EnhancedQuad#

model.element("EnhancedQuad", tag, nodes, section[, pressure, rho, b1, b2])
Parameters:

  • tag – integer, unique element object 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 Materials

  • 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

Fig. 30 EnhancedQuad element node numbering#

This element implements the Q1/E4 assumed strain interpolation. 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#