Q4-Q9

A Quad element uses the standard Lagrange isoparametric formulation.

PythonTcl

Model.element("Quad", tag, nodes, section[, pressure, rho, b1, b2])

Construct a BasicQuad and add it to the Model.

Parameters:

tag: integer

unique Element tag

nodes: tuple of four, eight or nine Node tags

a tuple of four element nodes in counter-clockwise order.

section

tuple or int. If int, it is the tag of a previously defined PlaneStress or PlaneStrain section. If tuple, it is a tuple of the form (thick, type, material) where

thick float	element thickness
type str	string representing material behavior. The type parameter can be either "PlaneStrain" or "PlaneStress"
material integer	tag of an Multiaxial

pressure: float

surface pressure (optional, default = 0.0)

rho: float

element mass density (per unit volume) from which a lumped element mass matrix is computed (optional, default=0.0). See Mass Sources for more information.

b1: float

constant body forces defined in the domain (optional, default=0.0)

b2: float

constant body forces defined in the domain (optional, default=0.0)

Quad element node numbering

Output

The valid eleResponse queries to this element are "forces", "stresses", and "material $matNum matArg1 matArg2 ..." where matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.

Furthermore, stresses can be extrapolated from quadrature points to nodes using the "stressAtNodes" response. The stresses are computed at the four gauss points of the element and then extrapolated to the nodes using the inverse of the interpolation matrix. For a four-node quadrilateral this is given by:

\[\begin{split}\left[\begin{array}{cccc} 1+\frac{1}{2} \sqrt{3} & -\frac{1}{2} & 1-\frac{1}{2} \sqrt{3} & -\frac{1}{2} \\ -\frac{1}{2} & 1+\frac{1}{2} \sqrt{3} & -\frac{1}{2} & 1-\frac{1}{2} \sqrt{3} \\ 1-\frac{1}{2} \sqrt{3} & -\frac{1}{2} & 1+\frac{1}{2} \sqrt{3} & -\frac{1}{2} \\ -\frac{1}{2} & 1-\frac{1}{2} \sqrt{3} & -\frac{1}{2} & 1+\frac{1}{2} \sqrt{3} \end{array}\right]\end{split}\]

Examples

Quadrilateral Elements

../../../../../examples/plane/plane-0002.html

References

Code Developed by: Michael H. Scott, Claudio M. Perez