Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation
Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation
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DOI：
10.1007/s00161-020-00915-y
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发表时间：
2020-08
影响因子：
2.6
通讯作者：
B. Wang;S. Oterkus;E. Oterkus
中科院分区：
文献类型：
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作者：
B. Wang;S. Oterkus;E. Oterkus
周期动力学方程的数值解通常采用均匀空间离散。虽然统一离散化的实现很简单，但它可以显著增加某些问题的计算时间。相反，可以使用非均匀离散化，并且可以在解决方案域的不同部分使用不同的离散化大小。此外，周期长度尺度参数Horizon也可以在整个解域中变化。这种情况需要额外的关注，因为必须满足守恒定律。为了处理这些问题，引入了双水平周期动力学，使得非均匀离散化和可变水平大小都可以被利用。本文利用欧拉-拉格朗日方程推导了基于状态的周期动力学的双水平周期动力学公式。此外，还对边界条件的应用和表面修正系数的确定进行了说明。最后，通过考虑板的受拉和板的振动两个基准问题，验证了本文公式的正确性。
The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate.