A STOCHASTIC-SPECTRAL FINITE ELEMENT METHOD FOR ANALYSIS OF ELASTO-DYNAMIC PROBLEMS

A stochastic-spectral finite element method is presented and applied to elastodynamic problems in this research paper. The presented method is a new hybridized numerical method incorporating stochastic finite element and spectral finite element methods. Although spectral finite element is a well-established method for solving elastodynamic problems such as wave propagation, it cannot consider randomness in its standard form. On the other hand, analysis of stochastic engineering systems is undergoing a revolution considering the advances in computers. Therefore, this research proposes a spectral finite element method reformulated by stochastic finite element method to solve linearly stochastic elastodynamic problems. Diagonal mass matrix, accelerated pre-processing stage (Karhunen–Loève expansion) and reduction of mesh number maintaining suitable accuracy are the main advantageous of the proposed method which apart from new abilities, uses the features of the both methods in order to solve stochastically linear elastodynamic problems with suitable computational efficiency and accuracy. Two numerical examples are prepared to demonstrate advantages of the proposed stochastic spectral finite element method