Static Interval Analysis of Structural Uncertain Problems
|School||Wuhan University of Technology|
|Keywords||structural uncertain problems interval analysis interval finite element control equation static analysis genetic algorithm global optimization|
The methods to analysis and design in the project structure are generally models of mathematics based on deterministic structure parameters. However, a large number of errors and uncertainties exist in the actual project structure, and the reason that produced these errors or uncertainties is various. Though these errors or uncertainties may be small under most situations, it combined together may bring unexpected large deviation or unpredictability of structure response, especially in structure assembled with many parts.Strictly speaking, the structural parameter and outside-load all have errors or uncertainties to a certain extent, especially the load uncertainty. With the improvement of design and analysis standard of structure, the rational model which take the uncertain parameters as a determined and modeled quantity should be select to make the analysis and design reflect the truth structural station further. As for the model to deal with uncertainty, there are mainly probability model, fuzzy model and interval model. Among these models, the interval model required the fewest quantum of information, only uncertain bound of structural parameters is needed, as is always easy to do in the actual project. So the interval model to deal with uncertain structure has simple practical unique advantage.The interval analysis method used to analysis the structure with uncertain parameters just came forth in recent years, and more study is to determine the structure static displacement response now. Based on interval analysis and displacement finite element method, the static displacement response analysis of structure comes down to solve the interval finite element control equation. The solution of interval finite control equation is often equated to solving the interval linear equation group. In fact, the latter can’t consider the interdependence of the rigidity matrix element, so the width of solution would deviate from the actual width far away. At the same time, researcher always focuses their attention on the stress of structure in practical engineering problems. According to the static analysis steps of finite element method, executed interval operation to the interval displacementsolution, the bound of structural uncertain stress can know. Not considering the interdependence between the matrix elements, the stress solution departed from the truth far away and can’t acquire the request engineering precision. Therefore, it is important to investigate the static interval analysis of structural uncertain problems.In this paper, after introduced the interval analysis theory combined with finite element method to solve the structural uncertain problems, centered on the static interval analysis of structural uncertain problems, some problems are discussed here.1 .Whereas the defect resulted from transferred solving the interval finite element control equation to solving the interval linear equation group, separated the coefficient matrix in the interval finite element control equation by uncertain structural parameters, an improved iterative method and modified method is presented. Whereas the truncation property of interval parameters perturbation method, a calculated stop rule of perturbation is introduced. For solving structural uncertain problems with large uncertain parameters, a method called the interval analyzed and composed method is present.2. Whereas the defect that the stress solution calculated according to displacement finite element method can’t acquire the request engineering precision, based on the finite element analysis theory resulted from a matrix order-force method, the interval finite element analysis method is present to determine the interval stress solution of structural uncertain problems.3.whereas the engineering practice that it is necessary to determine the bound of the structural static response, an optimization method based on genetic algorithm is present for solving the static control equation of structural uncertain problems.