A finite element method enriched for wave propagation problems

By Seounghyun Ham, Klaus-Jürgen Bathe. 2012

217 citations recorded by the source corpus.

An enriched finite element method is presented to solve various wave propagation problems. The proposed method is an extension of the procedure introduced by Kohno, Bathe, and Wright for one-dimensional problems [1]. Specifically, the novelties are: two-dimensional problems are solved (and three-dimensional problems would be tackled similarly), a scheme is given to overcome ill-conditioning, the method is presented for time-dependent problems, and focus is on the solution of problems in solids and structures using real arithmetic only. The method combines advantages of finite element and spectral techniques, but an important point is that it preserves the fundamental properties of the finite element method. The general formulation of the procedure is given and various examples are solved to illustrate the capabilities of the proposed scheme.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e2c3493c9d7785b50f29d4eedb0abff5fd9a983b

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, background): “Unfortunately, in dynamic calculation the wave propagation is significantly affected by the uniformity of the mesh [83].”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, background): “A detailed evaluation of the following methods is compiled: (i) analytical methods, (ii) semi-analytical methods, (iii) the local interaction simulation approach (LISA), (iv) finite element methods (FEMs), and (v) miscellaneous methods such as mass-spring lattice models (MSLMs), boundary element met”
The finite element method enriched by interpolation covers (2013, unknown): “[7–17,39].”
Performance of an implicit time integration scheme in the analysis of wave propagations (2013, methodology): “As an example, we consider a Lamb problem, in which waves are propagating in a semi-infinite elastic domain in plane strain conditions [23].”