EnhancedQuad

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EnhancedQuad#

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

Theory#

../../../../../_images/Q4.svg

EnhancedQuad element node numbering#

This element implements the Q1/E4 assumed strain interpolation [4]. The formulation is generally credited to Taylor, Beresford, and Wilson (1976) [1]. A variational basis for the formulation is given by Simo and Rifai (1990) [2].

\[\begin{split}\mathbf{M}_{\xi}=\left[\begin{array}{llll} \xi & 0 & 0 & 0 \\ 0 & \eta & 0 & 0 \\ 0 & 0 & \xi & \eta \end{array}\right]\end{split}\]

For linear-elastic response, the formulation is equivalent to a Hellinger-Reissner element [3] with interpolation

\[\begin{split}\mathbf{P}_{\xi}=\left[\begin{array}{cccccccc} 1 & 0 & 0 & \eta & 0 & \xi \eta & 0 & 0 \\ 0 & 1 & 0 & 0 & \xi & 0 & \xi \eta & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & \xi \eta \end{array}\right]\end{split}\]

References#

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