线性弹性方程在非均匀错位网格上的位移-应力配方的 MAC 方案
数值分析
2026-01-13 v1 数值分析
摘要
发展一种用于在非均匀错位网格上求解二维和三维线性弹性位移-应力配方的标记-细胞有限差分方法。该方法采用错位网格布局，其中位移分量在单元边中点处近似，法向应力在单元中心处定义，切向应力在网格点处定义。这种结构确保局部守恒特性，避免应力近似中的伪波动。present a rigorous mathematical analysis, establishing the stability of the scheme and proving the second-order L2-error super-convergence for both displacement and stress. The proposed method is locking-free with respect to the Lame constant, making it suitable for both compressible and nearly incompressible elastic materials. Numerical experiments demonstrate the efficiency and robustness of the finite difference scheme, and the computed results show excellent agreement with the theoretical predictions.
引用
@article{arxiv.2601.07174,
title = {The MAC scheme for linear elasticity in displacement-stress formulation on non-uniform staggered grids},
author = {Hongxing Rui and Weijie Wang},
journal= {arXiv preprint arXiv:2601.07174},
year = {2026}
}