Transient quasi-static Ritz vector (TQSRV) method by Krylov subspaces and eigenvectors for efficient contact dynamic finite element simulation

Abstract

This paper presents a novel model order reduction (MOR) method called the transient quasi-static Ritz vector (TQSRV) method for efficient transient finite element (FE) analysis. Comparing with frequency response analysis, linear transient FE analysis with a fixed time step takes less computation time as an effective dynamic stiffness matrix assembled before time marching procedure is factorized once. Nevertheless as the number of degrees of freedom of a FE model has been dramatically increased for accurate engineering simulation, even the state-of-the-art computer and software often face their limitations. For fast but accurate transient FE analysis, we present a new MOR scheme called the TQSRV method with Krylov bases spanned at multiple angular velocities and several lowest eigenvectors. By calculating transient responses of reduced FE models and comparing it with the responses of full FE models, the effectiveness and accuracy of the TQSRV method are demonstrated.