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基于逆向三维重建模型的嵌入域等几何分析方法

Isogeometric Analysis of 3D Reconstruction Model Based on Embedded Domain Method

  • 摘要: 逆向工程可从产品的现有产品物理模型中重建出CAD模型, 从而缩短产品的二次开发周期. 然而, 传统逆向工程的CAD建模和CAE分析采用不同的模型表示, 导致模型交互烦琐, 影响了产品开发效率. 为实现逆向建模模型的快速性能分析, 本文提出一种面向逆向重建模型的嵌入域等几何分析方法. 首先通过三维扫描获得对象的点云模型; 然后将点云嵌入到一个规则网格的分析域中, 根据点云位置将嵌入域中的单元划分为实单元、虚单元和裁剪单元; 接着采用一种适用于不规则区域的数值积分方法计算裁剪单元刚度矩阵, 从而实现复杂三维重建模型的等几何分析. 对艺术模型、齿轮轴、扳手和螺钉零件四个算例进行分析, 结果表明, 与传统有限元分析方法相比, 本文方法的分析结果最大值的相对误差不超过5%, 证明了其能够直接对逆向重建的点云模型进行高效准确的性能分析, 验证了本文方法的有效性与精确性.

     

    Abstract: Reverse engineering can reconstruct CAD models from existing physical models of a product, thereby shortening the secondary development cycle. However, in traditional reverse engineering, CAD modeling and CAE analysis use different model representations, which results in cumbersome model interactions and affects the efficiency of product development. To realize the fast structure analysis for reconstruction models, an embedded domain geometric analysis method tailored for reconstruction models is proposed. Firstly, the point cloud model of the object is obtained through three-dimensional scanning. Then, the point cloud is embedded into an analysis domain of regular elements, which are classified into solid, fictious and trimmed elements based on the positions of the point cloud. Subsequently, a numerical integration method suitable for irregular regions is used to compute the stiffness matrices of the trimmed elements, thereby enabling isogeometric analysis of complex 3D reconstructed models . Through the analysis of four examples including artistic models, gear shafts, wrenches, and screw parts, the results show that, compared to traditional finite element analysis methods, the proposed method has a relative error in maximum analysis results of no more than 5%. This demonstrates that the method can efficiently and accurately analyze the performance of point cloud models reconstructed via reverse engineering, which validates the effectiveness and accuracy of the proposed method.

     

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