Q4-Q9

A Quad element uses the standard Lagrange isoparametric formulation.

PythonOpenSeesPyTcl

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 element nodes in counter-clockwise order.

section: xara.PlaneSection

Section object defining element material, thickness, and plane stress/strain conditions.

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, optional

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

b2: float, optional

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

Plasticity

../../../../../examples/plane/plane-2001.html

References

Code Developed by: Michael H. Scott