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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

  ,  θx  ,  θy   (deflection  W    and    rotations    θ)

• two degrees of freedom θ_x  and  θ_y at mid side nodes.

Then, we impose no transverse shear deformation γ_xz = 0 and γ_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)  ,   θx=(

  ∂ W  ∂x

  )  ,  θy=(

  ∂ W  ∂y

  )

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 ω_k = 1 /3 and b_k mid side node.

See also

fe_mat, m_elastic, p_shell, fe_mk, feplot