Helmholtz Decomposition and Boundary Element Method Applied to Dynamic Linear Elastic Problems
E Klaseboer, Q Sun, DYC Chan
Journal of Elasticity | Springer Link | Published : 2019
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the longitudinal and transverse fields satisfy scalar Helmholtz equations that can be solved using a desingularized boundary element method (BEM) framework. The curl free longitudinal and divergence free transversal conditions can also be cast as additional scalar Helmholtz equations. When compared to other BEM implementations, the current framework leads to smaller matrix dimensions and a simpler conceptual approach. The numerical implementation of this appro..View full abstract
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Awarded by Australian Research Council
This work is supported in part by the Australian Research Council through a Discovery Early Career Researcher Award DE150100169 to QS and a Discovery Project Grant DP170100376 to DYCC.