Re: [Getfem-users] initial strains in structural analysis

[Yves Renard]

Le Jeudi 9 Novembre 2006 02:06, Julien Sylvestre a écrit :
> Yves Renard wrote:
> >Le Jeudi 2 Novembre 2006 02:33, Julien Sylvestre a écrit :
> >>Hello,
> >>    I'm very impressed by the quality of the getfem++ library. However,
> >>I've been trying without success to solve a linear elasticity problem
> >>where thermal strains are present. Given the coefficient of thermal
> >>expansion of a material and a range of temperature variation, how do I
> >>generate a brick to implement the thermal strain the material would
> >>actually develop?
> >
> >You mean that the temperature is given ?
> >Could you write down the expression of the term which takes into account
> > the thermal expansion (I am not a specialist). If it is a supplementary
> > term in the equation compared to the standard linearize elasticity, it
> > should be possible to build a brick which modify the linearized
> > elasticity brick adding a term in the stiffness matrix.
>
> That would be something like
> d Sxx / dx + d Sxy / dy + d Szx / dz = 0
> (and similarly in y,z)
> for Sij the stress component i,j, so that
> Sxx = G(1-nu) (du / dx - CTE DeltaT) + G nu (dv / dy + dw/dz)
> Sxy = G(1-2nu) (du/dy + dv/dx) / 2
> etc.
> (thermal strains only appear on Sii components, i.e. they don't show up
> in shear stresses)
>
> Here u, v, w are the displacement fields, CTE is the coefficient of
> thermal expansion, and DeltaT is the temperature excursion (which is
> provided as an external parameter).
>
> Is there an easy way to express the thermal strain term in terms of
> existing bricks in getfem?
>
> Merci,
> J

If I understand well, in your model the temperature expansion  appears like an 
additional pressure. The additional term in the weak formulation should be
 \int CTE DeltaT div(u) dx
This is exactly the term appearing in the incompressibility RHS of the 
incompressibility brick. So, writing the brick from the incompressibility 
brick is very easy. If you need, I can help you to do that.


-- 
Yves.

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  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
  Institut Camille Jordan - CNRS UMR 5208
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  http://math.univ-lyon1.fr/~renard
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