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Convergence in Geometrically nonlinear problems

Submitted by Awais Ahmed on

Dear all,

I have a queary regarding the convergence in large strain problems.

In large strain problems due to the nonlinear term in the strain the tangent stiifness  matrix composed of  material stiffness matrix, Km and geometrical stiffness matrix, Kg. which are now dependent on the displacement u, contarary to small strain problem. Hence, solving the problem using Newton Raphson method, after the 1st iteration when we get the first update of the variable du, we use this updated value for the second iteration. This affects the tangent matrix, which totally changes it as compare to the tangent matrix in 1st iteration. This result in the error in the energy norm greater than the error in energy norm obtained in the 1st iteration. However after the second iteration the error in energy norm reduces just like the linear problems. Is this behavior true..? Could any one comment on this please......?

 

Regards

Awais Ahmed 

 

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tlaverne

In the example of large rotations, the linear approximation tends to overestimate the energy due to rotation and you end up with model which look inflated. For example if you do a 45° rotation of a square the results in small strain approximation looks nothing like a square (though it should since rigid body motion should not change the solution...). So this is may be why you get a smaller energy norm in large deformations with a non-linear strain approximation (I guess you use Green-Lagrange?).

But in general the first step of the Newton-Raphson is just like a linear step (since in case of zero displacements the stiffness matrices are equal in both approximations), so you should get exactly the same result. Or may be you have initial strain, stress or displacement ?

 My blog on research on Hybrid Solvers: http://mechenjoy.blogspot.com/

Wed, 03/31/2010 - 08:40 Permalink
alokgautam

Dear Laverne,

 

i am trying to solve one dimensional non linear PDE using finite element method 

but i am not able to form K stiffness matrix. will You please help me with this.

 

Thanks in advance.

 

AG

Fri, 07/09/2010 - 00:04 Permalink
rajdrdl

Dear all,

I am trying to solve the thermal ratcheting of a hollow cylinder using elasto-plastic formulation.

I am applying the thermal gradient in axial direction. Our FEM code(Newton Raphson) is converging for first increment but after that it is diverging.

Anybody can help me that why it is happening?

Thanks

Raj

Sat, 07/10/2010 - 10:01 Permalink