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2-D 9-DOF Discrete Kirchhoff triangle
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 :
|, θx , θy (deflection W and rotations θ)|
Then, we impose no transverse shear deformation γxz = 0 and γyz = 0 at selected nodes to reduce the total DOF = 21 − 6*2 = 9 :
|W(x,y) , θx=(|
|) , θy=(|
The coordinates of the reference element's vertices are S_1 (0.,0.), S_2 (1.,0.) and S_3 (0.,1.).
Surfaces are integrated using a 3 point rule ωk = 1 /3 and bk mid side node.
fe_mat, m_elastic, p_shell, fe_mk, feplot