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

Jian Wang,Ming Fang,Hui Li

doi:10.1155/2020/8865255

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.

Highlights

Taking advantage of the enormous growth of computational capacities, finite element methods have become the most popular simulation techniques for large and complex structures with high fidelity
An adaptive MOR method based on the residual-elastic phase (AMCB-E) is developed, which can make further model order reduction for nonlinear structures in the residual-elastic phase. e nonlinear substructures in the residual-elastic phase are reduced using the tangentstiffness-based vibration modes. e duration spectrum of the residual-elastic phase is proposed to study the characteristics of the residual-elastic phase for nonlinear structures under strong ground motions
It is concluded that the duration of the residual-elastic phase generally occupies more than 60% of the duration of ground motion when the structure vibration period is longer than 0.3 s. is fact facilitates further model order reduction for nonlinear substructures under strong seismic excitations. e performance of the adaptive modified Craig–Bampton (AMCB)-E method is tested using a 12-story reinforced concrete frame structure

Summary

Introduction

Taking advantage of the enormous growth of computational capacities, finite element methods have become the most popular simulation techniques for large and complex structures with high fidelity. On the basis of the definition of the reduced dimensional space, the MOR methods mainly include the proper orthogonal decomposition (POD) [1,2,3], proper generalized decomposition (PGD) [4,5,6], reduced basis (RB) method [7,8,9,10], component mode synthesis (CMS) [11, 12], and machine learning approaches [13, 14] Such projection-based methods have been widely applied in linear systems and abbreviate an enormous computational burden. E GPR method builds a bridge between the projection coefficients and the system parameters and utilizes the reduced basis functions to construct the solution This strategy is only effective when applying to a large-scale structure with a predefined linear-nonlinear interface. During a nonlinear seismic analysis, the AMCB method is able to perform model order reduction onto the time-varying linear substructures for tall buildings in which the damage distribution is a priori unknown.

Damage Evolution and Duration Characteristic

Adaptive MOR Method Based on Damage Evolution

Findings

Conclusions