Multi-Wavelength Sized Finite Elements for Three Dimensional Elastic Wave Problems

三维弹性波问题的多波长有限元

• 批准号: EP/I018042/1
• 负责人: Omar Laghrouche
• 金额: $ 52.11万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI018042%2F1
• 关键词: Multi; Wavelength; Sized; Finite; Elements

Elastic wave propagation modelling arises in many engineering applications, including traffic vibrations from roads and railways, seismic induced vibrations and foundation construction, etc. The numerical modelling of these problems, in frequency domain by the conventional Finite Element Method (FEM), requires finite element grids sufficiently fine in comparison with the wavelengths, to get accurate results. When typically, the piecewise linear finite element is implemented, around ten nodal points per lower wavelength are needed, to ensure adequate resolution of the wave pattern. However, in the case of high frequency (small wavelength) and/or large domain of interest, the finite element mesh requires a large number of elements, and consequently the procedure becomes computationally expensive and impractical. The aim of the proposed work is to accurately model three-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The resulting improvement in computational efficiency will enable problems of practical interest to be simulated using computing facilities available in most engineering design offices.

弹性波传播模拟出现在许多工程应用中，包括公路和铁路的交通振动，地震诱发振动和基础建设等。这些问题的数值模拟，在频域中的传统有限元法（FEM），需要有限元网格足够细的波长相比，得到准确的结果。当典型地实施分段线性有限元时，需要每较低波长大约十个节点，以确保波图案的足够分辨率。然而，在高频（小波长）和/或感兴趣的大域的情况下，有限元网格需要大量的元素，因此该过程在计算上变得昂贵且不切实际。所提出的工作的目的是准确地模拟三维弹性波问题，具有更少的元素，能够包含许多波长每个节点间距，并在每个频率不细化网格。由此产生的计算效率的提高将使实际感兴趣的问题能够使用大多数工程设计办公室提供的计算设施进行模拟。

项目成果

Implementation and computational aspects of a 3D elastic wave modelling by PUFEM

• DOI: 10.1016/j.apm.2017.05.013
• 发表时间: 2017-09
• 期刊: Applied Mathematical Modelling
• 影响因子: 5
• 作者: M. Mahmood;O. Laghrouche;J. Trevelyan;A. Kacimi

High-order finite elements for the solution of Helmholtz problems

• DOI: 10.1016/j.compstruc.2017.06.010
• 发表时间: 2017-10
• 期刊: Computers & Structures
• 影响因子: 4.7
• 作者: K. Christodoulou;O. Laghrouche;M. S. Mohamed;J. Trevelyan

Error analysis for numerical solution by PUMFEM of 3D elastic wave problems

3D弹性波问题的PUMFEM数值求解误差分析

• 发表时间: 2013
• 作者: Mahmood M S

An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems

• DOI: 10.1002/nme.5440
• 发表时间: 2017-06
• 期刊: International Journal for Numerical Methods in Engineering
• 影响因子: 2.9
• 作者: M. Iqbal;H. Gimperlein;M. S. Mohamed;O. Laghrouche

Multi-wavelength sized ¯nite elements for three-dimensional elastic wave problems

三维弹性波问题的多波长尺寸有限元

• 发表时间: 2013
• 作者: Mahmood M S