Spectral stochastic isogeometric analysis of free vibration

Publisher:
Elsevier BV
Publication Type:
Journal Article
Citation:
Computer Methods in Applied Mechanics and Engineering, 2019, 350, pp. 1-27
Issue Date:
2019-06-15
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1-s2.0-S0045782519301379-main.pdfPublished version6.08 MB
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A novel spectral stochastic isogeometric analysis (SSIGA) is proposed for the free vibration analysis of engineering structures involving uncertainties. The proposed SSIGA framework treats the stochastic free vibration problem as a stochastic generalized eigenvalue problem. The stochastic Young's modulus and material density of the structure are modelled as random fields with Gaussian and non-Gaussian distributions. The basis functions, the non-uniform rational B-spline (NURBS) and T-spline, within Computer Aided Design (CAD) system are adopted within the SSIGA, which can eliminate geometric errors between design model and uncertainty analysis model. The arbitrary polynomial chaos (aPC) expansion is implemented to investigate the stochastic responses (i.e. eigenvalues and eigenvectors) of the structure. A Galerkin-based method is freshly proposed to solve the stochastic generalized eigenvalue problems. The statistical moments, probability density function (PDF) and cumulative distribution function (CDF) of the eigenvalues can be effectively obtained. Two numerical examples with irregular geometries are investigated to illustrate the applicability, accuracy and efficiency of the proposed SSIGA for free vibration analysis of engineering structures.
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