Abstract
In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.
Highlights
In last several decades, time dependent hyperbolic equations coupled with their calculation methods are widely used in various field
The numerical dissipation and accuracy of time integration method are usually measured by the amplitude decay (AD) and the period elongation (PE), respectively. e AD and PE results of the considered time integration methods are plotted in Figures 2 and 3, respectively
The Wen method is applied to the analysis of nonlinear dynamics. e calculation procedure of the Wen method for nonlinear analysis is proposed. e basic properties of the Wen method are provided
Summary
Time dependent hyperbolic equations coupled with their calculation methods are widely used in various field. Following the Bathe method, a lot of composite methods [19,20,21,22,23,24] have been proposed by adopting different combinations of trapezoidal rule and other formulas Among these methods, the Wen method [21] has excellent numerical dissipative properties and achieves high accuracy in linear analysis. According to the calculation procedure of the Wen method for linear system [21], the time steps corresponding to the three substeps are pΔt, (1 − p)Δt, and Δt, respectively. A parameter case of the Wen method is suggested for general linear dynamic problems to obtain desirable algorithmic properties including calculation accuracy, numerical dissipation, etc.
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