FEM.Elements package

Elements structures

Subpackages

• FEM.Elements.E1D package
  • Submodules
  • FEM.Elements.E1D.CubicElement module
    • CubicElement
      • CubicElement.dpsis()
      • CubicElement.psis()
  • FEM.Elements.E1D.Element1D module
    • Element1D
      • Element1D.draw()
      • Element1D.isInside()
      • Element1D.jacobianGraph()
  • FEM.Elements.E1D.EulerBernoulliElement module
    • EulerBernoulliElement
      • EulerBernoulliElement.dhermit()
      • EulerBernoulliElement.giveSolution()
      • EulerBernoulliElement.giveSolutionPoint()
      • EulerBernoulliElement.hermit()
  • FEM.Elements.E1D.LinealElement module
    • LinealElement
      • LinealElement.dpsis()
      • LinealElement.psis()
  • FEM.Elements.E1D.LinearScheme module
    • LinearScheme
  • FEM.Elements.E1D.QuadraticElement module
    • QuadraticElement
      • QuadraticElement.dpsis()
      • QuadraticElement.psis()
• FEM.Elements.E2D package
  • Submodules
  • FEM.Elements.E2D.Element2D module
    • Element2D
      • Element2D.draw()
      • Element2D.isInside()
      • Element2D.jacobianGraph()
  • FEM.Elements.E2D.LTriangular module
    • TRIANGULAR ELEMENT
      • Shape Functions
      • Shape Functions Derivatives
    • LTriangular
      • LTriangular.dpsis()
      • LTriangular.psis()
  • FEM.Elements.E2D.QTriangular module
    • TRIANGULAR SECOND ORDER ELEMENT
      • Shape Functions
      • Shape Functions Derivatives
    • QTriangular
      • QTriangular.dpsis()
      • QTriangular.psis()
  • FEM.Elements.E2D.Quadrilateral module
    • QUADRILATERAL ELEMENT
      • Shape Functions
      • Shape Functions Derivatives
    • Quadrilateral
      • Quadrilateral.dpsis()
      • Quadrilateral.psis()
  • FEM.Elements.E2D.RectangularScheme module
    • RectangularScheme
  • FEM.Elements.E2D.Serendipity module
    • QUADRILATERAL SERENDIPITY ELEMENT
      • Shape Functions
      • Shape Functions Derivatives
    • Serendipity
      • Serendipity.dpsis()
      • Serendipity.psis()
  • FEM.Elements.E2D.TriangularScheme module
    • TriangularScheme
• FEM.Elements.E3D package
  • Submodules
  • FEM.Elements.E3D.Brick module
    • BRICK ELEMENTS
      • Brick
      • BrickO2
    • Brick
      • Brick.dpsis()
      • Brick.psis()
    • BrickO2
      • BrickO2.dpsis()
      • BrickO2.psis()
  • FEM.Elements.E3D.BrickScheme module
    • BrickScheme
  • FEM.Elements.E3D.Element3D module
    • Element3D
      • Element3D.draw()
      • Element3D.isInside()
      • Element3D.jacobianGraph()
  • FEM.Elements.E3D.Tetrahedral module
    • TETRAHEDRAL ELEMENTS
      • Tetrahedral
      • TetrahedralO2
    • Tetrahedral
      • Tetrahedral.dpsis()
      • Tetrahedral.inverseMapping()
      • Tetrahedral.psis()
    • TetrahedralO2
      • TetrahedralO2.dpsis()
      • TetrahedralO2.inverseMapping()
      • TetrahedralO2.psis()
  • FEM.Elements.E3D.TetrahedralScheme module
    • TetrahedralScheme

Submodules

FEM.Elements.Element module

Element class

class FEM.Elements.Element.Element(coords: ndarray, _coords: ndarray, gdl: ndarray, border: bool = False, fast: bool = False)

Bases: object

Generates a generic element.

Parameters:

• coords (np.ndarray) – Vertical coordinates matrix

• _coords (np.ndarray) – Vertical coordinates matrix for graphical interfaces

• gdl (np.ndarray) – Degree of freedom matrix. Each row is a variable.

• border (bool) – True if the element is part of the border domain of another element.

J(z: ndarray) → ndarray

Calculate the jacobian matrix over a set of natural coordinates

Parameters:

z (np.ndarray) – Natural coordinates matrix. Each row is a dimension, each column is a point.

Returns:

Jacobian’s matrices and shape function derivatives

Return type:

np.ndarray

T(z: ndarray) → ndarray

Give the global coordinates of given natural coordiantes over element

Parameters:

z (np.ndarray) – Natural coordinates matrix. Each row is a dimension, each column is a point.

Returns:

Global coordinates matrix and shape functions

Return type:

np.ndarray

TS(z)

Returns the transformation of a given set of points in the element. This method is used for border elements

Parameters:

z (np.ndarray) – Natural coordinates matrix. Each row is a dimension, each column is a point.

Returns:

Global coordinates matrix

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.

• domain (str, optional) – Where to give the solution [‘domain’ or ‘gauss-points’]. Defaults to ‘domain’.

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

integrate(f: Callable) → float

Calculate the integral of f function over element domain

Parameters:

f (function) – Function to be integrated

Returns:

Integral value

Return type:

float

inverseMapping(x0: ndarray, n: int = 100) → ndarray

Give the natural coordinates of given global coordinates over elements using Newton’s method

Parameters:

• x0 (np.ndarray) – Global coordinates matrix

• n (int, optional) – Máximun number of iterations. Defaults to 100.

Returns:

Natural coordinates matrix

Return type:

np.ndarray

restartMatrix() → None

Sets all element matrices and vectors to 0

setUe(U: ndarray) → None

Assing element local solution

Parameters:

U (np.ndarray) – Global solution