Abstract
Outgoing waves arising from high-velocity impacts between soil and structure can be reflected by the conventional truncated boundaries. Absorbing boundary conditions (ABCs), to attenuate the energy of the outward waves, are necessary to ensure the proper representation of the kinematic field and the accurate quantification of impact forces. In this paper, damping layer and dashpot ABCs are implemented in the material point method (MPM) with slight adjustments. Benchmark scenarios of different dynamic problems are modelled with the ABCs configured. Feasibility of the ABCs is assessed through the velocity fluctuations at specific observation points and the impact force fluctuations on the structures. The impact forces predicted by the MPM with ABCs are verified by comparison with those estimated using a computational fluid dynamics approach.
Abstract
目的
在材料高速冲击结构物的过程中引起的应力波往往在材料中向边界逐渐传播, 并在传统固定或自由边界处反射回材料内部, 造成结构物附件的应力场和接触力数值的扰动。本文旨在在物质点法模拟中实现吸收边界的应用, 在模型边界处吸收材料中的应力波, 减少其反射及其对中心区域的干扰。
创新点
1. 对不同条件处的边界分别采用黏壶和阻尼层的吸收边界, 优化边界处应力波的吸收效果;2. 建立物质点法分析模型, 对吸收边界的效果进行量化评估。
方法
1. 在边界网格节点上采用黏壶吸收边界, 并通过数学推导, 确定不同时刻对节点处速度的调整量, 以实现对应力波的充分吸收;2. 在距离边界一定距离的厚度内, 设置阻尼层, 对材料瞬态速度进行一定程度的调整, 使其达到所需的稳态值, 即对应力波完成吸收;3. 采用物质点法建立一维压缩、海底滑坡冲击管线和管线贯入模型, 对吸收边界的使用效果进行评估, 并对两种吸收边界的使用场景进行分析。
结论
1. 黏壶吸收边界通过对波动方程的推导, 使其在自由边界处的使用更加灵活;2. 阻尼层吸收边界需要在计算区域外侧设置一定厚度的阻尼层, 且阻尼值不宜过大;3. 在一定条件下, 两种吸收边界组合使用可以优化对应力波的吸收。
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Project supported by the Key Science and Technology Plan of PowerChina Huadong Engineering Corporation (No. KY2018-ZD-01), China and the National Natural Science Foundations of China (No. 51909248)
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You-kou DONG and Zhi-gang SHAN: conceptualization, methodology, validation, investigation, writing-original draft; Zhe-xian LIAO: data curation, formal analysis; Lan CUI: visualization, project administration; You-kou DONG and Dong WANG: writing-review & editing.
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Zhi-gang SHAN, Zhe-xian LIAO, You-kou DONG, Dong WANG, and Lan CUI declare that they have no conflict of interest.
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Shan, Zg., Liao, Zx., Dong, Yk. et al. Implementation of absorbing boundary conditions in dynamic simulation of the material point method. J. Zhejiang Univ. Sci. A 22, 870–881 (2021). https://doi.org/10.1631/jzus.A2000399
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DOI: https://doi.org/10.1631/jzus.A2000399