pyva.geometry.meshClasses.RegShape2D

class pyva.geometry.meshClasses.RegShape2D(X0, Y0, X1, Y1, NX, NY, doftype=DOFtype(typestr='displacement'), shape=<function RegShape2D.<lambda>>)

Bases: RegMesh2D

This class deals with shapes mapped on regular and flat 2D meshes. These meshes are very useful for radiation stiffness calculation of vibrating structures

Check if required, usefull for function based shapes. Note, that there is no frequency depence!

__init__(X0, Y0, X1, Y1, NX, NY, doftype=DOFtype(typestr='displacement'), shape=<function RegShape2D.<lambda>>)

Class constructor of RegShape2D

Parameters:

X0 (float) – lowest X position
Y0 (float) – lowest Y position
X1 (float) – highest X position
Y1 (float) – highest Y position
NX (float) – number of nodes in X-direction
NY (float) – number of nodes in Y-direction
doftype (DOFtype, optional) – type of shape. The default is dof.DOFtype(typestr=’displacement’).
shape (function of (x,y), optional) – Function for shape. The default is a function that is 1.

Returns:

None. – shape: shape of mesh, 2D fun or ndarray of shape NX,NY function is only defines in mesh area the rest is ignored
Examples – >>> regShape(0,0,0.8,0.9,10,10)

Methods

`Zvec`([normalise])	Vector of shape values
`__init__`(X0, Y0, X1, Y1, NX, NY[, doftype, ...])	Class constructor of RegShape2D
`distance`()	Calculate the distances between nodes of mesh
`mean_square`(normalise)	mean square value
`nodes`([index])	Node coordinates
`normalised_shape`([N])	Normalised reshape considering integration over element area
`plot3d`([fig])	3D plot for shapes
`shapefun`(X, Y)	Shape function with consideration of mesh limits

Attributes

`Nmesh`	Number of nodes
`X`	x-coordinates of mesh
`Y`	y-coordinates of mesh
`area`	Returns area of full mesh.
`dA`
`ks`	Wavenumber parameter from Langley [Lan2007]
`shape`

property Nmesh

Number of nodes

Return type:: int

property X

x-coordinates of mesh

Returns:: x-node positions.
Return type:: ndarray

property Y

y-coordinates of mesh

Returns:: y-node positions.
Return type:: ndarray

Zvec(normalise=False)

Vector of shape values

Parameters:: normalise (bool, optional) – switch if normalisation shall be used. The default is False.
Returns:: shape vector.
Return type:: ndarray

property area

Returns area of full mesh. inlcuding edge elements

Returns:: mesh area.
Return type:: float

distance()

Calculate the distances between nodes of mesh

This method provides the occuring distances in a mesh in a reduced way. Regular meshes have many repeating distances, thus this method returns a unique array of distances and an index to reconstruct the upper triangular matrix

dist[index] gives the full triangular matrix

Returns:

ndarray – dist : unique distances
nd.adday of int – index : index to reconstruct all distances from dist

property ks

Wavenumber parameter from Langley [Lan2007]

Technically with is the wavenumber that korresponds to the smallest allowed wavelength of the mesh represented by the diagonal length of the element

Returns:: wavenumber.
Return type:: float

mean_square(normalise)

mean square value

Parameters:: normalise (bool) – switch if normalisation shall be used.
Returns:: mean square.
Return type:: float

nodes(index='all')

Node coordinates

Parameters:

index (int or str, optional) – index of node. The default is ‘all’.

Returns:

ndarray – x,y coordinates of mesh or x of 1st index.
float – y of 2nd index.

normalised_shape(N=2)

Normalised reshape considering integration over element area

Integrates the shape function around the node to get better results when nodal shape value if not representing the average value in the node vincinity

Parameters:: N (int) – oversamping for integration. The default is 2.
Returns:: normalised shape
Return type:: ndarray

plot3d(fig=1)

3D plot for shapes

Parameters:: fig (int, optional) – figure identifier. The default is 1.
Return type:: None.

shapefun(X, Y)

Shape function with consideration of mesh limits

Parameters:

X (float) – x-coordinate.
Y (TYPE) – y-coordinate.

Returns:

res – of shape dimension.

Return type:

ndarray