(S)GCMQ

Generalised Conforming Mixed Quadrilateral With Drilling DoFs

• Number of Nodes: 4
• Number of DoFs: 3 (Translation, Translation, Rotation)
• DoF Label: U1, U2, UR3
• Supports Body Force
• Constant Consistent Mass Matrix With Same Order Integration

References

1. 10.1002/nme.6066
2. 10.1016/j.engstruct.2019.109592
3. 10.1016/j.engstruct.2020.110760

Syntax

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element GCMQI (1) (2...5) (6) [7] [8]
element GCMQL (1) (2...5) (6) [7] [8]
element GCMQG (1) (2...5) (6) [7] [8]
# (1) int, unique element tag
# (2...5) int, node i, j, k, l
# (6) int, material tag
# [7] double, element thickness, default: 1.0
# [8] double, objective length, default: -1.0 (disabled)

element SGCMQI (1) (2...5) (6) [7] [8]
element SGCMQL (1) (2...5) (6) [7] [8]
element SGCMQG (1) (2...5) (6) [7] [8]
# (1) int, unique element tag
# (2...5) int, node i, j, k, l
# (6) int, material tag
# [7] double, element thickness, default: 1.0
# [8] double, objective length, default: -1.0 (disabled)

Remarks

• Three integration schemes are available: "I", "L" and "G".
• "I": Five-Point Irons Scheme
• "L": 3^rd Order Lobatto Scheme
• "G": 3^rd Order Gauss Scheme
• GCMQ is the full version described in 10.1002/nme.6066 with enhanced strain, SGCMQ is a PS like element with no enhanced strain, the direct result of which is less computation is required (less than CP8R).

The default approach interpolates translations from drilling rotations using edge length, potentially causing severe mesh dependency for drilling DoFs. This is only an issue if the simulation actually uses drilling DoFs, as it can skew the accuracy of connected components. To prevent this, providing a positive objective length [8] triggers an alternative formulation that relies on this specific length for interpolation.