A new visco- and elastodynamic time domain Boundary Element formulation

1997 ◽  
Vol 20 (5) ◽  
pp. 452-459 ◽  
Author(s):  
M. Schanz ◽  
H. Antes
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Element Formulation

Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1750007
Author(s):  
Pooneh Maghoul ◽  
Behrouz Gatmiri
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Unsaturated Soils ◽  
Water Pressure ◽  
Domain Boundary ◽  
Fundamental Solutions ◽  
Element Formulation ◽  
Inertia Effects ◽  
Coupled Equations ◽  
The Time Domain

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.

Singularity cancellation method for time-domain boundary element formulation of elastodynamics: A direct approach

2020 ◽  
Vol 80 ◽  
pp. 647-667 ◽  
Author(s):  
Guizhong Xie ◽  
Yudong Zhong ◽  
Fenglin Zhou ◽  
Wenliao Du ◽  
Hao Li ◽  
...  
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Direct Approach ◽  
Element Formulation

Implementation of Viscoelastic Behavior in a Time Domain Boundary Element Formulation

1993 ◽  
Vol 46 (11S) ◽  
pp. S41-S46 ◽  
Author(s):  
M. Schanz ◽  
L. Gaul
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Constitutive Equations ◽  
Domain Boundary ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Viscoelastic Behavior ◽  
Element Formulation ◽  
Field Equations ◽  
Primary Interest

The boundary element method (BEM) provides a powerful tool for the calculation of elastodynamic response in frequency and time domain. Field equations of motion and boundary conditions are cast into integral equations, which are discretized only at the boundary. The boundary data often are of primary interest because they govern the transfer dynamics of members and the energy radiation into a surrounding medium. Formulations of BEM currently include conventional viscoelastic constitutive equations in the frequency domain. In the present paper viscoelastic behaviour is implemented in a time domain approach as well. The constitutive equations are generalized by taking fractional order time derivatives into account.

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