Recursive approach for random response analysis using non-orthogonal polynomial expansion

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)309-320
Journal / PublicationComputational Mechanics
Volume44
Issue number3
Publication statusPublished - Aug 2009

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. © 2009 Springer-Verlag.

Research Area(s)

  • Galerkin method, Non-orthogonal polynomial expansions, Random structural systems, Stochastic finite element method

Citation Format(s)

Recursive approach for random response analysis using non-orthogonal polynomial expansion. / Huang, Bin; Li, Qiu Sheng; Tuan, Alex Y. et al.
In: Computational Mechanics, Vol. 44, No. 3, 08.2009, p. 309-320.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review