A Hamiltonian particle method for non‐linear elastodynamics
A Hamiltonian particle method for non‐linear elastodynamics
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非线性弹性动力学的哈密顿粒子法
DOI：
10.1002/nme.2222
复制
发表时间：
2008
影响因子：
2.9
通讯作者：
S. Koshizuka
中科院分区：
文献类型：
--
作者：
Yukihito Suzuki;S. Koshizuka
粒子法是一种无网格模拟技术，其中连续体的运动由有限数量粒子的离散动力学近似。它们具有很大程度的灵活性，例如，在处理复杂的大变形或固体破碎时。本文在拉格朗日离散化的基础上，建立了可压缩和不可压缩材料非线性弹性动力学的质点方法，并利用最小作用量原理导出了弹性动力学的控制方程。离散化的拉格朗日通过勒让德变换得到有限维哈密顿系统。如果材料不可压缩，则哈密顿系统伴随着完整约束。根据材料是可压缩还是不可压缩，数值时间积分采用的辛格式分别为Störmer/Verlet格式或RATTLE方法。所得质点法继承了弹性动力学控制方程所具有的辛结构。在不可压缩材料的情况下，不可压缩性在每个时间步都是严格执行的。一些数值试验表明，除了线动量和角动量守恒法外，机械能守恒法也有其优越性。版权所有©2007 John Wiley & Sons， Ltd
Particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles. They have a great degree of flexibility, for instance, in dealing with complex large deformations or the fragmentation of solids. In this paper, a particle method for non‐linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the Lagrangian from which the governing equations of elastodynamics are derived using the principle of least action. The discretized Lagrangian leads to a finite‐dimensional Hamiltonian system via the Legendre transformation. If the material is incompressible, the Hamiltonian system is accompanied by holonomic constraints. Depending on whether the material is compressible or incompressible, the symplectic scheme adopted for numerical time integration is either the Störmer/Verlet scheme or the RATTLE method, respectively. The resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics. In the case of incompressible materials, incompressibility is strictly enforced at each time step. Some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta. Copyright © 2007 John Wiley & Sons, Ltd.
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DOI：
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发表时间：
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期刊：
影响因子：
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DOI：
10.1002/fld.1650200824
发表时间：
1995-04-30
影响因子：
1.8
作者：
LIU, WK;JUN, S;ZHANG, YF
通讯作者：
ZHANG, YF
影响因子：
1.2
作者：
Koshizuka, S;Oka, Y
通讯作者：
Oka, Y