Domain Decomposition-based Hierarchical Stochastic Finite Element Method

Analyzing a problem with deterministic modeling approach can lead to a wrong result because of the uncertainty in nature,so considering the uncertainty factors such as structure material parameters and load of stochastic finite element method was put forward and used,including spectral stochastic finite element method(SSFEM)is a kind of method has a good convergence,has been increasingly used in recent years,but with the improvement of model accuracy,SSFEM calculation will be swelling,for existing computing devices is a very big challenge.Aiming at the problem of large scale of spectral stochastic finite element calculation,this paper firstly adopts Schur complement process regional decomposition method to solve spectral stochastic finite element equation.This method will structure is divided into several sub areas,according to the spectral stochastic finite element method(fem)way to list the adjacent two order expansion order equation of each area,adjust the degrees of freedom sorting and degrees of polycondensation,respectively,using the condensation equation of the parallel interface of random response component obtained by conjugate gradient method,finally back to the generation of internal degree of freedom to get all the response.The application of square plate stochastic response analysis shows that this method can greatly improve the computational efficiency and the overall computational efficiency shows a trend of first increasing and then decreasing with the increase of the number of subregions.A stratified stochastic finite element method based on regional decomposition is proposed to solve the large-scale interface equations generated by spectral stochastic finite element method.In this method,the structure is first divided into several subregions,the expanded equations of each sub-region of two adjacent orders are listed in accordance with the spectral stochastic finite element method,the degree of freedom is adjusted,and degree-of-freedom polycondensation is carried out respectively.The order of degrees of freedom of the high-order polycondensation equation in each subregion was adjusted,mapped to the total interface equation and split,and the second layered stochastic finite element equation was substituted with the random response low-order component to obtain the right-handed vector of the equation.The order of degrees of freedom of the higher order polycondensation equation was adjusted and split,and the corresponding terms of each subregion of the left end matrix of the second equation were taken from the lower right block,and the newly generated equation was solved by using the parallel conjugate gradient method.The results of the interface stochastic response are sorted out and put into the expanded equation of each subregion to obtain all the structural stochastic response.This method transforms the large scale interface equation generated by the spectral stochastic finite method of the regional decomposition method into the solution of two smaller equations,which can greatly reduce the solving efficiency of the interface equation under the condition of ensuring the accuracy of the final result,and then improve the solving efficiency of the whole model.The method proposed in this paper,spectral stochastic finite element method based on regional decomposition and Monte-Carlo simulation were used to analyze the random response of the plane square plate and bearing support respectively.The results showed that the layered method would not lead to large errors in the calculation results of the structural response.The calculation time of the interface equation can be greatly reduced by using the layered method,thus improving the overall calculation efficiency.