由点云定义的域的直接结构分析
Direct structural analysis of domains defined by point clouds
AI总结：
本文提出基于有限胞元法的点云直接数值分析方法，仅需内外信息即可施加边界条件，精度可由点云密度控制，并成功应用于历史结构三维分析。
摘要：
本文提出了一种旨在对由有向点云表示的固体进行数值分析的方法。该方法基于有限胞元法，这是一种高阶浸入边界技术，在规则背景有限元网格上进行计算，仅需几何模型的内部-外部信息。研究表明，有向点云为这些点隶属分类提供了足够的信息。此外，我们提出了一种无需网格细分的轮廓积分公式，使得无需恢复底层表面即可在点云上施加诺伊曼边界条件。二维线弹性基准算例表明，该方法能够提供与传统连续表面描述所计算相同的精度，因为相关误差可通过点云密度进行控制。在历史结构点云上计算的三维算例展示了该方法如何用于建立数字形状测量技术与数值分析之间的无缝连接。
英文摘要：
This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a regular background grid of finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficient information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
