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.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