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

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.