PML3DElement

PML3DElement(ndof: int, material: Material, PML_Thickness: float, meshType: str, meshTypeParameters: Union[List[float], str], gamma: float = 0.5, beta: float = 0.25, eta: float = 1.0 / 12.0, ksi: float = 1.0 / 48.0, m: float = 2.0, R: float = 1e-08, Cp: Optional[float] = None, alpha0: Optional[float] = None, beta0: Optional[float] = None, **kwargs)

Bases: Element

Three-dimensional perfectly matched layer continuum element.

This eight-node element augments the standard brick with additional PML degrees of freedom, requiring 9 DOFs per node. It is used to absorb outgoing waves at domain boundaries in 3D wave-propagation analyses.

Tcl form

element PML <tag> <n1> ... <n8> <matTag> <thick> "<meshType>" <params...> "-Newmark" <gamma> <beta> <eta> <ksi> [-alphabeta alpha0 beta0 | -m m -R R [-Cp Cp]]

Warning

The assigned material must be a 3D ElasticIsotropicMaterial. Other nDMaterial types are rejected at construction time.

Note

meshType must be box or general (case-insensitive).
meshTypeParameters must provide six numeric values describing the local PML mesh orientation and extent.
Either alpha0 and beta0 must both be supplied, or neither.

Attributes:

Name	Type	Description
`PML_Thickness`		Physical thickness of the PML layer.
`meshType`		PML mesh type passed to OpenSees (`box` or `general`).
`meshTypeParameters`		Six numeric mesh-orientation parameters.
`gamma`		Newmark gamma parameter.
`beta`		Newmark beta parameter.
`eta`		Newmark eta parameter.
`ksi`		Newmark ksi parameter.
`m`		PML attenuation parameter used when `alpha0`/`beta0` are omitted.
`R`		PML reflection parameter used when `alpha0`/`beta0` are omitted.
`Cp`		Optional P-wave speed override for the PML formulation.
`alpha0`		Optional PML alpha parameter paired with `beta0`.
`beta0`		Optional PML beta parameter paired with `alpha0`.

Example

from femora.core.model import Model

model = Model()
mat = model.material.nd.elastic_isotropic(
    user_name="PMLMat",
    E=2.0e7,
    nu=0.25,
    rho=2200.0,
)
ele = model.element.brick.pml3d(
    ndof=9,
    material=mat,
    PML_Thickness=1.0,
    meshType="box",
    meshTypeParameters=[1.0, 0.0, 0.0, 0.0, 1.0, 0.0],
)
print(ele.tag)

Create a PML3DElement with validated PML and Newmark parameters.

Parameters:

Name	Type	Description	Default
`ndof`	`int`	Number of DOFs per node. Must be 9 for this element.	required
`material`	`Material`	Managed isotropic elastic 3D `nDMaterial`.	required
`PML_Thickness`	`float`	Thickness of the PML layer.	required
`meshType`	`str`	`box` or `general` mesh type passed to OpenSees.	required
`meshTypeParameters`	`Union[List[float], str]`	Six numeric values or a comma-separated string describing the PML mesh orientation.	required
`gamma`	`float`	Newmark gamma parameter.	`0.5`
`beta`	`float`	Newmark beta parameter.	`0.25`
`eta`	`float`	Newmark eta parameter.	`1.0 / 12.0`
`ksi`	`float`	Newmark ksi parameter.	`1.0 / 48.0`
`m`	`float`	PML attenuation parameter when `alpha0`/`beta0` are omitted.	`2.0`
`R`	`float`	PML reflection parameter when `alpha0`/`beta0` are omitted.	`1e-08`
`Cp`	`Optional[float]`	Optional P-wave speed override.	`None`
`alpha0`	`Optional[float]`	Optional PML alpha parameter; must be paired with `beta0`.	`None`
`beta0`	`Optional[float]`	Optional PML beta parameter; must be paired with `alpha0`.	`None`
`**kwargs`		Additional element parameters stored on the base element.	`{}`

Raises:

Type	Description
`ValueError`	If the material is incompatible, if `ndof` is not 9, or if any PML or Newmark parameter is invalid.