基于Woodbury+OpenMP的结构非线性地震反应并行分析方法

余丁浩,李钢

振动与冲击 ›› 2023, Vol. 42 ›› Issue (3) : 21-29.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (3) : 21-29.
论文

基于Woodbury+OpenMP的结构非线性地震反应并行分析方法

  • 余丁浩,李钢
作者信息 +

Parallel analysis method of structural nonlinear seismic response based on Woodbury+OpenMP

  • YU Dinghao, LI Gang
Author information +
文章历史 +

摘要

非线性地震反应分析已成为评价工程结构抗震性能的重要技术手段,随着结构规模的增大,非线性引发的大规模刚度矩阵迭代更新成为制约结构分析效率的关键因素。基于Woodbury公式的结构非线性地震反应分析法(Woodbury方法)是一类新型高效数值分析方法,此类方法利用结构在地震作用下的局部非线性特征,能够在保证较高迭代收敛速率的同时有效避免结构刚度矩阵实时变化及由此导致的计算效率低下问题。然而,当前相关研究均基于串行计算模式,并未充分利用计算硬件的并行计算能力。本文引入OpenMP模式对Woodbury方法进行并行加速,提出了一种用于结构高效非线性地震反应分析的并行计算方法,该方法首先将每个迭代计算步划分为非线性相关系数矩阵计算更新、基于Woodbury公式的位移响应求解、单元状态确定三个主要计算部分,随后通过建立非线性相关系数矩阵的分块计算方法、将Woodbury公式的计算过程拆解为六个可并行的计算步、对各单元状态进行单独判定,分别建立了适用于三者的OpenMP并行加速策略,实现了算法的全过程并行优化。最后,通过对一个高层结构进行地震反应分析验证了本文方法的准确性和高效性。

Abstract

Nonlinear seismic response analysis has become the most important method for evaluating the seismic performance of engineering structures. With the increase of the size of structure, the change of large-scale stiffness matrix caused by nonlinearity become the main factor that slows down the computational efficiency. The Woodbury formula based structural nonlinear analysis methods can be classified as a kind of novel numerical tool for efficient nonlinear analysis. By utilizing localization characteristic of structural nonlinear deformation to construct a structural governing equation with low-rank perturbation form and adopting the Woodbury formula to efficiently solve this equation, the Woodbury formula based nonlinear analysis methods can avoid the recalculation of the global stiffness on the premise of without losing iterative convergence rate. However, almost all of existing researches in this aspect were implemented based on sequential computing mode and do not take advantage of the parallel computational capacity of computer hardware. In this study, a novel parallel Woodbury formula based structural nonlinear seismic response analysis method (Woodbury method) is presented by introducing the OpenMP parallel computation technology. The present method firstly divides the computational process of Woodbury method per iteration into three main computing parts, which are nonlinearity-related coefficient matrices updating, Woodbury formula implementation and element state determination. Then, by establishing block calculation approach of the nonlinearity-related coefficient matrices, by decomposing the Woodbury formula into six sub-steps that are able to be computed using parallel technology respectively and by determining the nonlinear state of each element independently, the proposed method presents parallel programming strategy for these three parts. Thus, the whole analysis process of Woodbury method can be parallelization. Finally, a high-rise building is selected to perform nonlinear seismic response analysis and the results verify high efficiency of the proposed method.

关键词

地震反应分析 / 结构非线性 / Woodbury公式 / OpenMP并行计算

Key words

Seismic response analysis / Structural nonlinearity / Woodbury formula / OpenMP parallel computation

引用本文

导出引用
余丁浩,李钢. 基于Woodbury+OpenMP的结构非线性地震反应并行分析方法[J]. 振动与冲击, 2023, 42(3): 21-29
YU Dinghao, LI Gang. Parallel analysis method of structural nonlinear seismic response based on Woodbury+OpenMP[J]. Journal of Vibration and Shock, 2023, 42(3): 21-29

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