NonReflectingBC

Applies Lysmer damper in the normal and tangential directions to soil boundary.

Description

This BC models a Lysmer damper (Lysmer and Kuhlemeyer, 1969) that absorbs the waves hitting a boundary. To understand Lysmer dampers, let us consider a uniform, linear elastic soil column and say a 1D vertically propagating P wave is traveling through this soil column. Then the normal stress at any location in the soil column is given by:

$(1)var element = document.getElementById("moose-equation-b0073e34-f388-4c40-a14f-cc898b52213b");katex.render(" \\sigma = E \\epsilon = E \\frac{du}{dx} = \\frac{E}{V_p} \\frac{du}{dt}= \\rho V_p \\frac{du}{dt}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-1a657c11-1a8b-4504-b4a2-cba1f9b0d236");katex.render("E", element, {displayMode:false,throwOnError:false});$ is the Young's modulus, $var element = document.getElementById("moose-equation-110e4474-24b0-4b37-810b-0499915488d0");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the normal stress, $var element = document.getElementById("moose-equation-2cbfcfe3-41c9-48c3-a9af-c6e3a6972b34");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false});$ is the normal strain, $var element = document.getElementById("moose-equation-f8d5b71c-f927-4e35-bab0-d454a520f8d2");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the density, $var element = document.getElementById("moose-equation-c5ea7c19-0f78-481b-9589-03ae0902a056");katex.render("V_p = \\sqrt{\\frac{E}{\\rho}}", element, {displayMode:false,throwOnError:false});$ is the P-wave speed and $var element = document.getElementById("moose-equation-97b4812d-888c-4f85-917e-be7a50c617b5");katex.render("\\frac{du}{dt}", element, {displayMode:false,throwOnError:false});$ is the particle velocity. Note that for a 2D or a 3D problem, the P-wave speed is

$(2)var element = document.getElementById("moose-equation-58065848-d4b8-43a9-9a3b-b6d4e2a8b779");katex.render(" V_p = \\sqrt{\\frac{E(1-\\nu)}{(1+\\nu)(1-2\\nu)}}", element, {displayMode:true,throwOnError:false});$

Note that stress in the above equation is directly proportional to the particle velocity, which makes this boundary condition analogous to a viscous damper with damping coefficient of $var element = document.getElementById("moose-equation-fc68bb5e-9d6c-4bcb-a49c-8d50a578a03b");katex.render("\\rho V_p", element, {displayMode:false,throwOnError:false});$ . Therefore, truncating the soil domain and placing this damper at the end of the domain is equivalent to simulating wave propagation in an infinite soil column provided the soil is made of linear elastic material and the wave is normally incident on the boundary.

If the soil is not linear elastic or if the wave is incident at an angle, the waves are not completely absorbed by the Lysmer dampers. However, if this non-reflecting boundary is placed sufficiently far from the source, the reflected waves will be dissipated through Rayliegh damping or material hysteresis (provided the soil material models hysteresis) before it reaches the region of interest again.

Input Parameters

betaThe beta parameter for Newmark time integration.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The beta parameter for Newmark time integration.
boundaryThe list of boundary IDs from the mesh where this boundary condition will be applied
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this boundary condition will be applied
densityDensity of the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Density of the material.
gammaThe gamma parameter for Newmark time integration.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The gamma parameter for Newmark time integration.
p_wave_speedP-wave speed of the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:P-wave speed of the material.
shear_wave_speedshear wave speed of the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:shear wave speed of the material.

Required Parameters

accelerationsThe vector of acceleration variables that are coupled to the displacement variables. The size of this vector must be same as that of displacements.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The vector of acceleration variables that are coupled to the displacement variables. The size of this vector must be same as that of displacements.
active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
alpha0The alpha parameter for HHT time integration.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The alpha parameter for HHT time integration.
displacementsThe vector of displacement variables. The size of this vector must be same as the number of dimensions.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The vector of displacement variables. The size of this vector must be same as the number of dimensions.
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
velocitiesThe vector of velocity variables that are coupled to the displacement variables. The size of this vector must be same as that of displacements.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The vector of velocity variables that are coupled to the displacement variables. The size of this vector must be same as that of displacements.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.

Advanced Parameters

Input Files

(test/tests/bcs/nonreflecting_bc/non_reflecting_bc_error.i)

References

J. Lysmer and R. L. Kuhlemeyer. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 95(4):859–878, 1969.

@article{lysmer1969finite,
    author = "Lysmer, J. and Kuhlemeyer, R. L.",
    title = "Finite dynamic model for infinite media",
    journal = "Journal of the Engineering Mechanics Division",
    volume = "95",
    number = "4",
    pages = "859--878",
    year = "1969",
    publisher = "ASCE"
}

(test/tests/bcs/nonreflecting_bc/non_reflecting_bc_error.i)

# This input file will not run and should not, it is used for error checking.

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[BCs]
  [./test]
    type = NonReflectingBC
    displacements = 'disp_x disp_y'
    accelerations = 'disp_x disp_y'
    velocities = 'disp_x disp_y'
    variable = 'disp_x'
    component = 0
    boundary = 'left'
    beta = 1
    gamma = 1
    shear_wave_speed = 1.0
    p_wave_speed = 3.5
    density = 1.0
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  num_steps = 1
[]

[Outputs]
[]

Description
Input Parameters
Input Files
References

Usage

Development

Demonstration