I need some information about suitable absorbing boundaries and their performance and modeling methods.if it's possible please introduce some references.
thanks
Hi,
the three approaches I know are BEM, LTB, and PML. See references below. Unfortunately, I don't have references including comparative studies.
Boundary Element Methods (BEM):
Beer, G. et al. (2008), 'The Boundary Element Method with Programming', Springer-Verlag Wien
Local Transmitting Boundaries (LTB):
Lysmer, J. & Kuhlemeyer, R. (1969), ‘Finite dynamic model for infinite media’, J Eng Mech Div, ASCE 95, 877–895
Hagstrom, T. & Warburton, T. (2004), 'A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems’, Wave Motion 39(4), 327–338
Perfectly Matched Layer (PML):
Chew, W. & Liu, Q. (1996), ‘Perfectly matched layers for elastodynamics: A new absorbing boundary condition’, Journal of Computational Acoustics 4(04), 341–359
Matzen, R. (2011), ‘An efficient finite element time-domain formulation for the elastic second-order wave equation: A non-split complex frequency shifted convolutional PML’, IJNME 88(10), 951–973
Kausel, E. & Oliveira Barbosa, J. M. (2012), ‘PMLs: A direct approach’, IJNME 90(3), 343–352
Regards
Hi Sahand,
Most software dealing with soil-structure interaction have an element known as the infinite elements. You place this element around boundary of your model. The damping components of this element takes care of returning wave. This element is based on work of Lysmer. Alternative you can add spring and dash-pot to the boundary to simulate the transmitting boundary.
Such boundary is known as "quite" boundary.
Hi Sahand
If you'll model the halfspace in Finite Eement, you can use with some efficiency several layers of finite elements near the boundary with increasing damping coefficient or damping ratio in the material. It works well but needs a lot of computer resources.
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