The selection of spectral element polynomial orders for high frequency numerical wave propagation
The selection of spectral element polynomial orders for high frequency numerical wave propagation
复制标题
高频数值波传播谱元多项式阶数的选择
DOI：
10.1117/12.2009243
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
D. Ozevin
中科院分区：
文献类型：
--
作者：
Z. Heidary;D. Ozevin
了解弹性波在材料中的传播特性是导波超声、声发射等基于波传播的定量无损检测方法的基础。传统的有限元公式要求非常精细的网格划分和小的时间步长，以防止高频的色散污染。谱有限元通过使用高阶正交多项式来定义节点坐标的位置，减少了动力有限元模型所需的自由度和时间积分的计算。在本研究中，频谱单元优于传统有限元频率高达400khz的结构钢板的平面应力模型。激励频率从60khz到400khz不等。选取了3、4、5阶的勒让德正交多项式。确定了消除三个多项式阶的数值误差所需的细化（即元素大小）。结果对不同多项式阶的元尺寸选择具有一定的指导意义。通过与传统有限元结果的比较，验证了谱元公式的有效性。
Understanding the propagating elastic wave characteristics in materials is the foundation for quantitative Nondestructive Testing methods based on wave propagation such as guided wave ultrasonic and acoustic emission. The conventional finite element formulation requires very fine meshing and small time steps to prevent the dispersion pollution at high frequencies. The spectral finite elements reduce the required degrees of freedoms and the computation of time integration for dynamic finite element models via using high order orthogonal polynomials to define the locations of nodal coordinates. In this study, the advantage of spectral elements over conventional finite elements for frequencies up to 400 kHz is demonstrated on plane stress model of a structural steel plate. The excitation frequency is varied from 60 kHz to 400 kHz. The Legendre orthogonal polynomials with the orders of 3, 4 and 5 are selected. The required h refinements (i.e. element size) to eliminate the numerical error for three polynomial orders are identified. The results provide a guide for selecting the element sizes for different polynomial orders. The validity of the spectral element formulation is demonstrated via comparison with conventional finite element results.