Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids
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DOI：
10.1016/j.cma.2011.01.018
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发表时间：
2011-05
影响因子：
7.2
通讯作者：
N. Nguyen‐Thanh;H. Nguyen-Xuan;S. Bordas;T. Rabczuk
中科院分区：
文献类型：
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作者：
N. Nguyen‐Thanh;H. Nguyen-Xuan;S. Bordas;T. Rabczuk
等几何分析由于其在处理复杂几何形状方面的灵活性，已成为标准有限元的一种强有力的替代方法。基于NURBS的等几何有限元的主要缺点之一是局部加密效率低。在这项研究中，我们提出了一种替代基于NURBS的等几何分析，允许局部细化。这个想法是基于多项式样条，并利用局部细化的T-网格的灵活性。形函数满足非负性、局部支撑和单位分解等重要性质。数值算例表明了本文方法的可靠性。
Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.