有限元方法在复杂CAD和图像几何模型非线性结构分析中的综述
A review of the finite cell method for nonlinear structural analysis of complex CAD and image-based geometric models
AI总结：
本文综述了有限元方法在复杂几何非线性结构分析中的应用，包括p-有限元和B-样条版本，展示其在弹性力学中的解行为，并扩展到非线性弹性及多孔介质传输等应用。
摘要：
有限元方法（FCM）属于浸入边界方法，结合了虚域方法、高阶近似、自适应积分和弱施加不匹配狄利克雷边界条件。对于复杂几何分析，它避免了昂贵且可能出错的网格化过程，同时保持高收敛率。本文综述了FCM在结构力学中的最新进展。首先，使用p-和B-样条版本的FCM回顾基本组件。其次，展示线弹性在1D中的典型解行为。第三，展示将FCM扩展到非线弹性是直接的。我们还概述了FCM可扩展到其他应用，如多孔介质传输过程。最后，通过两个应用示例展示了FCM的优势，即由T-样条CAD表面描述的船桨振动分析和基于CT的金属泡沫非线性压缩测试。
英文摘要：
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. For the analysis of complex geometries, it circumvents expensive and potentially error-prone meshing procedures, while maintaining high rates of convergence. The present contribution provides an overview of recent accomplishments in the FCM with applications in structural mechanics. First, we review the basic components of the technology using the p- and B-spline versions of the FCM. Second, we illustrate the typical solution behavior for linear elasticity in 1D. Third, we show that it is straightforward to extend the FCM to nonlinear elasticity. We also outline that the FCM can be extended to applications beyond structural mechanics, such as transport processes in porous media. Finally, we demonstrate the benefits of the FCM with two application examples, i.e. the vibration analysis of a ship propeller described by T-spline CAD surfaces and the nonlinear compression test of a CT-based metal foam.
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