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


Geometry
---------


.. image:: images/100010F20000170C000012808E18687B306C9DB4.svg
    :width: 297
    :height: 238


.. _RefImage_100010F20000170C000012808E18687B306C9DB4.svg:

All three bars have the same length :math:`L=\mathrm{1m}`, and are :math:`l\mathrm{=}\mathrm{1m}` apart.


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

Standard perfect thermo-elastoplastic behavior law, with VonMises criterion. The plastic deformations are zero in the initial state.


.. image:: images/1000066000001AAA00000968D17847C225C345D8.svg
    :width: 297
    :height: 238


.. _RefImage_1000066000001AAA00000968D17847C225C345D8.svg:


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

The three bars have a blocked movement following :math:`\mathit{Oy}` at the upper end points, where they are articulated, and they are clamped at the lower points :math:`{P}_{\mathrm{1,}}{P}_{\mathrm{2,}}{P}_{3}`, which can be represented by a rigid frame forced to move vertically, of length :math:`\mathrm{4l}`, on which the three bars are articulated. The bars are free of mechanical force.

The loading path is described by the evolution of the temperature, uniform in each bar (:math:`{T}^{\mathit{max}}\mathrm{=}330°C`):


.. _1292719494: