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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A quadrature-based superconvergent isogeometric frequency analysis with macro-integration cells and quadratic splines
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A quadrature-based superconvergent isogeometric frequency analysis with macro-integration cells and quadratic splines

机译：具有宏积分单元和二次样条的基于正交的超收敛等几何频率分析

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A quadrature-based superconvergent isogeometric method is presented for efficient frequency analysis with macro-integration cells and quadratic splines. The present development particularly refers to the isogeometric analysis of scalar wave equations. The single element, two-element and three-element macro-integration cells are proposed to develop a set of explicit superconvergent quadrature rules with a 6th order frequency accuracy, in contrast to the 4th order frequency accuracy associated with the standard isogeometric formulation with consistent mass matrix. The 1D quadrature rules with various macro-integration cells are derived from the condition of exact integration of the higher order mass matrix as well as the stiffness matrix. Consequently, 3-point, 5-point and 7-point quadrature rules with identical precision are established for the single element, two-element and three-element macro-integration cells, respectively. By construction these quadrature rules exactly recover the isogeometric higher order mass matrix formulation with frequency superconvergence in 1D case. The 2D and 3D superconvergent quadrature rules with versatile integration cells are directly constructed through the tensor product formulation of the 1D integration algorithms. It is shown that the multidimensional isogeometric analysis employing the proposed quadrature rules for both mass and stiffness matrices does produce the frequency superconvergence simultaneously without the wave propagation direction dependence problem, which needs special treatments for the multidimensional higher order mass matrix formulation. The proposed approach is featured by its simplicity for numerical implementation and efficiency using macro-integration cells. Numerical examples confirm the efficacy of the present methodology. (C) 2017 Elsevier B.V. All rights reserved.
机译：提出了一种基于正交的超收敛等几何方法，可对宏积分单元和二次样条进行有效的频率分析。当前的发展尤其涉及标量波动方程的等几何分析。建议使用单元素，二元素和三元素宏积分单元来开发一组具有六阶频率精度的显式超收敛正交规则，这与质量恒定的标准等几何公式相关的四阶频率精度相反矩阵。具有各种宏积分单元的一维正交规则是从高阶质量矩阵以及刚度矩阵的精确积分条件得出的。因此，分别为单个元素，两个元素和三个元素的宏积分单元建立了具有相同精度的3点，5点和7点正交规则。通过构造这些正交规则，可以在一维情况下通过频率超收敛精确地恢复等几何高阶质量矩阵公式。通过一维积分算法的张量积公式可直接构建具有通用积分单元的2D和3D超收敛正交规则。结果表明，对于质量和刚度矩阵，采用拟议的正交规则进行的多维等几何分析确实同时产生了频率超收敛，而没有波传播方向相关性的问题，对于多维高阶质量矩阵公式，需要进行特殊处理。所提出的方法的特点是，它对于数值实现的简单性以及使用宏积分单元的效率。数值示例证实了本方法的有效性。 （C）2017 Elsevier B.V.保留所有权利。

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