Element#

class felupe.Quad[source]#

Bases: Element

Quadrilateral element with linear shape functions.

              ^ s
 3 (-1/ 1)    |            2 ( 1/ 1)
  o-----------|-----------o
  |           |           |
  |           |           |
  |           |           |
  |           |           |
  |      -----|-----------|-----> r
  |           |           |
  |           |           |
  |                       |
  |                       |
  o-----------------------o
0 (-1,-1)                  1 ( 1/-1)

points#

Array with point locations in natural coordinate system

Type: ndarray

function(rs)[source]#

Linear quadrilateral - shape functions.

\[\begin{split}\boldsymbol{h}(\boldsymbol{r}) = \frac{1}{4} \begin{bmatrix} (1-r)(1-s) \\ (1+r)(1-s) \\ (1+r)(1+s) \\ (1-r)(1+s) \end{bmatrix}\end{split}\]

Parameters: rs (ndarray) – Point as coordinate vector for shape function evaluation
Returns: Shape functions evaluated at given location
Return type: ndarray

gradient(rs)[source]#

Linear quadrilateral - gradient of shape functions.

\[\begin{split}\frac{\partial \boldsymbol{h}}{\partial \boldsymbol{r}} = \frac{1}{4} \begin{bmatrix} -(1-s) & -(1-r) \\ (1-s) & -(1+r) \\ (1+s) & (1+r) \\ -(1+s) & (1-r) \end{bmatrix}\end{split}\]

Parameters: rs (ndarray) – Point as coordinate vector for gradient of shape function evaluation
Returns: Gradient of shape functions evaluated at given location
Return type: ndarray

class felupe.Hexahedron[source]#

Bases: Element

function(rst)[source]#: linear hexahedron shape functions

gradient(rst)[source]#: linear hexahedron gradient of shape functions

class felupe.Triangle[source]#

Bases: Element

function(rs)[source]#: linear triangle shape functions

gradient(rs)[source]#: linear triangle gradient of shape functions

class felupe.Tetra[source]#

Bases: Element

function(rst)[source]#: linear tetrahedral shape functions

gradient(rst)[source]#: linear tetrahedral gradient of shape functions

class felupe.ConstantQuad[source]#

Bases: Element

Quadrilateral element with constant shape functions.

              ^ s
 3 (-1/ 1)    |            2 ( 1/ 1)
  o-----------|-----------o
  |           |           |
  |           |           |
  |           |           |
  |           |           |
  |      -----|-----------|-----> r
  |           |           |
  |           |           |
  |                       |
  |                       |
  o-----------------------o
0 (-1,-1)                  1 ( 1/-1)

points#

Array with point locations in natural coordinate system

Type: ndarray

function(rst)[source]#

Constant quadrilateral - shape functions.

\[\boldsymbol{h}(\boldsymbol{r}) = \begin{bmatrix} 1 \end{bmatrix}\]

Parameters: rs (ndarray) – Point as coordinate vector for shape function evaluation
Returns: Shape functions evaluated at given location
Return type: ndarray

gradient(rst)[source]#

Constant quadrilateral - gradient of shape functions.

\[\frac{\partial \boldsymbol{h}}{\partial \boldsymbol{r}} = \begin{bmatrix} 0 \end{bmatrix}\]

Parameters: rs (ndarray) – Point as coordinate vector for gradient of shape function evaluation
Returns: Gradient of shape functions evaluated at given location
Return type: ndarray

class felupe.ConstantHexahedron[source]#

Bases: Element

function(rst)[source]#: constant hexahedron shape functions

gradient(rst)[source]#: constant hexahedron gradient of shape functions

class felupe.QuadraticHexahedron[source]#

Bases: Element

function(rst)[source]#: quadratic serendipity hexahedron shape functions

gradient(rst)[source]#: quadratic serendipity hexahedron gradient of shape functions

class felupe.TriQuadraticHexahedron[source]#

Bases: Element

function(rst)[source]#: quadratic hexahedron shape functions

gradient(rst)[source]#: quadratic hexahedron gradient of shape functions

class felupe.QuadraticTriangle[source]#

Bases: Element

function(rs)[source]#: quadratic triangle shape functions

gradient(rs)[source]#: quadratic triangle gradient of shape functions

class felupe.QuadraticTetra[source]#

Bases: Element

function(rst)[source]#: quadratic tetrahedral shape functions

gradient(rst)[source]#: quadratic tetrahedral gradient of shape functions

class felupe.TriangleMINI(bubble_multiplier=1.0)[source]#

Bases: Element

function(rs)[source]#: linear bubble-enriched triangle shape functions

gradient(rs)[source]#: linear bubble-enriched triangle gradient of shape functions

class felupe.TetraMINI(bubble_multiplier=1.0)[source]#

Bases: Element

function(rst)[source]#: linear bubble-enriched tetrahedral basis functions

gradient(rst)[source]#: linear bubble-enriched tetrahedral derivative of basis functions

felupe.ArbitraryOrderLagrangeElement#: alias of ArbitraryOrderLagrange