等几何分析：概述与计算机实现方面
Isogeometric analysis: an overview and computer implementation aspects
AI总结：
本文通过清晰的Matlab实现，介绍了等几何分析（IGA）在有限元方法中的应用及计算机实现，并展示了扩展IGA在断裂问题中的使用。
摘要：
等几何分析（IGA）是计算力学中最近发展起来的一项技术，它提供了将分析和计算机辅助设计（CAD）方法集成到单一、统一过程中的可能性。对实际工程设计场景的影响是深远的，因为从设计到分析的时间大大减少，从而带来效率的显著提高。IGA中CAD和分析的紧密耦合需要两个领域的知识，本文的目标之一是概述常用的符号。在本文中，通过清晰简单的Matlab实现，我们介绍了应用于有限元（FE）方法的IGA及相关计算机实现方面。此外，还介绍了通过单位分解法（PUM）纳入富集函数的扩展IGA的实现，其中展示了二维和三维断裂的几个示例。本文附带的开源Matlab代码可应用于一维、二维和三维问题的线弹性、线弹性断裂力学、结构力学（包括大位移和大转动的梁/板/壳）以及带或不带富集的泊松问题。还纳入了允许在T样条几何上高效进行有限元分析的Bezier提取概念。文章总结了IGA领域的最新趋势和发展。
英文摘要：
Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA.
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