A Woodbury solution method for efficient seismic collapse analysis of space truss structures based on hybrid nonlinearity separation

• Published in: Earthquake engineering & structural dynamics 2022-01, Vol.51 (1), p.86-107
• Main Authors: Yu, Ding‐Hao, Li, Gang, Li, Hong‐Nan
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis; Collapse; Earthquakes; Efficiency; Geometric nonlinearity; hybrid nonlinearity separation; Mathematical analysis; Mathematics; Nonlinear analysis; Nonlinear systems; Nonlinearity; Perturbation; Reference systems; Seismic activity; seismic collapse analysis; Seismic response; space truss structure; Stiffness matrix; Structural response; Structures; Trusses; Woodbury formula
• ISSN: 0098-8847; 1096-9845
• DOI: 10.1002/eqe.3557

This study presents a fast algorithm for collapse behavior simulation of space truss structures under extreme earthquake excitation by introducing the Woodbury formula to efficiently solve the structural response caused by material and geometric nonlinearity (hybrid nonlinearity). The Woodbury formula, which is an efficient tool in mathematics for solving low‐rank perturbation problems, has successfully been used to improve the efficiency of local material nonlinear analysis but still has difficulties with seismic collapse analysis in which geometric nonlinearity should be considered. In this study, by implementing stiffness matrix decomposition according to the unchanged reference configuration, the effects of hybrid nonlinearity on the change in tangent stiffness of truss structures are uniformly formulated in the form of hybrid nonlinear perturbation to the reference elastic stiffness. Thus, a hybrid nonlinearity separated governing equation can be established, in which the hybrid nonlinear behaviors are depicted by the additional nonlinear degrees of freedom (NLDOFs) separated from the reference system. This allows for employing the Woodbury formula to perform seismic collapse analysis of space truss structures for avoiding the repeated updating of the global stiffness. To overcome the adverse effect of the large NLDOF number caused by the global characteristics of geometric nonlinearity on the efficiency advantages of the Woodbury formula during seismic collapse analysis, an element state judgment strategy and an adaptive restart mechanism are presented to activate only a small number of NLDOFs within critical local regions. The accuracy and efficiency of the proposed method are verified by two numerical examples.