Spectral Stochastic Isogeometric Analysis

Abstract

The traditional stochastic analysis methods are becoming increasingly unappreciated for modern engineering practices. The inconsistency between intentionally designed CAD model and the traditional stochastic analysis model inevitably obstructs the accuracy, efficiency, and applicability of the traditional stochastic analysis methods. However, these requirements are becoming increasingly significant in contemporary engineering practices. Therefore, it is requisite to develop a new stochastic analysis framework complied with the requirements of modern engineering practices.

This dissertation presents a CAD-CAE integrated spectral stochastic isogeometric analysis (SSIGA) framework. And a series of structural analysis problems with uncertainties are investigated within the proposed framework. Firstly, the SSIGA is developed and investigated for the stochastic linear elasticity problem. Then, the SSIGA is further developed for the stochastic linear elasticity problem of composite plates. Moreover, the SSIGA is extended for the structural free vibration problem, namely, the stochastic eigenvalue problem. After that, the extended support vector regression (X-SVR) method is adopted within SSIGA framework for the stochastic linear stability analysis of plates. The accuracy, efficiency, and applicability of the proposed SSIGA framework for different structural problems are comprehensively investigated and verified through several elaborately selected numerical examples.

The proposed SSIGA framework provides a CAD-CAE integrated stochastic analysis framework for the modern engineering practices. By meticulously adopting the basis functions within CAD system, the SSIGA framework can maintain the exact geometries of the structures and the random fields between the CAD model and the SSIGA stochastic analysis model, even for those complex geometries inspired from real-life engineering practices. Such rigor can thoroughly eliminate the geometric errors that permanently embedded in traditional approaches. The stochastic analysis by SSIGA framework will be assuredly implemented on the intentionally designed model in CAD system. Moreover, basis functions within CAD system are always higher-order continuous over the whole physical domain. Therefore, the novel SSIGA approach can guarantee a globally smooth random field modelling and finally a globally smooth stochastic analysis result. Additionally, by implementing stochastic analysis directly on the CAD model and avoiding the mesh process in traditional stochastic analysis routines, SSIGA framework will promise an efficient stochastic analysis method for real-life engineering practices.