模糊变分原理在求解结构屈曲临界载荷中的应用  

APPLICATION OF THE FUZZY VARIATIONAL PRINCIPLE IN SOLVING THE CRITICAL BUCKLING LOAD OF STRUCTURES

作　　者：张旭东[1] 邱志平[1] 李琦[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《工程力学》2015年第8期29-35,共7页Engineering Mechanics

基　　金：高等学校学科创新引智计划项目(B07009);国家自然科学基金项目(11372025;11002013);航空科学基金项目(2012ZA51010)

摘　　要：首先在结构屈曲临界载荷的瑞利商变分中引入模糊参数,得到了结构屈曲临界载荷问题的模糊变分原理。进而基于模糊变分原理推导了模糊里兹法和模糊有限元法。这两种方法都可以直接得到问题的模糊解,避免了传统区间方法要先将模糊参数转化为区间参数求解,之后再由区间解构造模糊解的计算过程。因此,所提方法可以很大程度上减少计算量。最后通过数值算例表明了所提方法的可行性。The fuzzy variational principle （FVP） of solving the critical buckling load of structures is derived by introducing fuzzy parameters into the Rayleigh quotient variation of the critical buckling load. Thereafter, the FVP is used to formulate the fuzzy Ritz method （FRM） and the fuzzy finite element method （FFEM）, both of which are able to obtain fuzzy solutions in solving the critical buckling load. Compared with conventional interval methods, the presented two methods circumvent the processes that fuzzy parameters need to be transformed into interval parameters before constructing fuzzy solutions. The present methods significantly reduce computational cost. Numerical examples are employed to illustrate the applicability of the present methods.

关 键 词：模糊变分原理 模糊里兹法 模糊有限元法 屈曲 临界载荷 

分 类 号：O317[理学—一般力学与力学基础] O159[理学—力学]