The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density
The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density
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DOI：
10.1002/ar.21358
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发表时间：
2011-04-01
影响因子：
2
通讯作者：
Rayfield, Emily J.
中科院分区：
文献类型：
--
作者：
Bright, Jen A.;Rayfield, Emily J.
有限元（FE）模型为连续问题提供离散解决方案。因此，为了得到正确的解决方案，确保FE模型包含足够数量的元素以完全解决连续体结构中遇到的所有细节是至关重要的。网格收敛测试是比较连续更精细的网格以确定收益递减点的过程;增加分辨率对结果的影响很小，进一步的细节将变得昂贵且不必要。从历史上看，在大多数涉及复杂几何形状（如颅骨）的基于CT的生物力学重建中并未考虑收敛，因为生成此类模型非常耗时。为了评估网格收敛如何影响结果，使用线性和二次四面体元素，比较了18个越来越精细的基于CT的家猪头骨模型，以确定应变和位移的收敛点。并不是头骨的所有区域都以相同的速度收敛，出乎意料的是，高应变区域比低应变区域收敛得更快。线性模型比二次模型稍硬，但收敛速度并不慢。正如预期的那样，不够密集的模型低估了应变和位移，并且未能解决等高线图中值得注意的应变“热点”。除了定量差异外，这些图的视觉评估通常会为许多比较研究中得出的结论提供信息，强调在进行进一步分析之前，应在所有有限元模型上进行网格收敛。Anat Rec，294：610-620，2011. (C)2011 Wiley-Liss，Inc.
Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT-based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time-consuming. To assess how mesh convergence influences results, 18 increasingly refined CT-based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low-strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain "hot-spots'' notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place. Anat Rec, 294:610-620, 2011. (C) 2011 Wiley-Liss, Inc.