Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics
Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics
复制标题
瞬态弹性动力学中平面平方双二次偶然有限元的网格离散分析
DOI：
10.1002/nme.4539
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发表时间：
2013
影响因子：
2.9
通讯作者：
D. Gabriel
中科院分区：
文献类型：
--
作者：
R. Kolman;J. Plesek;M. Okrouhlík;D. Gabriel
有限元法对连续介质的空间离散化会给应力波传播的数值解带来色散误差。引入了相速度和群速度误差以及波传播的散射。当这些传播现象由FEM建模时，单个谐波的速度取决于其频率。寄生效应不存在于“理想的”无界连续体中。对于高阶有限元，光谱中存在光学模式，导致尖锐波前附近的应力和速度分布的寄生振荡。原则上，这些解不能消除色散误差和杂散振荡，但可以在一定程度上抑制。为了通过有限元法得到可靠的数值解，应该分析和确定色散误差。研究了平面正方形四次偶然性有限元的色散特性，并与双线性有限元进行了比较。对一致质量矩阵和集中质量矩阵进行了色散分析。本文提出了一种色散的“改进”的双二次偶然单元集中质量矩阵。本文最后建议选择的允许无量纲波长的双线性和双二次偶然有限元网格。版权所有© 2013约翰威利父子有限公司.
The spatial discretisation of a continuum by the FEM introduces dispersion errors to the numerical solution of stress wave propagation. Errors of phase and group velocities and the scatter of wave propagation are induced. When these propagating phenomena are modelled by the FEM, the speed of a single harmonic wave depends on its frequency. Parasitic effects do not exist in an ‘ideal’ unbounded continuum. With higher order finite elements, there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts. In principle, the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent. For reliable numerical solutions by the FEM, the dispersion errors should be analysed and determined. The dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one. Dispersion analysis is carried out for the consistent and lumped mass matrices. A dispersive ‘improved’ lumped mass matrix for biquadratic serendipity elements is proposed. The paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes. Copyright © 2013 John Wiley & Sons, Ltd.