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
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