Development of a Composite Implicit Time Integration Scheme for Three-Dimensional Discontinuous Deformation Analysis
Development of a Composite Implicit Time Integration Scheme for Three-Dimensional Discontinuous Deformation Analysis
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DOI：
10.3390/math11183881
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发表时间：
2023-09
期刊：
影响因子：
2.4
通讯作者：
Guoyang Liu;Junjie Liu;Shouyi Luo;Wu Bo;Jiashuo Kang;Jianbin Miao
中科院分区：
文献类型：
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作者：
Guoyang Liu;Junjie Liu;Shouyi Luo;Wu Bo;Jiashuo Kang;Jianbin Miao
不连续变形分析（DDA）是一种基于不连续体的隐式方法，用于研究块体系统的变形行为。传统的DDA采用具有无条件稳定特点的恒加速积分(CAI)方案。本研究指出了CAI方案在DDA中时间步长方面存在的问题。 CAI方案中采用的时间步长太大或太小都会对DDA计算产生不利影响。为了克服这些弱点，在三维（3D）DDA方法中实现了一种替代的复合隐式时间积分（CITI）方案，该方案结合了梯形规则和三点向后欧拉方法。验证实例和坡度数值模拟说明了所提出方法的准确性和有效性。结果表明，CITI方案能够克服大时间步长带来的数值误差，且算法阻尼与时间步长和所选分裂参数密切相关。
Discontinuous deformation analysis (DDA) is a discontinuum-based and implicit method for investigating the deformational behavior of block systems. The constant acceleration integration (CAI) scheme characterized by unconditional stability is employed in the traditional DDA. In this study, the problems of the CAI scheme regarding the time step in DDA are pointed out. A too large or too small time step size adopted in the CAI scheme will have adverse effects on the DDA computation. To overcome the weaknesses, an alternative composite implicit time integration (CITI) scheme, which is a combination of the trapezoidal rule and the three-point backward Euler method, is implemented in the three-dimensional (3D) DDA method. Verification examples and slope numerical simulations are presented to illustrate the accuracy and effectiveness of the proposed methodology. The results showed that the CITI scheme can overcome the numerical error caused by the large time step size, and the algorithm damping is closely related to the time step size and the selected splitting parameter.