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| A collocation-based spectral stochastic finite element analysis——stochastic response surface approach |
| Revised:March 18, 2005 |
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| DOI：10.7511/jslx20072034 |
| KeyWord:stochastic finite elements,stochastic response surface,random fields,Karhunen-Loeve expansion,polynomial chaos expansion |
| HUANG Shu-ping |
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| Abstract: |
| A collocation-based stochastic finite element method(SRSM) has been developed,the formalism of the proposed method is similar to the spectral stochastic finite element method(SSFEM) in the sense that both of them utilize Karhunen-Loeve(K-L) expansion to represent the input,and polynomial chaos expansion to represent the output.However,the calculation of the coefficients in the polynomial chaos expansion is different: Analytical SSFEM uses a probabilistic Galerkin approach while SRSM uses a probabilistic collocation approach.Numerical example shows that compared to the Analytical SSFEM,the advantage of SRSM is that the finite element coee can be treated as a black box,as in the case of a commercial code.The proposed SRSM is also compared to a black box version SSFEM,and found to require less FEM evaluations for the same accuracy.The collocation points in the proposed method need to be selected for minimizing the mean square error,and from high probability regions,thus leading to fewer function evaluations for high accuracy. |
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