论文标题
渐近兼容的复制核搭配和无线纳维尔方程的无网格搭配
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
论文作者
论文摘要
在这项工作中，我们研究了Peridynynamic Navier方程的繁殖核（RK）搭配方法。我们首先在位移和扩张上施加线性RK近似，然后在后替代扩张，然后以纯粹的位移形式求解Peridynynamic Navier方程。 RK搭配方案会收敛到非局部限制，并随着非局部相互作用的消失而收敛到局部极限。通过使用傅立叶分析将搭配方案与标准盖尔金方案进行比较，显示了稳定性。然后，我们将RK搭配应用于准二散的Peridynamic Navier方程，并在固定非局部长度尺度和离散参数之间的比率时，将其收敛到正确的局部限制。该分析是针对带有有限支持的指定内核的RK搭配方法的特殊的直线笛卡尔网格家族进行的。我们假设Lamé参数满足$λ\geqμ$，以避免在非局部内核上增加额外的约束。最后，进行数值实验以验证理论结果。
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilatation, then back-substitute dilatation, and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. We then apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lamé parameters satisfy $λ\geq μ$ to avoid adding extra constraints on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.
