几何组成分析中约束等效变换思想的应用

Application of the Constrained Equivalent Transformation Thought in Geometric Composition Analysis

几何组成分析是结构力学课程的重要内容,也是结构进行内力和变形计算的必要步骤。在求解多样化的平面杆件体系时,学生不仅需要灵活运用解题技巧,更需要在碰到复杂平面体系时,有突破和创新的思维。对于无法直接采用基本组成规则分析的复杂平面体系,除采用“零载法”等需要进行烦琐内力计算的方法外,还可通过等效变换的思想快速简化原体系而进行几何构造的分析。为此,该文基于支座链杆与体系链杆等效、虚铰与实铰等效和支座链杆平移等效等约束的等效变换思想,高效、合理地简化体系,进而利用基本组成规则进行几何组成分析。灵活、综合地运用约束等效变换思想,可为复杂平面体系的几何组成分析提供新的思路,最终提高学生在结构力学课程中对平面体系类型和组成规律的理解能力。

As an important content of the Structural Mechanics course,geometric composition analysis is also a necessary step in the calculation of internal force and deformation of structures.When solving a variety of planar member systems,students not only need to use problem-solving skills flexibly,but also need to have break⁃through and innovative thinking when encountering complex planar systems.For complex planar systems that can⁃not be directly analyzed by the basic composition rules,in addition to the“zero-load method”and other methods that require cumbersome internal force calculations,the original system can be quickly simplified by the idea of equivalent transformation to analyze the geometric structure.For this reason,this paper simplifies the system effi⁃ciently and reasonably based on the equivalent transformation ideas constrained by the equivalent of the support link and the system link,the equivalent of the virtual hinge and the real hinge,and the translation equivalent of the support link,and then uses the basic composition rules for geometric composition analysis.The flexible and comprehensive use of the ideas of constrained equivalent transformation can provide new ideas for the analysis of the geometric composition of complex planar systems,and ultimately improve students’ability to understand the types and composition laws of planar systems in the course of Structural Mechanics.