Stochastic spectral cell method for structural dynamics and wave propagations

Abstract

AbstractThe spectral element method when enriched with the concept of fictitious domain constitutes the spectral cell method which is appropriately able to model geometrically complicated problems by simplifying the mesh generation. In this paper, we propose a new computational framework called stochastic spectral cell method (SSCM) as a stochastic development of the spectral cell method for uncertainty quantification applied to structural dynamics and wave propagations. The stochastic form of spectral cell method has not been developed yet. Hence, the SSCM is a novel stochastic method comprising the advantages of spectral cell method for computational mechanics considering the geometrical complexity resulting from computer‐aided design. The SSCM is established by incorporating the polynomial chaos and Karhunen‐Loève expansions for the uncertainty quantification, and the interpolation functions of spectral elements for the spatial discretization. In the SSCM, the numerical solution of the Fredholm integral equation of the second kind required in Karhunen‐Loève expansion is obtained using the spectral cell method. The use of Cartesian mesh, diagonal mass matrix, and higher order interpolation functions of spectral elements for stochastic dynamic analysis lead to desirable computational efficiency and accuracy of the SSCM. The capability, effectiveness, and accuracy of the proposed SSCM are demonstrated with several numerical examples of wave propagation as well as dynamic analysis of structures.