Dear Jean,
Thanks very much for your help and support. I do really appreciate your 
time and know you are really busy. The fact is that my code ran just for 
the first time step and can not solve for the other time step. when I 
refine the global mesh twice, this problem happened, however, with 
increasing the number of global refine mesh, the whole geometry is 
distorted. In fact, it is a thermo-elastic problem which I should use two 
different Neumann B.C for the curved side of my domain. I just want to know 
whether applying this type was true or not. In addition, could you please 
help me more how I should use load-following algorithm in dealii? It should 
be noted that I have multiplied the Neumann magnitude by time-ramp 
(current_time/time_step). Looking forward to hearing from you.

On Friday, December 2, 2016 at 12:50:03 AM UTC-6, Jean-Paul Pelteret wrote:
>
> Dear Benhour,
>
> Thank you for taking my point heart and providing more specifics about 
> your actual problem.
>
> For the horizontal axis, I have considered the zero displacement along 
>> y-axis because of symmetry. Is it correct? Should I fix the center of the 
>> circle as well? 
>>
>
> If you don't provide at least one Dirichlet constraint for each of the 
> solution components then your problem is indeterminate. So if you only 
> constrain the x-DoFs along the y-axis and have no other Dirichlet 
> constraints then this could be the source of some troubles. 
>  
>
>> How Can I do that? In other words, How can I fix one point (vertex) in 
>> 2-D? 
>>
>
> You have to manually add such a point constraint to the constraint matrix 
> or map of boundary values. If your centre point is coincident with a vertex 
> of the triangulation then you can achieve this with the help of the 
> cell->vertex_dof_index() function. There have been plenty of posts 
> <https://groups.google.com/forum/#!searchin/dealii/vertex_dof_index%7Csort:date>
>  
> in the past on how this function works, so I need not explain it again in 
> detail.
>
> I should also note that for highly nonlinear problems, if your load 
> increment is too large between time steps then this could also be 
> problematic (unless you're using a load-following algorithm like the 
> arc-length method). It may be of use to reduce the magnitude of the applied 
> traction while you're debugging this.
>
> Regards,
> Jean-Paul
>

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