Adaptive time-stepping increment-dimensional precise integration method for solving structural dynamic equations

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (14) : 198-203.

HUANG Yuxi1,CUI Ying2,YANG Guogang1

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Abstract

The increment-dimensional precise integration method is a high-precision step-by-step integration algorithm for solving structural dynamic equations. The step size will have a great influence on the calculation accuracy of the algorithm, and it is difficult to determine the appropriate step size in practical applications. To meet the requirements of accuracy and efficiency in the calculation, an estimation method of calculation error was proposed, and an adaptive time-stepping increment-dimensional precise integration method was established based on the estimation error and iterative convergence speed. The numerical results of three structural dynamic equations show that when considering all kinds of linear and nonlinear vibration problems, the proposed method can quickly and effectively control the calculation step size under the premise of ensuring the calculation accuracy, and only requires less additional calculation consumption, which significantly improves the efficiency of the increment-dimensional precise integration method， making the method more computationally advantageous and practical in solving structural dynamic equations.

Key words

increment-dimensional precise integration / adaptive time-stepping / structural dynamic equation / error estimate

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HUANG Yuxi1,CUI Ying2,YANG Guogang1. Adaptive time-stepping increment-dimensional precise integration method for solving structural dynamic equations[J]. Journal of Vibration and Shock, 2023, 42(14): 198-203

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