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

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (3) : 21-29.

YU Dinghao, LI Gang

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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.

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

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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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