弹性介质模糊有限元控制方程的快速解法

线弹性模糊有限元方法是分析弹性介质体模糊特性对结构响应产生不确定性影响的有效方法。即使对弹性介质体而言,模糊有限元控制方程的求解时间问题也是困扰其推广应用的主要障碍。为获得可靠可行的模糊有限元控制方程的快速求解方法,在深入研究弹性介质体的模糊源特点基础上,提出当引起结构模糊特性的力学参数为单源模糊数时,可以利用单源模糊数的运算特点来求解模糊有限元的控制方程,进而利用合成运算求解结构的模糊位移和模糊应力的分布。推导了基于单源模糊数运算的弹性介质模糊应力和模糊位移的计算表达式。应用模糊有限元求解的区间解法和快速解法对算例进行比较分析,结果表明了快速解法的正确性。

FAST SOLUTION OF THE GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD ON ELASTIC MEDIA

Linear elastic fuzzy finite element method is an effective technique used to analyze the uncertain response of structures due to the vague information in the elastic media. The time consuming problem of the solution of fuzzy governing equations is one of the main obstacles preventing fuzzy finite element method from development and application, even for elastic media. To seek reliable and feasible solving technique, emphasis is put on the study of the source of fuzzy characteristics of elastic media. It is proposed that fuzzy governing equations could be solved using operational principle of mono-source fuzzy number, when mechanical parameters are mono-source fuzzy numbers. Fuzzy stresses and fuzzy displacements could be obtained using synthesizing operation. Based on operational principle of mono-source fuzzy number, formulas of fuzzy stresses and fuzzy displacements of elastic media are deduced. Computed results of interval solution of fuzzy finite element method are compared with that of fast solution. The validity of fast solution is illustrated from the results.