高层结构地震弹塑性全过程分析的数值子结构并行计算方法

A parallel method of numerical substructure for seismic elastoplastic analysis of high-rise building structures

为充分利用建筑结构在地震作用下的局部非线性特征,采用数值子结构方法将原本复杂的非线性结构分析转化为主结构等效线弹性分析和屈服构件隔离子结构非线性分析,可有效兼顾计算效率和模拟精度。然而,该方法中主结构串行计算,其应用于超大规模结构的非线性分析中仍有一定局限性。为此,将数值子结构方法与传统的区域分解法相结合,提出了数值子结构并行计算方法。将整体结构划分为若干弹性子域,各子域同时进行等效线弹性分析,子域内屈服构件由隔离子结构进行非线性分析。在子域回代求解时,设计了降阶的牛顿迭代算法,以子域内屈服构件单元的位移场作为基本未知量,可进一步降低子域迭代分析的矩阵运算规模。以一15层3跨平面钢框架结构的地震弹塑性全过程分析为例进行数值模拟,结果表明,所提出的方法准确、可靠,当应用于具有局部材料非线性的大规模结构分析时,该方法可以大幅降低矩阵运算规模,显著提高计算效率,将大问题简化为若干小的子问题,可实现更大、更复杂结构的非线性分析。

Taking full advantage of the nonlinear localization for building structures under earthquakes, the numerical substructure method changed the original complex structural nonlinear analysis to the equivalent linear elastic analysis of a master structure, as well as nonlinear analyses of yield members in substructures separated from the master structure. However, there are some limitations in applications of nonlinear analysis of the super large-scale structure, due to the serial computation of the master structure. This paper presents a parallel numerical substructure method by the combination of the numerical substructure method with the traditional domain decomposition method. In the presented method, the whole structure can be divided into several elastic subdomains, of which the equivalent elastic analyses can be carried out in parallel. Nonlinear behaviors of yield members in each subdomain are computed in isolated substructures. In back substitution solutions of each subdomain, a reduced-order Newton-Raphson iterative scheme is proposed where nodal displacements associated with yielding member elements are regarded as basic unknown quantities, and consequently the size of matrix operation can be further reduced. A 15-story 3-bay plane steel frame structure under seismic loadings is analyzed, and simulation’s results show that the presented method is accurate and reliable. When applied to large-scale structures with local material nonlinearities, the dimensionality of matrix operations can be greatly reduced and the efficiency will be significantly improved. In addition, the large problem can be simplified into several small sub-problems, and therefore nonlinear analysis of much larger and more complex structures can be achieved.