The accuracy of digital image-based finite element models
The accuracy of digital image-based finite element models
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DOI：
10.1115/1.2798314
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发表时间：
1998-04-01
影响因子：
1.7
通讯作者：
Charras, GT
中科院分区：
文献类型：
--
作者：
Guldberg, RE;Hollister, SJ;Charras, GT
基于数字图像的有限元网格划分是一种替代耗时的传统网格划分技术的方法，用于生成复杂结构的逼真三维（3D）模型。尽管不限于生物学应用，但基于数字图像的建模已用于产生结构特异性（即，非通用的）全骨和松质骨微观结构的模型。然而，问题仍然存在的解决方案的精度提供的数字网格的方法，特别是在模型或材料的边界。本研究的目的是比较数字和传统的光滑边界模型的准确性的基础上的理论解的二维（2D）压缩板和三维圆形悬臂梁。对于板和梁分析，数字模型边界处的预测解的特征在于局部振荡，这在单个边界元素内产生潜在的高误差。然而，值得注意的是，数字模型边界解近似地围绕理论解振荡。因此，通过考虑由几个元素组成的区域内的平均结果，实现了解决方案的精度显着提高。例如，在梁横截面上平均的Von Mises应力的绝对误差收敛到小于4%，悬臂梁的预测自由端位移在理论解的1%以内，在几种梁方向和网格分辨率下的分析表明，在梁横截面上最少离散三到四个数字有限元，以避免高数值刚化误差，弯曲。
Digital image-based finite element meshing is an alternative approach to time-consuming conventional meshing techniques for generating realistic three-dimensional (3D) models of complex structures. Although not limited to biological applications, digital image-based modeling has been used to generate structure-specific (i.e., nongeneric) models of whole bones and trabecular bone microstructures. However questions remain regarding the solution accuracy provided by the digital meshing approach, particularly at model or material boundaries. The purpose of this study was to compare the accuracy of digital and conventional smooth boundary models based on theoretical solutions for a two-dimensional (2D) compression plate and a 3D circular cantilever beam. For both the plate and beam analyses, the predicted solution at digital model boundaries was characterized by local oscillations, which produced potentially high errors within individual boundary elements. Significantly, however, the digital model boundary solution oscillated approximately about the theoretical solution. A marked improvement in solution accuracy was therefore achieved by considering average results within a region composed of several elements. Absolute errors for Von Mises stress averaged over the beam cross section, for example, converged to less than 4 percent, and the predicted free-end displacement of the cantilever beam was within 1 percent of the theoretical solution, Analyses at several beam orientations and mesh resolutions suggested a minimum discretization of three to four digital finite elements through the beam cross section to avoid high numerical stiffening errors under bending.