论文标题
Dirichlet和Neumann边界条件中的弹力动力学晶格玻尔兹曼方法
Dirichlet and Neumann boundary conditions in a Lattice Boltzmann Method for Elastodynamics
论文作者
论文摘要
最近，Murthy等人。 [2017]和Escande等。 [2020]采用了晶格玻尔兹曼方法（LBM）来对各向同性固体的线性弹性动力学行为进行建模。 LBM作为弹性动力求解器具有吸引力，因为它可以轻松地并行化并借出精细离散化的动态连续模拟，从而使瞬时现象有效地建模。 这项工作提出了简单的局部边界规则，该规则近似于Dirichlet和Neumann边界条件的行为，其弹性固体的LBM。均考虑了晶格构成和非晶格构造的弯曲边界几何形状。 为了进行验证，我们比较了LBM通过分析溶液突然加载固定裂纹的结果。此外，我们研究了使用有限元（FEM）模拟作为参考的LBM对带有圆形孔的瞬态张力载荷的性能。
Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be parallelised readily and lends itself to finely discretised dynamic continuum simulations, allowing transient phenomena such as wave propagation to be modelled efficiently. This work proposes simple local boundary rules which approximate the behaviour of Dirichlet and Neumann boundary conditions with an LBM for elastic solids. Both lattice-conforming and non-lattice-conforming, curved boundary geometries are considered. For validation, we compare results produced by the LBM for the sudden loading of a stationary crack with an analytical solution. Furthermore, we investigate the performance of the LBM for the transient tension loading of a plate with a circular hole, using Finite Element (FEM) simulations as a reference.
