An Adaptive Model Order Reduction Method Based on the Damage Evolution for Nonlinear Seismic Analysis

Abstract

Nonlinear seismic analysis, an approach to evaluate the seismic performance of a structure, is facing the challenge of computational efficiency for large-scale and high-fidelity simulation. This paper proposes an adaptive model order reduction (MOR) method based on the damage evolution among the overall structure to alleviate the computational burden. The damage state of each component during seismic loadings is distinguished as the initial-elastic phase, the plastic-damage phase, and the residual-elastic phase. In order to exploit the potential of model order reduction based on the damage evolution, a duration spectrum analysis is utilized to evaluate the characteristics of the residual-elastic phase for SDOF systems with bilinear hysteretic behaviour. Thus, an adaptive MOR method has been proposed to handle the nonlinear dynamic analysis of structures during different damage evolution phases. The overall structure is adaptively partitioned into linear substructures and nonlinear substructures on the basis of the time-varying damage distribution. The model order of linear substructures is reduced using the initial stiffness-based vibration modes, while nonlinear substructures that keep in the residual-elastic phase are reduced using the tangent-stiffness-based vibration modes. The residual displacements of nonlinear substructures are treated as the initial deformation during the residual-elastic phase. Compared with the traditional time step integration method, the proposed adaptive MOR method is able to increase the computational efficiency as yielding comparative results.