High-performance aggregation element-by-element Ritz-gradient method for structure dynamic response analysis

Abstract

The article presents the high-performance Ritz-gradient method for the finite element (FE) dynamic response analysis. It is based on the generation of the orthogonal system of the basis vectors. The gradient approach with two-level aggregation preconditioning on the base of element-by-element technique is applied to minimize the Rayleigh quotient for the preparation of each basis vector. It ensures the evolution of the regular basis vector toward the lowest eigenmode without aggregating and decomposing the largescale stiffness matrix. Such method often happens to be more effective for dynamic response analysis, when compared to the classical modal superposition method, especially for seismic response analysis of the large-scale sparse eigenproblems. The proposed method allows one to apply arbitrary types of finite elements due to aggregation approach, and ensures fast problem solution without considerable exigencies concerning the disk storage space required, which is due to the use of EBE technique. This solver is implemented in commercial programs RobotV6 and Robot97 (software firm RoboBAT) for the seismic analysis of large-scale sparse problems and it is particularly effective when the consistent mass matrix is used.