A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain

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• 作者：P. Zakian ; N. Khaji
• 关键词：Karhunen–Loève expansion (KLE) ; Polynomial chaos expansion (PCE) ; Stochastic finite element method ; Spectral finite element method ; Wave propagation ; Stochastic structural dynamics
• 刊名：Meccanica
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：51
• 期：4
• 页码：893-920
• 全文大小：9,809 KB
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• 作者单位：P. Zakian (1)
  N. Khaji (1)
  
  1. Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box 14115–397, Tehran, Iran
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

This article proposes a stochastically-tuned spectral finite element method (SFEM) which is applied to elastodynamic problems. Stochastic finite element method is an efficient numerical method incorporating randomness for uncertainty quantification of engineering systems. On the other hand, SFEM is an excellent remedy for solving dynamic problems with fine accuracy, which employs Lobatto polynomials leading to reduction of domain discretization and making diagonal mass matrices. The presented method simultaneously collects the advantages of the both methods in order to solve stochastically linear elastodynamic problems with suitable computational efficiency and accuracy. Furthermore, spectral finite element is also proposed for numerical solution of Fredholm integral equation associated with Karhunen–Loève expansion followed by the presented hybrid method which enhances the efficiency of the methodology. Various types of numerical examples are prepared so as to demonstrate advantages of the proposed stochastic SFEM.