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为了使结构分析模型好地逼近实际结构,本文基于模糊数学的隶属度概念,提出了刚体位移与弹性体位移之间的“模糊位移”的概念,以转角位移为例研究了弹簧实现“模糊转角”的方案,推导了相应的单元刚度阵,建议了隶属度与弹簧刚度之间的映射关系。平面框架结构数值实验表明,本文提出的概念和方法有利于更好地使用有限元程序,建立结构分析的数学模型,进一步逼近复杂的工程结构。
In order to make the structural analysis model close to the actual structure, this paper proposes the concept of “fuzzy displacement” between rigid body displacement and elastic body displacement based on the concept of membership degree of fuzzy mathematics. The scheme of the unit has deduced the corresponding unit stiffness matrix and proposed the mapping relationship between the membership degree and the spring stiffness. The numerical experiments of planar frame structure show that the concepts and methods presented in this paper are conducive to better use of finite element programs, establish a mathematical model of structural analysis, and further approach the complex engineering structure.