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


Geometry
---------

Geometry of the four substructures (:math:`\mathrm{TRI1}`, :math:`\mathrm{TRI2}`,,, :math:`\mathrm{TRI3}`, :math:`\mathrm{TRI4}`):


.. image:: images/100002000000022A0000018B208D3244A46E1CA3.png
    :width: 3.1492in
    :height: 2.2445in


.. _RefImage_100002000000022A0000018B208D3244A46E1CA3.png:


.. image:: images/1000000000000589000003900C18A21AECEFF724.jpg
    :width: 4.7244in
    :height: 3.0311in


.. _RefImage_1000000000000589000003900C18A21AECEFF724.jpg:

Substructure meshing

Triangle geometry :math:`(m)`:



 :math:`C=1`

 thickness: :math:`e=0.01`

Node coordinates:

 :math:`\mathrm{NO1}=(1.0\mathrm{,0}.0)`

 :math:`\mathrm{NO43}=(0.687,0.108)`

Mesh group:

 :math:`\mathrm{BASE}`: set of nodes forming the base of the triangle

 :math:`\mathrm{GAUCHE}`: set of nodes forming the right side of the triangle

 :math:`\mathrm{DROITE}`: set of knots forming the left side of the triangle

 :math:`\mathrm{TOUT}`: set of nodes forming the triangle


Elastic properties of materials
-----------------------------------


* Young's modulus: :math:`E=2.1E11\mathrm{Pa}`


* Poisson's ratio: :math:`\nu =0.3`


* volume density: :math:`\rho =7800.0{\mathrm{kg.m}}^{-3}`


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


*
    **Substructure:* :math:`\mathrm{TRI1}`:


        * Compulsory trips:


            * :math:`\mathrm{TOUT}`: :math:`\mathrm{DRZ}=0.0`


            * :math:`\mathrm{BASE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


*
    *
        *
            * Interfaces:


                * :math:`\mathrm{BASE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`


*
    *
        **Substructure:* :math:`\mathrm{TRI2}`:


            * Nautical angles :math:`(\alpha ,\beta ,\gamma )`: :math:`(0.0\mathrm{,0}.0\mathrm{,180}.0)`


*
    *
        *
            * Compulsory trips:


                * :math:`\mathrm{TOUT}`: :math:`\mathrm{DRZ}=0.0`


                * :math:`\mathrm{BASE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


                * :math:`\mathrm{DROITE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


                * :math:`\mathrm{GAUCHE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


*
    *
        *
            * Interfaces:


                * :math:`\mathrm{BASE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`


                * :math:`\mathrm{GAUCHE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`


                * :math:`\mathrm{DROITE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`


*
    *
        **Substructure*: :math:`\mathrm{TRI3}`:


            * Compulsory trips:


                * :math:`\mathrm{TOUT}`: :math:`\mathrm{DRZ}=0.0`


                * :math:`\mathrm{BASE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


                * :math:`\mathrm{DROITE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


*
    *
        *
            * Interfaces:


                * :math:`\mathrm{DROITE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`


*
    *
        **Substructure:* :math:`\mathrm{TRI4}`:


            * Nautical angles :math:`(\alpha ,\beta ,\gamma )`: :math:`(0.0\mathrm{,180}.0\mathrm{,0}.0)`


*
    *
        *
            * Compulsory trips:


                * :math:`\mathrm{TOUT}`: :math:`\mathrm{DRZ}=0.0`


                * :math:`\mathrm{BASE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


                * :math:`\mathrm{DROITE}`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0`


*
    *
        *
            * Interfaces:


                * :math:`\mathrm{DROITE}`: type: CRAIGB, mask: :math:`\mathrm{DRZ}`