摘要
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 model of structure analysis closer to the real structure and raise the design reliability,this paper, based on the concept of 'degree of membership' in fuzzy set theory, proposes the concept 'fuzzy displacement' between 'the rigid displacement' and 'the elastical displacement'. 'The degree of membership not only reflects the degree that node belongs to the rigid one, but also enriches the simple 0-1 relation of nodal qualification number of displacement by using the real number. In example of angle displacement the paper studies a-way using spring to achive 'the fuzzy angle displacement',derives the element stiffness matrix and the equivalent force vector of beam's end on the basis of the principle of least total potential energy, suggests the mapping relation between the degree of membership and spring stiffness, and accomplishes the program of plane framwork.The numerical experiments illustrate that the concepts and method can make better use of finite element program to establish the mathematical model of structure analysis which approaches the complex engineering structure better. It is an effective way that uses 'fuzzy' method to reach the precision goal.
