Potential energy and equilibrium 1

[idly123]

Greetings !
I have a Basic querry.
1) Is the potential energy for a given discretized continuum constant?
2) How does the potential energy of the system vary with increase in the number of elements?
3) If there is a variation the what is the value of PE coreesponding to equlibrium? Doe this have more than one discretization pattern
regards
raj Raj

 

[brad]

My off-the-cuff thoughts . . .
1) It should nearly be (for the same structure and loading, just with varying mesh densities and/or mesh assumptions).
2) If it does significantly, this would be a symptom of not being near converged solution.
3) Since there shouldn't be a significant variation . . .

Any particular reason why you're asking?
Bra

 

[idly123]

The reason being , i read in a paper that PE does vary with mesh density or refinement or rather increase or reduction in discreetization.
An increased elements although amounts to better solution , but also amounts more discontiniuties and more force imbalance at these artifical boundaries which become pronounced.That is something to do with configurational forces.
do u have any more idea in this regard -bradh? Raj

 

[brad]

Raj,
Sorry about the delay in answer. I don't know about this particular statement regarding configurational forces and artifical boundaries. I must admit that I may be missing the essence of your point in this regard. I would think that the PE should remain nearly constant (and should certainly converge), just on a first-principles basis.

If I have a given set of loads/displacements on my structure, the only way my external work changes is by a stiffness change to the structure (which we know happens with mesh discretization). Once structural stiffness has converged, then the external work will converge to a constant value. As the problem is formulated such that the potential energy in the system balances this external work, this implies that the potential energy in the system should not change if the external work is unchanging.

I would therefore expect that any significant changes in potential energy in the structure are due to mesh-convergence issues, and as the mesh is refined this does converge to an actual number.

Raj--what is the paper that you are referencing?
Brad

 

[idly123]

BRadh please refer
IJNME 2002 volume 53 page number 1557-1574
On configurational forces in context of FEM by Mulleret al
regds Raj

 

[idly123]

Bradh :
Did u check that paper. If u havent then just have a lookin to this book

" Mechanics in MAterial space " with Applications to Defect and Fracture MEchanics
by
Reinhold Kienzler and george Herrmann

regds
raj Raj

 

[brad]

Raj,
I apologize that I don't have ready access to the paper nor the book.
Sorry.
Brad