CP4

Bilinear Quadrilateral

• Number of Nodes: 4

• Number of DoFs: 2 (Translation, Translation)

• DoF Label: U1, U2

• Integration Scheme: 2nd Order Gaussian (Full) or 1st Order Gaussian (Reduced)

• Supports Body Force

• Constant Consistent Mass Matrix With Same Order Integration

encoding

Syntax

element CP4 (1) (2...5) (6) [7] [8] [9] [10]
# (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] bool string, reduced integration switch, default: false
# [9] bool string, nonlinear geometry switch, default: false
# [10] double, hourglassing penalty multiplier, default: 1.0

Remarks

• The CP4 element resembles CPS4 and CPE4 elements in ABAQUS.

• The full integration scheme uses 2-by-2 Gaussian scheme and the reduced integration uses a single integration point at the center of the element.

• The reduced integration scheme also imports anti-hourglassing technique.

For the hourglassing control, see 10.1016/0045-7825(84)90067-7. The hourglassing penalty multiplier (denoted as $\mu$) is an overall multiplier that is applied to the hourglassing stiffness matrix.

$$\mu\mathbf{\gamma}\mathbf{\gamma}^\mathrm{T}.$$

In the above, $\mathbf{\gamma}$ is identical to Eq. (19) in the reference paper. Thus, $\mu$ shall be set to some value proportional to the elastic modulus.