Structural Uncertainty Analysis Based On Interval Finite Element Method

Conventional engineering structures are often analyzed deterministically,and the selected structural calculation parameters are determined quantities.However,under actual engineering conditions,uncertainties exist in the physical properties of materials,loads,and so on.Although such uncertainties may be small,they may have an impact on the function of the structure.Therefore,uncertainty analysis of the structure is required.While the routinely used probabilistic analysis method can solve the uncertainty problem but requires more sample data,the interval analysis method,which only requires knowing the interval range of uncertain parameters,has been increasingly used because of its simple calculation process.This paper is based on interval mathematical methods,by intervalizing the uncertain parameters of the structure and interval expanding the terms of the uncertain parameters contained in the control equation by introducing a dimensionality reduction algorithm,and then obtaining the upper and lower bounds of the response of the objective function,and finally verifying the correctness of the methods in this paper by arithmetic examples,which include the following:1.Based on the dimensionality reduction algorithm,a structural static interval uncertainty analysis method is proposed.The uncertainty variables existing in the static structure are regarded as interval parameters,and the stiffness matrix and load vector are converted into the sum of univariate or bivariate functions by the dimensionality reduction algorithm,and then the expressions for the upper and lower limits of the displacement response interval under uncertain load and structural uncertainty conditions are derived,and the displacement response interval of the structure is finally obtained.2.In response to the problem of interval expansion in the analysis of structural inherent frequency uncertainty based on Deif theory,this paper proposes a method of structural inherent frequency analysis based on the dimensionality reduction interval finite element method,which combines the dimensionality reduction algorithm and interval mathematics to derive the expression formulas for the interval midpoint and interval radius of the stiffness matrix and mass matrix,and then find out the interval midpoint and interval radius of each order of the eigenvalues,and finally obtain the interval of the eigenvalues The upper and lower limits are obtained.The analysis results show that the method in this paper has higher computational accuracy compared with the Deif interval analysis method.3.Based on the interval finite element method,the dynamic response of the structure is studied.Considering the uncertainties of physical properties,dimensional parameters and applied loads in it,the expressions for the upper and lower limits of displacement,velocity and acceleration response intervals with time are derived based on the interval analysis method and the reduced dimensional expansion formula,and the upper and lower intervals are calculated.