逐段刚化法在材料力学中的应用

Application of piecewise rigidization method in mechanics of materials

目前材料力学教材中对逐段刚化法讲解不够详细,并且仅应用于求解梁的变形,但逐段刚化法其实质是叠加法的一种,为材料力学的一种基本方法,可应用于多种问题的求解,尤其是较为复杂的材料力学问题。文章在分析逐段刚化法原理的基础上,结合教学体会,对其在超静定拉压杆、阶梯轴、变截面梁和平面刚架问题的应用作了阐述。

At present, the piecewise rigidization method in mechanics of materials is not explained in detail, which is only applies to solve the deformation of beam. In fact, it is a kind of superposition method. As a basic method in mechanics of materials, it can be applied to solve a variety of problems, especially complex mechanics problems. Based on the analysis of principle of the piecewise rigidization method, combining with my own teaching experience, the application is discussed in depth on the statically indeterminate tension and compression bar, stepped shaft, non-uniform beam and plane rigid frame.