Recursive approach for random response analysis using non-orthogonal polynomial expansion |
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Authors: | Bin Huang Qiu Sheng Li Alex Y Tuan Hongping Zhu |
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Affiliation: | (1) School of Civil Engineering and Architecture, Wuhan University of Technology, 430070 Wuhan, China;(2) Department of Building and Construction, City University of Hong Kong, Jiulong, Hong Kong;(3) Department of Civil Engineering, Tam Kang University, Tam Kang, Taiwan;(4) School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, 430074 Wuhan, China |
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Abstract: | Using non-orthogonal polynomial expansions, a recursive approach is proposed for the random response analysis of structures
under static loads involving random properties of materials, external loads, and structural geometries. In the present formulation,
non-orthogonal polynomial expansions are utilized to express the unknown responses of random structural systems. Combining
the high-order perturbation techniques and finite element method, a series of deterministic recursive equations is set up.
The solutions of the recursive equations can be explicitly expressed through the adoption of special mathematical operators.
Furthermore, the Galerkin method is utilized to modify the obtained coefficients for enhancing the convergence rate of computational
outputs. In the post-processing of results, the first- and second-order statistical moments can be quickly obtained using
the relationship matrix between the orthogonal and the non-orthogonal polynomials. Two linear static problems and a geometrical
nonlinear problem are investigated as numerical examples in order to illustrate the performance of the proposed method. Computational
results show that the proposed method speeds up the convergence rate and has the same accuracy as the spectral finite element
method at a much lower computational cost, also, a comparison with the stochastic reduced basis method shows that the new
method is effective for dealing with complex random problems. |
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Keywords: | Random structural systems Non-orthogonal polynomial expansions Stochastic finite element method Galerkin method |
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