FEM.Elements.E1D package¶

Collection of 1D Elements

Submodules¶

FEM.Elements.E1D.CubicElement module¶

Lineal element definition

class FEM.Elements.E1D.CubicElement.CubicElement(coords: ndarray, gdl: ndarray, n: int = 4, **kargs)¶

Bases: Element1D

Create a cubic element

Parameters:

coords (np.ndarray) – Element coordinates matrix
gdl (np.ndarray) – Element degree of freedom matrix
n (int, optional) – Number of gauss points. Defaults to 4.

dpsis(z: ndarray) → ndarray¶

Calculates the shape functions derivatives of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function derivatives evaluated in Z points
Return type:: np.ndarray

psis(z: ndarray) → ndarray¶

Calculates the shape functions of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function evaluated in Z points
Return type:: np.ndarray

FEM.Elements.E1D.Element1D module¶

1D Elements general class

class FEM.Elements.E1D.Element1D.Element1D(coords: ndarray, gdl: ndarray, n: int, **kargs)¶

Bases: Element, LinearScheme

Create a 1D Element

Parameters:

coords (np.ndarray) – Coordinates matrix
gdl (np.ndarray) – Degree of freedom matrix
n (int) – Number of Gauss Points used in integration

draw() → None¶: Create a element graph over domain

isInside(x: ndarray) → ndarray¶

Test if a given points is inside element domain

Parameters:: x (np.ndarray) – Point to be tested
Returns:: Bolean array of test result
Return type:: np.ndarray

jacobianGraph() → None¶: Jacobian is constant in lineal elements

FEM.Elements.E1D.EulerBernoulliElement module¶

Creates a 1D beam element

class FEM.Elements.E1D.EulerBernoulliElement.EulerBernoulliElement(coords, gdl, n=2, nvn=2)¶

Bases: LinealElement

Creates a 1D beam element

dhermit(z: ndarray) → ndarray¶

Calculates the shape functions derivatives of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function derivatives evaluated in Z points
Return type:: np.ndarray

giveSolution(SVSolution: bool = False, domain: str = 'domain') → ndarray¶

Calculate the interpolated solution over element domain

Parameters:: SVSolution (bool, optional) – To calculate second variable solutions. Defaults to False.
Returns:: Arrays of coordinates, solutions and second variables solutions.
Return type:: np.ndarray

giveSolutionPoint(Z: ndarray, SVSolution: bool = False) → ndarray¶

Calculate the interpolated solution over given set of points

Parameters:

Z (np.ndarray) – Natural coordintas to extract the solution
SVSolution (bool, optional) – To calculate second variable solution. Defaults to False.

Returns:

Arrays of coordinates, solutions and second variables solutions.

Return type:

np.ndarray

hermit(z: ndarray) → ndarray¶

Calculates the shape functions of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function evaluated in Z points
Return type:: np.ndarray

FEM.Elements.E1D.LinealElement module¶

Lineal element definition

class FEM.Elements.E1D.LinealElement.LinealElement(coords: ndarray, gdl: ndarray, n: int = 2, **kargs)¶

Bases: Element1D

Create a lineal element

Parameters:

coords (np.ndarray) – Element coordinates matrix
gdl (np.ndarray) – Element degree of freedom matrix
n (int, optional) – Number of gauss points. Defaults to 3.

dpsis(z: ndarray) → ndarray¶

Calculates the shape functions derivatives of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function derivatives evaluated in Z points
Return type:: np.ndarray

psis(z: ndarray) → ndarray¶

Calculates the shape functions of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function evaluated in Z points
Return type:: np.ndarray

FEM.Elements.E1D.LinearScheme module¶

Defines a linear scheme for lineal elements

class FEM.Elements.E1D.LinearScheme.LinearScheme(n: int, **kargs)¶

Bases: object

Creates a Linear Scheme

Parameters:: n (int) – Number of gauss points

FEM.Elements.E1D.OriHinge module¶

class FEM.Elements.E1D.OriHinge.OriHinge(coords: ndarray, gdl: ndarray, **kargs)¶

Bases: LinealElement, LinearScheme

calculate_theta()¶

calculate_vectors()¶

dia(a, b)¶

elementMatrix()¶

elementMatrixNonLineal()¶

get_M(theta)¶

get_internal_force()¶

get_kf(theta)¶

get_theta_from_u()¶

jacobian()¶

set_internal_force(internal_force)¶

set_kf(kf: Callable)¶

FEM.Elements.E1D.QuadraticElement module¶

Lineal element definition

class FEM.Elements.E1D.QuadraticElement.QuadraticElement(coords: ndarray, gdl: ndarray, n: int = 4, **kargs)¶

Bases: Element1D

Create a quadratic element

Parameters:

coords (np.ndarray) – Element coordinates matrix
gdl (np.ndarray) – Element degree of freedom matrix
n (int, optional) – Number of gauss points. Defaults to 3.

dpsis(z: ndarray) → ndarray¶

Calculates the shape functions derivatives of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function derivatives evaluated in Z points
Return type:: np.ndarray

psis(z: ndarray) → ndarray¶

Calculates the shape functions of the lineal element of a given natural coordinates

Parameters:: z (np.ndarray) – Natural coordinates matrix
Returns:: Shape function evaluated in Z points
Return type:: np.ndarray