弹性介质边坡模糊有限元方法研究

Study on theory of fuzzy finite element method of elastic media slope

针对弹性介质体边坡内存在的模糊特性,从弹性力学的基本方程式入手,应用模糊运算法则、模糊积分和模糊微分等方法,推导了弹性力学几何方程、物理方程和平衡方程的模糊表达形式。利用最小模糊位能原理,建立了考虑多参数模糊性的模糊有限元控制方程。数值算例表明,弹性介质体边坡考虑模糊特性影响的情况下的分析成果,能更全面地反映出计算参数模糊特性变化引起的边坡内力和位移的改变情况。

Fuzzy character widely exists in elastic media slope. A fuzzy finite element method is proposed to describe the variation of the displacement and stress of slope due to the fuzzy feature of the mechanical parameters. Based on the construction of basic equations for elastic media, fuzzy operations and fuzzy integral and fuzzy differential are employed to deduce fuzzy expression form of geometrical equations and physical equations and equilibrium equations. Governing equations of fuzzy finite element method in which the parameters are considered as fuzzy number are constructed by using minimal fuzzy power principle. Case study illustrates that the numerical results obtained from fuzzy finite element method could objectively describe the effect of fuzzy character of mechanical parameters on calculated stress and displacement.