Wave motion and its dispersive properties in a finite element model with distortional elements

Abstract Solutions are obtained for wave motion in a hybrid-mass distortional finite element model by employing the extended method of lattice dynamics. The dispersion equations of wave motion are also given through the solutions. The dispersive properties of a plane wave and the existential condition of an inhomogeneous wave are studied. The results show that the ability of the hybrid-mass model to resist the distortion of element shape is greater than that of the consistent-mass model but lower than that of the lumped-mass model. The velocities of wave propagation in the lumped-mass model are not always lower than that in the corresponding continuum. When the element shape is highly distorted, the velocities in the lumped-mass model may exceed those in the continuum. The effects of discretization in time domain on wave propagation are also discussed.

[1]  Z. Bažant,et al.  SPURIOUS REFLECTION OF ELASTIC WAVES IN NONUNIFORM FINITE ELEMENT GRIDS , 1978 .

[2]  Z. Celep,et al.  Finite element solution for reflection of plane harmonic waves from the free surface of a half-space , 1987 .

[3]  Z. Celep.  Plane elastic waves in meshes of bilinear finite elements , 1985 .

[4]  Robert J. Rogers,et al.  Effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation , 1990 .

[5]  Robert J. Rogers,et al.  Control of elastic plane wave dispersion in two-dimensional finite element meshes , 1985 .

[6]  T. Hughes,et al.  Stability and accuracy analysis of some fully-discrete algorithms for the one-dimensional second-order wave equation , 1984 .

[7]  Liu Jingbo,et al.  In-plane wave motion in finite element model , 1992 .

[8]  Zdeněk P. Bažant,et al.  Spurious reflection of elastic waves due to gradually changing finite element size , 1983 .

[9]  J. Z. Zhu,et al.  The finite element method , 1977 .

[10]  Peter M. Pinsky,et al.  Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem , 1990 .

[11]  T. Belytschko,et al.  Dispersion analysis of finite element semidiscretizations of the two‐dimensional wave equation , 1982 .

[12]  Zdeněk P. Bažant,et al.  Spurious reflection of elastic waves in nonuniform meshes of constant and linear strain unite elements , 1982 .

[13]  Peter M. Pinsky,et al.  Finite element dispersion analysis for the three‐dimensional second‐order scalar wave equation , 1992 .