Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

Abstract

In this work, the edge-based smoothed finite element method (ES-FEM) is incorporated with the Bathe time integration scheme to solve the transient wave propagation problems. The edge-based gradient smoothing technique (GST) can properly soften the “overly soft” system matrices from the standard finite element approach; then, the spatial numerical dispersion error of the calculated solutions for wave problems can be significantly reduced. To effectively solve the transient wave propagation problems, the Bathe time integration scheme is employed to perform the involved time integration. Due to the appropriate “numerical dissipation effects” from the Bathe time integration method, the spurious oscillations in the relatively large wave numbers (high frequencies) can be effectively suppressed; then, the temporal numerical dispersion error in the calculated solutions can also be notably controlled. A number of supporting numerical examples are considered to examine the capabilities of the present approach. The numerical results show that ES-FEM works very well with the Bathe time integration technique, and much more numerical solutions can be reached for solving transient wave propagation problems compared to the standard FEM.

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

“…To increase the solution quality of the traditional FEM in solving MEE structures, Zhou and his co-workers have employed a series of smoothed finite element methods (SFEMs) [32][33][34][35] and smoothed point interpolation methods (SPIMs) [36][37][38], which can be regarded as an effective combination of the traditional FE approach and the generalized gradient smoothing technique [39][40][41][42][43][44][45], to analyze the MEE structures. In their studies, both dynamic and static behaviors of MEE structures subjected to various external excitations are investigated in great detail.…”

A computational framework for finite element modeling of traveling loads on bridges in dynamic regime

“…On the other hand, the typical approach to represent traffic loads (Calgaro, 1998; CEN, 2003) is to perform static analyses where the three‐dimensional (3D) effects are approximated using geometric distribution factors (Courbon, 1976) and dynamic effects are considered using amplification factors (Caprani et al., 2012; Da Silva, 2004; Deng et al., 2015; González et al., 2008, 2011; Li et al., 2006). Loads are usually applied along the bridge on specific locations maximizing the effects according to influence line diagrams (Adeli & Ge, 1989; Adeli & Mak, 1990).…”