Two-dimensional elastodynamics by the time-domain boundary element method: Lagrange interpolation strategy in time integration

2012 ◽  
Vol 36 (7) ◽  
pp. 1164-1172 ◽  
Author(s):  
J.A.M. Carrer ◽  
W.L.A. Pereira ◽  
W.J. Mansur
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Lagrange Interpolation ◽  
Domain Boundary ◽  
Time Integration ◽  
Two Dimensional ◽  
Interpolation Strategy ◽  
The Time Domain ◽  
Element Method

Horn effect prediction based on the time domain boundary element method

2017 ◽  
Vol 82 ◽  
pp. 79-84 ◽  
Author(s):  
Yang Zhang ◽  
Chuan-Xing Bi ◽  
Yong-Bin Zhang ◽  
Xiao-Zheng Zhang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
The Time Domain ◽  
Element Method

scholarly journals Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

2017 ◽  
Author(s):  
Jayantheeswar Venkatesh ◽  
Anders Thorin ◽  
Mathias Legrand
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Unilateral Contact ◽  
Dimensional System ◽  
One Dimensional ◽  
The Time Domain ◽  
Element Method

Finite elements in space with time-stepping numerical schemes, even though versatile, face theoretical and numerical difficulties when dealing with unilateral contact conditions. In most cases, an impact law has to be introduced to ensure the uniqueness of the solution: total energy is either not preserved or spurious high-frequency oscillations arise. In this work, the Time Domain Boundary Element Method (TD-BEM) is shown to overcome these issues on a one-dimensional system undergoing a unilateral Signorini contact condition. Unilateral contact is implemented by switching between free boundary conditions (open gap) and fixed boundary conditions (closed gap). The solution method does not numerically dissipate energy unlike the Finite Element Method and properly captures wave fronts, allowing for the search of periodic solutions. Indeed, TD-BEM relies on fundamental solutions which are travelling Heaviside functions in the considered one-dimensional setting. The proposed formulation is capable of capturing main, subharmonic as well as internal resonance backbone curves useful to the vibration analyst. For the system of interest, the nonlinear modeshapes are piecewise-linear unseparated functions of space and time, as opposed to the linear modeshapes that are separated half sine waves in space and full sine waves in time.

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