基于Woodbury+OpenMP的结构非线性地震反应并行分析方法

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

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。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。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3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6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该方法的准确性和高效性。

Nonlinear seismic response analysis becomes an important technical means to evaluate aseismic performance of engineering structures.With increase in structure size,large-scale stiffness matrix iterative updating induced by nonlinearity becomes a key factor to restrict efficiency of structural analysis.Woodbury formula-based nonlinear seismic response analysis method for structures,i.e.,Woodbury method,is a new type efficient numerical analysis method.Using local nonlinear characteristics of structure under seismic action,this method can not only ensure higher iterative convergence rate and but also effectively avoid real-time change of structural stiffness matrix and the resulting low computational efficiency.However,the current studies are based on serial computing mode and don’t make full use of parallel computing capabilities of computation hardware.Here,OpenMP mode was introduced to accelerate Woodbury method in parallel,a parallel calculation method for efficient nonlinear seismic response analysis of structures was proposed.Firstly,each iteration calculation step was divided into 3 main calculation parts of updating nonlinear correlation coefficient matrix calculation,solving displacement response based on Woodbury formula,and determining element state.Then,a block calculation method of nonlinear correlation coefficient matrix was established,the calculation process of Woodbury formula was decomposed into 6 parallelizable calculation steps,and each element state was determined separately,OpenMP parallel acceleration strategies suitable for these 3 things were established,respectively to realize parallel optimization for the proposed method’s whole process.Finally,the correctness and efficiency of the proposed method were verified with seismic response analysis of a high-rise structure.