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Numerical Dispersion and Its Control for 1-D Finite Element Simulation of Stress Wave Propagation  

이종세 (한양대학교 공학대학 토목ㆍ환경공학과)
유한규 (한양대학교 공학대학 토목ㆍ환경공학)
윤성범 (한양대학교 공학대학 토목ㆍ환경공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.17, no.1, 2004 , pp. 75-82 More about this Journal
Abstract
With an aim at eliminating the numerical dispersion error arising from the numerical simulation of stress wave propagation, numerical dispersion characteristics of the wave equation based one-dimensional finite element model are analyzed and some dispersion control scheme are proposed in this paper The dispersion analyses are carried out for two types of mass matrix, namely the consistent and the lumped mass matrices. Based on the finding of the analyses, dispersion correction techniques are developed for both the implicit and explicit schemes. For the implicit scheme, either the weighting factor for the spatial derivatives of each time level or the lumping coefficient for mass matrix is adjusted to minimize the numerical dispersion. In the case of the explicit scheme an artificial dispersion term is introduced in the governing equation. The validity of the dispersion correction techniques proposed in this study is demonstrated by comparing the numerical solutions obtained using the Present techniques with the analytical ones.
Keywords
wave equation; finite element model; dispersion error; dispersion correction techniques.;
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