准对称结构利用对称性求解内力时的应用研究

Study on the Application of Symmetry in Solving Internal Force of Quasi-Symmetric Structures

对称性在结构力学中有着广泛应用,往往能为结构的复杂分析打开便利之门。特别是在求解超静定结构内力时,无论是力法,还是位移法,都是十分复杂的。但对于对称结构或准对称结构,利用对称性,可使结构内力计算大为简化。对称结构利用对称性分析,人们都很习惯;至于准对称结构,则不然。为此,本文对准对称结构利用对称性求解内力时的应用进行了研究,包括提出了准对称结构的定义,对准对称结构的特点进行了分析,并介绍了准对称结构利用对称性求解内力时的应用案例分析。结果表明,准对称结构要利用对称性求解内力是有条件的,利用对称性求解超静定结构时,可取准对称的基本体系。具有对称形式的结构利用对称性能够最大程度简化结构,提高结构内力计算效率。

Symmetry is widely used in structural mechanics, and it often opens the door for complex analysis of structures. Especially , when solving the internal forces of statically indeterminate structures , both force method and displacement method are very complicated. But for symmetric structures or quasi symmetric structures , symmetry can be used to simplify the calculation of internal forces of structures. People are used to symmetrical structure by using symmetry analysis;As for quasi-symmetric structures , they are not. Therefor , in this paper , Study on the application of symmetry in solving internal force of quasi-symmetric structures , including the definition of quasi 一symmetric structure and the analysis of the characteristics of quasi-symmetric structure , the application case analysis of quasi-symmetric structures using symmetry to solve internal force is also introduced. The results show that , It is conditional for quasi-symmetric structures to use symmetry to solve internal forces. In solving statically indeterminate structures by symmetry , the quasi symmetric basic system is desirable. The use of symmetry in structures with symmetric forms can simplify the structure to the greatest extent and improve the efficiency of internal force calculation of structures.