Abstract
ABSTRACT The objective of this paper is to present a finite element solution for the wave propagation problems with a reduction of the velocity dispersion and spurious reflection. To this end, a high-order two-step direct integration algorithm for the wave equation is adopted. The suggested algorithm is formulated in terms of two Hermitian finite difference operators with a sixth-order local truncation error in time. The two-node linear finite element presenting the fourth-order of local truncation error is considered. The numerical results reveal that although the algorithm competes with higher-order algorithms presented in the literature, the computational effort required is similar to the effort required by the average acceleration Newmark method. More than that, the integration with the lumped mass model shows similar results to the integration using the average acceleration Newmark for the consistent mass model, which involves a higher number of computational operations.
Highlights
In the numerical computation of wave equations, numerical wave velocity dispersion and spurious reflections for non-uniform meshes are a persistent problem arising from the inadequate discretization of the continuous
A lot of research effort has been devoted to dispersion and spurious reflections in the numerical integration of wave equations by finite element method Belytschko and Mullen [2], Liu, Sharan, and Yau [3] and Bazant [4]
The numerical results indicate that for the fine mesh ( a > 50 and b > 50 ) the numerical wave velocity dispersion obtained by the adopted algorithm considering the lumped mass model are similar to the results obtained by the average acceleration Newmark method that considers the consistent mass model, for which the amount of operations is two times greater
Summary
In the numerical computation of wave equations, numerical wave velocity dispersion and spurious reflections for non-uniform meshes are a persistent problem arising from the inadequate discretization of the continuous. A lot of research effort has been devoted to dispersion and spurious reflections in the numerical integration of wave equations by finite element method Belytschko and Mullen [2], Liu, Sharan, and Yau [3] and Bazant [4]. Idesman [5] presented the optimal reduction in numerical dispersion for wave propagation problems using two-dimensional isogeometric elements. The single parametric Wilson method [8] was developed with improvements in the numerical damping but presenting initial displacement overshoot. Hughes, and Taylor [9] presented a new and efficient method with improvements in numerical dissipation. Bazzi and Anderheggen [10] developed a direct integration algorithm with new improved numerical dissipation and Hoff and Pahl [11] developed an improved variant of the Wilson method. Recently Soares Jr. [13] proposes a locally stabilized central difference method of four order accurate
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