Analysis And Research Of Fuzzy And Stochastic Finite Element Method Dynamic Problems

A great deal of problems are connected with analysis and design of system which is interfered by enviroment's uncertainties.This kind of uncertainties are due to different sources.One kind of disturbation sources happen because of unefficient conditions which lead to the uncertain cause and effect relation which show the uncertainies on the happening or not of the affair.It is the so called stochastic character.The other kind of disturbation sources are the character that it is both this and that which appears in the transition of the thing's difference which is called the fuzzy character.The third disturbation sources are the uncertainty which happens due to the effect of the fuzzy character and stochastic character which is called the fuzzy and stochastic character.The theory of fuzzy system and stochastic system is established on the basis of the theory of certain system which are independent and parallel.The first theory is used to solve the problems of fuzzy system,the latter is used to solve the problem of stochastic system.The fuzzy stochastic system theory is the advanced theory which is established on the ground of fuzzy system and stochastic system theory.It can solve the system problems which contain both fuzzy factor and stochastic factor.Recently,with the rapid development of finite element method,it is used in engineering greatly.At the same time,stochastic finite method and fuzzy finite element method are used in the engeneering to solve many problems.Considering the fuzziness of some boundary conditions enviroment media,and especially some loads in the engineering structure analysis,we go further into the computation based on the dynamic problem of fuzzy finite element(FFE),study further and systematically the analysis and solution.The principle of fuzzy minimum potential energy is established,and the balance equation of fuzzy finite element is reasoned by making fuzzy variation.At the same time,the dynamic balance equation of stochastic by making stochastic variation,also the fuzzy stochastic dynamic balance equation is deduced.Based the theory that the degree of the fuzziness and probability can be measured,in the other word,by using the concept of fuzzy entropy and entropy,pure fuzzy dynamic structure is given through transforming the probability to fuzziness.For the fuzzy parameter can be regarded as a fuzzy vector with dimensions,the structure's eigenvalue ,by the theory of small parameterperturbation technique, eigenvector and displacement are spread near the average value of fuzzy vector via Tailor series to get a group of recursive equations.So the fuzzy eigenvalue fuzzy eigenvector and fuzzy displacement can be solved.Concrete example is given and the dynamic analysis program of fuzzy stochastic finite element is programmed to test and verify the feasibility of the paper's view and method.As a continued research of the stochastic dynamic structure,it has greater referenced value in further discussing and consummating fuzzy stochastic theory.