论文标题
平面线性弹性的混合等几何离散
Mixed Isogeometric Discretizations for Planar Linear Elasticity
论文作者
论文摘要
在本文中，我们建议基于平面线性弹性的同几何分析（IGA）的两种离散化方法。一方面，我们将众所周知的弱施加的对称性的Ansatz用于应力张量，并获得良好的混合配方。这种修改的混合问题已经由不同的作者研究。但是，我们集中于对IgA结果的开发，以处理弯曲的边界几何形状。另一方面，我们考虑了强烈对称性的更复杂的情况，即我们将所谓的Hellinger-Reissner变异原理确定的混合弱形式离散。我们显示出适当的近似字段的存在，导致sup稳定的鞍点问题。对于两种离散化方法，我们都证明了收敛性陈述，在弱对称性的情况下，我们通过几个数值实验说明了近似行为。
In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a well-posed mixed formulation. Such modified mixed problems have been already studied by different authors. But we concentrate on the exploitation of IGA results to handle also curved boundary geometries. On the other hand, we consider the more complicated situation of strong symmetry, i.e. we discretize the mixed weak form determined by the so-called Hellinger-Reissner variational principle. We show the existence of suitable approximate fields leading to an inf-sup stable saddle-point problem. For both discretization approaches we prove convergence statements and in case of weak symmetry we illustrate the approximation behavior by means of several numerical experiments.
