The Discrete Kirchoff Quadrilateral (DKQ) plate-bending formulation is an isoparametric thin-shell formulation for plate-bending behavior. The formulation is based on the Kirchoff assumption that neglects shear strain energy.

References

1. Kansara, K. "Development of Membrane, Plate, and Flat Shell Elements in Java." Thesis Submitted at Virginia Polytechnic Institute & State University. May 2004

Degrees of Freedom

The DKQ formulation contains three degrees-of-freedom (DoFs) at each node:

1. z-translation
2. x-rotation
3. y-rotation

There are four nodes defined for this formulation. These nodes are numbered from 1 to 4 in a counter-clockwise direction. An additional four mid-side nodes are introduced during the formulation, but they do not appear in the final stiffness matrix.

The local stiffness matrix is formulated with the following degree-of-freedom order:

$\begin{bmatrix}w_1 & \theta_{1,x} & \theta_{1,y} & w_2 & \theta_{2,x} & \theta_{2,y} & w_3 & \theta_{3_x} & \theta_{3,y} & w_4 & \theta_{4,x} & \theta_{4,y} \end{bmatrix}$

Where:

$w_k=$Local z-translation at node $k$

$\theta_{k,x}=$Rotation about the local x-axis at node $k$

$\theta_{k,y}=$Rotation about the local y-axis at node $k$

Node Numbering

Nodes are numbered in the standard counter-clockwise convention.

Nodes 1, 2, 3 and 4 are vertex nodes.

Nodes 5, 6, 7 and 8 are mid-side nodes that do not appear in the stiffness matrix.