deformation is different. In this paper, several forms of the deformation coordination equation are discussed in the textbook for the tension and pressure problem of the rod. On this basis, it is proposed that the formation of the deformation coordination equation by using the projection method is simple and easy to understand, especially in the complex bar system which is not easy to conduct the qualitative judgment of the tension and pressure.