dktp

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dktp

Purpose

2-D 9-DOF Discrete Kirchhoff triangle

Description

In a model description matrix, element property rows for dktp elements follow the standard format

 [n1 n2 n3 MatID ProID EltID Theta]

giving the node identification numbers ni, material MatID, property ProID. Other optional information is EltID the element identifier, Theta the angle between material x axis and element x axis (currently unused)

The elements support isotropic materials declared with a material entry described in m_elastic. Element property declarations follow the format described in p_shell.

The dktp element uses the et*dktp routines.

There are three vertices nodes for this triangular Kirchhoff plate element and the normal deflection W(x,y) is cubic along each edge.

We start with a 6-node triangular element with a total D.O.F = 21 :

five degrees of freedom at corner nodes :

W(x,y) ,

¶ W

¶x
,

¶ W

¶y
, _x , _y (deflection W and rotations )
two degrees of freedom _x and _y at mid side nodes.

Then, we impose no transverse shear deformation

_xz = 0 and

_yz = 0 at selected nodes to reduce the total DOF = 21 - 6*2 = 9 :

three degrees of freedom at each of the vertices of the triangle.

W(x,y) , _x=(

¶ W

¶x
) , _y=(

¶ W

¶y
)

The coordinates of the reference element's vertices are S₁^{^} (0.,0.), S₂^{^} (1.,0.) and S₃^{^} (0.,1.).

Surfaces are integrated using a 3 point rule