Set Finite Element Method And Application Based On Response Surface And Optimization Theory

The traditional stochastic relibility method is an important tool to handling with uncertainties, and is widely used in engineering. Yet stochastic reliability method is strongly depends upon the available information, but in engineering, often only limited information is available, which greatly restricts the applications of stochastic reliability method in engineering. However, the convex model only requires the bounds of uncertainties. This makes the convex model an alternative way to analyze uncertainty when a limited amount of information is available. This text has proposed the method of set finite element based on non-probability convex model theory in term of solving practical problem of the project, and has set up non-stochastic reliability theory on this foundation. The detail contents were as follows.(a) Based on the convex modeling of uncertainties, some arithmetic rules for fuzzy cariables were developed.(b) Concrete to introduce several algorithm of reliability response surface FEM and constrained optimize algorithm, combine this text actual conditions is it respond surface FEM algorithm and optimize algorithms to select for use, and has realized respond surface equation calculation and optimization operation in ANSYS and MATLAB software.(c) A new non-probabilistic reliability theory for structure was founded. A non-probabilistic reliability model based on interval analysis was presented. A procedure for non-probabilistic reliability analysis of structure were put forward. We also compared the presented non- probabilistic reliability method with the traditional stochastic reliability method in the modeling of uncertainties, formulations for computation, and reliability design of structures, etc. Alike with the convex modeling of uncertainties, the presented method requires less for available information than probabilistic method, thereby, which provided a possible choice for the reliability analysis and design of structures when availableinformation is lack or limited.(d) The uncertain parameters of structures are expressed by non-probabilistic convex model. By means of combining convex model with response surface FEM and optimization theory,the set FEM for structure uncertainty analysis is presented. Commonly more used non-probability convex model.(e) Assemble set FEM with non-probabilistic reliability theory combine, propose the reliability measurement method based on set,rFEM. The presented method can solve the reliability problem with uncertain data information less and parameter probability can't be provided.There is an important meaning to analyse about the uncertainty of the large-scale complicated structure.(f) Use set FEM and reliability measurement method proposed to analyse to the actual project some concrete gravity dam draw the fetching value ranges of the stress , safety coefficient , the influence on quantity of responding of the uncertain parameter, the susceptibility analysis of the parameter and dependability index.