BasicQuad

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BasicQuad#

A BasicQuad element uses the standard Lagrange isoparametric formulation.

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, 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 General

  • 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)

  • 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)

../../../../../_images/Q9.svg

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:

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

Example#

The following example constructs a quad element for use in a plane stress problem with tag 1 between nodes 1, 2, 3, 4 with an nDMaterial of tag 1.

model.element("quad", 1, (1,2,3,4), (1.0, "PlaneStress", 1), (b1, b2, b3))

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

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