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inverse problem

How to study a inverse problem? Know the orbit, solve the constraint condition.

Dear all,

Now I face a noval problem, and I do not know how to deal with it, even cannot begin the first step.

As we know, the formulation of a classical mechanical question  is given the initial condition and the constraint condition, and solve the unknown orbit. Now I face a inverse problem. I know the initial condition and the orbit, and would like to solve the unknown constraint condition.

Is there anyone could give some seggestion, I don't know how to do it. Thanks.

Best. 

waquino's picture

inverse problem image

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Frank Richter's picture

Inverse problem in beam bending, elastic-ideally plastic material

Dear iMechanica,

suppose you have a beam with a square cross-section, manufactured from an elastic-ideally plastic material.

Now apply a load that rises linearly in time, but is locally constant along the beam length. Upon sagging, the beam will develop a plastic zone beginning in the top and surface regions at mid-length.
This is the "straight" problem solved in Prager, Hodge: Theory of perfectly plastic solids, publisher: Springer

Sébastien Turcaud's picture

Inverse eigenstrain analysis based on residual strains in the case of small strain geometric nonlinearity

Hi,

I was wondering if someone knows literature related to "Inverse eigenstrain analysis based on residual strains in the case of small strain geometric nonlinearity"? (elongated bodies)

In the case of lineralized elasticity I guess one could postulate an eigenstrain distribution as the sum of a finite set of basic eigenstrain distribution and minimize the difference between the predicted and the actual residual strain distribution (retrieved from a synchroton mapping for example).

As done in the paper:

Open PhD position: Inverse identification from full field measurements

The part of full field displacement measurements is increasing in
experimental mechanics. Their taking into account relies on the
development of suited identification approaches, which have to be able
to take advantage of their richness. When dealing with composites, they
offer the possibility to perform the identification at a scale where
the material is heterogenenous. The goal of this thesis is to apply
inverse approaches on the challenging case of the identification of
heterogeneous elasticity and develop a robust identification

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