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

[Julien Sylvestre]

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