Smoothed finite element method with the node‐based strain smoothing domains (NS‐FEM) is remarkable for the upper‐bound feature and insensitivity to the volumetric locking. As a mesh‐based methodology, its application is limited by the burdensome meshing for which elements align with the physical domain. We extend the strain smoothing in NS‐FEM to the numerical manifold method (NMM) with unfitted meshes, and propose a novel methodology named physical patch‐based smoothed NMM. Benchmark problems demonstrate the optimal convergence, stability in term of the condition number, upper‐bound property, suppression of the volumetric locking, as well as the stress stability.

中文翻译：

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具有基于物理补丁的平滑域的平滑数字流形方法以实现线性弹性

具有基于节点的应变平滑域（NS-FEM）的平滑有限元方法对于上限特征和对体积锁定的不敏感性非常出色。作为基于网格的方法，其应用受到繁重的网格划分的限制，网格划分的要素与物理域对齐。我们将NS‐FEM中的应变平滑扩展到具有不拟合网格的数值流形方法（NMM），并提出了一种新的方法，称为基于物理补丁的平滑NMM。基准问题证明了最佳收敛性，条件数的稳定性，上限特性，抑制体积锁定以及应力稳定性。