The Discrete Kirchoff Triangle (DKT) plate-bending formulation is an isoparametric thin-shell formulation for plate-bending behavior.

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

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

There are three nodes defined for this formulation. These nodes are numbered from 1 to 3 in a counter-clockwise direction.

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

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

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 $k$

Stiffness Matrix Formulation

The DKT element is an isoparametric element and is formulated in the natural triangular coordinate system, $\xi$ and $\eta$.

The local stiffness matrix is computed using a strain-displacement matrix and a constitutive matrix. Gauss integration is performed on the product of $[B]^T [D_b] [B]$ using a three-point triangular Gauss integration scheme.

$[K_e]=\int_A [B]^T [D_b] [B] \,dx\,dy$

$[K_e]=\int\limits_{0}^{1}\int\limits_{0}^{1-\eta} B^T D_b B \det J \,d \xi\,d \eta$