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Subject: Re: Superelement in ANSYS/Substructuring
Author: K.S. Raghavan
Date: 2001-02-02 04:35:00

Christopher Wright wrote:

> >If you deliberately keep mismatching mesh densities some nodes
> >of the finer mesh remain free and hence the results will be erroneous.
> This depends on the problem. The St Venant principle governs
> substructures and sub-models. If the loading imposed on the cut surface
> of the sub model is statically equivalent to that imposed by the
> surrounding structure in the full model, then the results at points more
> than a couple of thicknesses from the cut won't be affected by the
> mismatched node densities. I suspect that if your model isn't linear, or
> at least isn't linear in the range of the sub-model, you're out of luck
> with either substructuring or sub-modeling.

> > submodelling is the best bet.
> Maybe I'll quibble a little with this too. Sub-modelling works real well
> to get local stresses, but again, when non-linearities are present or
> when there are doubts about the interpolation of boundary displacements
> between connection points with the full model, it gets iffy. In any
> event, both sub-modelling and substructuring both depend on the St Venant
> principle for accuracy. And in both cases you're using the modeled
> response (either stiffness or displacements resulting from the stiffness)
> of a large region to provide loading to a smaller connected region, using
> the assumption that the stiffness of the detailed sub-model and the
> submodelled region are equal.

> I'd also have qualms about predicting crack propagation using a sub-model
> with displacement controlled loading rather than a substructure with
> force controlled loading. I'm sticking my neck out here because I don't
> really know what the user is trying to accomplish, but intuitively I'd
> think the strain energy/external work relationships are different in the
> two situations, affecting crack growth.

> I confess I've never been able to convince myself how external loads
> should be applied to a sub-model if such loads exist over the
> sub-modelled region in the full model. On the one hand the loading
> present on the sub modelled portion must be reflected in the cut boundary
> displacements and therefore the load needn't be re-applied--seems as if
> the loading would be applied twice. OTOH intuitively you want all the
> loads carried by the sub-model that were present in the full model, so
> the external loads _should_ be applied. Or maybe the sub-model is always
> so stiff by comparison with the full model that it doesn't make any
> difference. I've sworn to check this out very carefully before I do a
> loaded sub-model, but the occasion hasn't arisen. Maybe some day.

> Christopher Wright P.E. |"They couldn't hit an elephant from
> chrisw@s... | this distance" (last words of Gen.
> ___________________________| John Sedgwick, Spotsylvania 1864)

Chris,

Your points are well taken. I have one major point of disagreement.
Whereas submodeling is based on St. Venant principle , substructuring is not.

Substructuring is based on static condensation technique and no approximation

is involved in the formulation. The results are exact provided , of course ,
that there is
one to one match between the connection nodes on common boundaries.

Suppose there is a mismatch (which , however is not a classical substructures

procedure). The boundary nodes which do not find match in the adjoining
superelement will be treated as internal nodes in the first phase of
substructures
analysis. Results for these nodes will be available only in the second phase
,
that is backsubstitution phase , of analysis. The displacements for such
"floating" nodes
will be as if they are not connected to the other superelement. Physically
the situation
is analogous to the presence of a slit. Mathematically the situation appears
to be similar to what
is done in submodeling approach though there are conceptual inconsistencies.

In submodeling approach the displacements of the intermediate nodes are
computed
by interpolation .Thus though there is approximation there is no conceptual
error.
In fact the submodeling problem is solved as an independent problem retaining

displacements (from coarse model) on cut boundaries and applied forces on
the
free boundaries. This addresses the doubt raised by you in the third
paragraph.

As the submodel is solved as an independent problem there will be no
difficulty
in introducing a crack tip in the submodel. The results will , of course , be
accurate
subject to the implications of St Venant theory.

Cheers .. raghavan (BHEL , Hyderabad , INDIA)

Posts possibly associated with message #20768AuthorDateScore
20651Superelement in ANSYS/Substructuringsbordas@2001/01/30 
20655Re: Superelement in ANSYS/SubstructuringMark Rodamaker2001/01/30 
20659Re: Superelement in ANSYS/SubstructuringK.S. Raghavan2001/01/30-10
20724Re: Superelement in ANSYS/SubstructuringChristopher Wright2001/01/31 
20730Re: Superelement in ANSYS/SubstructuringK.S. Raghavan2001/02/01 
20735Re: Superelement in ANSYS/SubstructuringJason Husband2001/02/01 
20740Re: Superelement in ANSYS/SubstructuringChristopher Wright1991/02/01 
20742Re: Superelement in ANSYS/SubstructuringOsman Buyukisik2001/02/01 
20747Re: Superelement in ANSYS/SubstructuringChristopher Wright1991/02/01 
20768Re: Superelement in ANSYS/SubstructuringK.S. Raghavan2001/02/02 
20783Re: Superelement in ANSYS/SubstructuringChristopher Wright2001/02/02