Reference problem
=====================

Geometry
---------


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    :height: 2.011in


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3D plate:

Length :math:`X`: :math:`{L}_{X}\mathrm{=}2.0m`

Length :math:`Y`: :math:`{L}_{Y}=1.0m`

Thickness: :math:`e=0.5m`

Local coordinates of points :math:`A`, :math:`B`,, :math:`C` and :math:`D`

:math:`{X}_{A}=0.0;{Y}_{A}=0.0;{Z}_{A}=0.0`

:math:`{X}_{B}=2.0;{Y}_{B}=0.0;{Z}_{B}=0.0`

:math:`{X}_{C}=2.0;{Y}_{C}=1.0;{Z}_{C}=0.0`

:math:`{X}_{D}=0.0;{Y}_{B}=1.0;{Z}_{B}=0.0`

The orientation of the plate in the global coordinate system is obtained by two rotations:

:math:`\alpha \mathrm{=}30°` around :math:`Z`

:math:`\beta \mathrm{=}60°` around the new :math:`X\text{'}` axis


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    :height: 3.2465in


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:math:`X;Y;Z`: global axes

:math:`X\text{'}\text{'};Y\text{'}\text{'};Z\text{'}\text{'}`: local axes in final position


Material properties
------------------------

Concrete:

Young's module: :math:`E={3.7272}^{10}\mathrm{Pa}`

Poisson's ratio: :math:`\nu =0.0`


Boundary conditions and loads
-------------------------------------

On points :math:`A` and :math:`B` we block the movements along :math:`X,Y,Z` and the rotations around the axes :math:`X,Y,Z`:

:math:`{D}_{X}^{A}=0.0;{D}_{Y}^{A}=0.0;{D}_{Z}^{A}=0.0;{\mathrm{DR}}_{X}^{A}=0.0;{\mathrm{DR}}_{Y}^{A}=0.0;{\mathrm{DR}}_{Z}^{A}=0.0`

:math:`{D}_{X}^{B}=0.0;{D}_{Y}^{B}=0.0;{D}_{Z}^{B}=0.0;{\mathrm{DR}}_{X}^{B}=0.0;{\mathrm{DR}}_{Y}^{B}=0.0;{\mathrm{DR}}_{Z}^{B}=0.0`

On points :math:`C` and :math:`D` we apply a loading according to :math:`Z`:

:math:`{F}_{Z}=-100.0N`