关于平面三角桁架结构小变形假设适用范围的讨论

在平面三角桁架结构的教学过程中,对于微小变形情况,使用材料力学中的小变形假设可用切线代替圆弧简化求解过程,在一定程度上满足工程实际的需求。在教学实践中发现,学生对于这种情况下小变形假设的适用范围缺乏具体的认识,对其适用范围理解尚不深入。本文以平面三角桁架结构为例,利用理论推导和有限元分析,通过具体算例定量地给出了典型结构的小变形假设适用的范围,并分析了其失效的原因。推导过程和分析方法具有可推广的一般性,便于帮助学生理解材料力学假设在工程实践中的应用,具有一定的工程应用价值和教学实践意义。

THE APPLICABLE RANGE OF SMALL DEFORMATION HYPOTHESIS FOR PLANAR TRIANGULAR TRUSS STRUCTURE

For the plane triangular truss structure, the assumption of small deformation in materials mechanics can be used to simplify the solution process by replacing arcs with tangents, to meet the actual needs of the project to a certain extent. The knowledge for the application scope of this small deformation hypothesis is important for students. In this paper, taking the plane triangular truss structure as an example, the theoretical derivation and the finite element analysis are used to quantitatively analyze the applicable range of the small deformation hypothesis of the typical structure through a specific calculation example. The derivation process and the analysis are generalizable, which can help students understand the application of materials mechanics assumptions in engineering practice.