Abstract We propose a mixed stress-displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von Mises plasticity. The discretization is based on isogeometric analysis (IGA) with non-uniform rational B-Splines (NURBS) as basis functions. As compared to conventional IGA Galerkin formulations, isogeometric collocation methods offer a high potential of computational cost reduction for higher-order discretizations as they eliminate the need for quadrature. In the proposed mixed formulation, both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues, which occur in displacement-based isogeometric collocation for nearly incompressible elasticity and von Mises plasticity. The performance of the proposed approach is demonstrated by several numerical examples.

中文翻译：

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几乎不可压缩的弹性和弹塑性的混合应力-位移等几何搭配

摘要 我们为几乎不可压缩的弹性材料和表现出冯米塞斯塑性的材料提出了一种混合应力位移等几何配置方法。离散化基于以非均匀有理 B 样条 (NURBS) 作为基函数的等几何分析 (IGA)。与传统的 IGA Galerkin 公式相比，等几何搭配方法为高阶离散化提供了降低计算成本的巨大潜力，因为它们消除了对正交的需要。在提出的混合公式中，应力和位移场都被近似为主要变量，目的是处理体积锁定和不稳定问题，这些问题发生在基于位移的等几何搭配中，几乎不可压缩的弹性和 von Mises 塑性。