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在研究模糊有限元分析基本理论以及借鉴前人研究成果的基础上,采用模糊变量表达结构参量的不确定性;并基于区间运算和区间有限元理论,提出了用于求解模糊有限元自由振动方程的1阶泰勒级数展开算法。该算法避免了由于2阶泰勒展开所造成的区间扩张问题,在保证精度的前提下大大减小了计算量;随后又基于APDL语言用大型有限元软件ANSYS进行了二次开发,通过参数化语言的方式实现了该算法。最后以某大跨拱桥为例,在对其刚度和质量进行模糊化的条件下,基于ANSYS软件的二次开发功能采用该算法对算例中拱桥的动力特性进行了模糊有限元计算,从而验证了该算法在实际结构动力设计中的可行性和有效性。
Based on the study of the basic theory of fuzzy finite element analysis and the research results of predecessors, fuzzy variables are used to express the uncertainty of the structural parameters. Based on the interval computation and the interval finite element theory, a new method is proposed for solving the finite element free vibration equation The first order Taylor series expansion algorithm. The algorithm avoids the interval expansion caused by the second-order Taylor expansion and greatly reduces the computational complexity under the premise of ensuring the accuracy. Secondly, based on the APDL language, the secondary development is carried out by using ANSYS, a large finite element software. Parametric language The way to achieve the algorithm. Finally, taking a large-span arch bridge as an example, under the conditions of the fuzzy and stiffness of its stiffness and quality, this algorithm is used to calculate the dynamic characteristics of the arch bridge in the example based on the secondary development function of ANSYS software, so as to verify The feasibility and effectiveness of this algorithm in the design of the actual structure dynamics.