摘要
本文定义了具有不同论域的模糊集与通常函数的乘积、乘积的导数和积分,给出了具有相同模糊特性的模糊载荷的数学表征。导出了细长直梁横向弯曲时模糊外载、模糊内力和模糊挠度之间的基本模糊关系。通过引入不同论域的模糊集的加法,讨论了在不同模糊特性的模糊载菏作用下模糊挠度的计算。最后,对梁的可靠度计算进行了讨论。
In this paper, the multiplication, the derivate and the integration of the multiplication between fuzzy set and general function with unidentical regions are defined: the mathematical expressions of the fuzzy loads with same fuzzy characteristic are given. The basic fuzzy relations among fuzzy external load, fuzzy internal force and fuzzy deflection are derived when thin, long and straight beams are bent in vertical direction. Then, the addition between the fuzzy sets in unidentical regions is introduced, Based on the addition, the calculation of fuzzy deflection is discussed when the fuzzy loads with unidentical fuzzy characteristics act on beams. Finally, the reliability calculstions of the beams are discussed.
关键词
结构力学
梁
强度
刚度
模糊集
fuzzy set, identical fuzzy characteristic, fuzzy load, reliability
