1. Reference problem#

1.1. Geometry#

The problem being treated is planar. The structure studied is 1 rectangle cut into 2 squares \(\mathit{ABCD}\) and \(\mathit{BEFC}\).

The solution is established with a mesh using 2 QUAD4 corresponding to the 2 squares.

elastic material:

\(E\mathrm{=}10.0\) S.I. units

\(\nu \mathrm{=}0.0\)

We take \(\nu \mathrm{=}0.0\) so that we can deal with this plane problem with a layer of 3D elements by having the plane solution.

	We apply a point force to point \(F\): \(\mathit{FY}\mathrm{=}4.0\) u.s.i.
	Blocks: Point \(A\): \(\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0.\) point \(D\): \(\mathit{DX}\mathrm{=}0.\)
	Linear relationships between degrees of freedom:

load case: cas1

\(1.0\mathit{DX}(E)\mathrm{-}0.5\mathit{DY}(D)\mathrm{-}0.5\mathit{DY}(C)\mathrm{=}0.0\)

\(1.0\mathit{DY}(E)+0.5\mathit{DX}(D)+0.5\mathit{DX}(C)\mathrm{=}0.0\)

load case: cas2

\(1.0\mathit{DY}(E)+0.5\mathit{DY}(D)+0.5\mathit{DY}(C)\mathrm{=}0.0\)

\(1.0\mathit{DY}(B)+0.5\mathit{DY}(C)+0.5\mathit{DY}(F)\mathrm{=}0.0\)

The initial conditions are not important here.