Spectral Stochastic Finite Element Analysis Of Grid Structure Considering The Randomness From Material And Wind Load

In the analysis of wind-induced structural vibration problems, generally only the randomness of wind load is assumed, while the material parameters (density, elastic modulus) are regarded as deterministic variables, the randomness of material parameters has been ignored. However, the material parameters of real engineering structures are of certain randomness because of the impact of construction procedure, manufacture environment etc. So the material parameters of structures should be assumed as random fields to be dealt with. As a method to deal with problems of structures with stochastic parameters, spectral stochastic finite element method (SSFEM) is of high calculation efficiency compared with traditional Monte Carlo finite element method. Grid structures are widely used in various architectural forms, it's of reference value for grid structures' wind-resistant design to analyze the stochastic response and reliability of grid structures under the effect of wind load considering the randomness of material parameters. In this paper, the SSFEM is used to analyze the wind-induced response of grid structure with stochastic material parameters, the main study work is as follows:1. The random fields of structure's material parameters and the random process of wind load are discretized on the basis of Karhunen-Loeve series expansion method. The Karhunen-Loeve series expansion coefficients of material random fields and wind load random process are obtained by solving the integral equation about covariance functions of random field and process. Meanwhile, the relative errors between covariance functions of approximate random field (process) and the original one are compared to examine the discretization accuracy of Karhunen-Loeve series expansion method.2. The SSFEM equation format of wind-induced structural vibration problems is established. The expressions of stochastic structure mass matrix, damping matrix, stiffness matrix, response vector and load vector are derived by combination of Karhunen-Loeve series expansion method and polynomial chaos expansion method. The expressions above are substituted into the structural dynamics finite element equation, then the expanded order dynamics finite element equation namely the SSFEM equation of wind-induced structural vibration problems is obtained. The statistical parameters of structure's dynamic stochastic response can be obtained by solving the expanded order equation.3. The wind-induced stochastic response analysis of grid structure with stochastic material parameters. Considering different assumptions of material random fields and spatial correlation of wind load, the wind- induced dynamic stochastic response of one plane truss structure is analyzed by the computer programs of SSFEM and Monte Carlo finite element method via coding with software MATLAB. And the results of the two methods are compared. Taking Monte Carlo finite element method as reference, the influence of the parameter changes on calculation accuracy and efficiency of SSFEM is studied. Finally, the wind-resistant reliability of structure is analyzed by SSFEM.