The BFGS method often gives a better convergence of the results than the Newton-Raphson's one. In fact, the question is why do you need to use the Newton-Raphson's method as it seems you got a converged solution with BFGS? If you need a solution with the Newton-Raphson's method, I think that the only way is to perform an incremental calculation and to reduce the load steps.

Dear Prof. Jean,

Thank you for valuable suggestion. I think, i can use any method for this problem. But nature of solution (hysteresis behavior ) till convergence looks better in Newton Raphon than BFGS. And also,if i put large value for convergence criteria, it will give better loop than small convergence criteria. It looks opposite. So i am worrying about the use of BFGS. Is there any specific reason for this problem.  To set convergence criteria in BFGS, when applying displacement load and force load is different? Is there any guideline or specific rule  available to set convergence criteria? 

Best Regards,

Chandani

In any FE code, the user can define a convergence criterion on the residue (force criterion) and a convergence criterion on the increment of displacement between 2 successive iterations of resolution (displacement criterion) and the convergence will be supposed to be reached if one of the two criteria is satisfied.

But, you must keep in mind that the convergence of the calculation will be effectively reached only if the residue reaches very small values compared to the external loading. If the iterations are stopped because only the displacement criterion is satified, you must verify that the residue is small enough so that the solution can be acceptable.

May be this is what happens in your case. With the BFGS method, the iterations could have been stopped because the displacement criterion is satisfied while the residue still keep too big values. In fact if the displacement increment is small (less than the displacement criterion entered by the user), this only means that the convergence will be slow and will need a lot of iterations.

I suggest that you put a very small value to the displacement criterion to force the convergence on the residue.

Best regards,

Jean-Michel

Thank you sir. There is energy criteria also. What about their combination. I can define any two or all three for force displacement relation? Which one is more sensitive for convergence to get accurate results?

The most sensitive for convergence is the force criterion.

Best regards,

Jean-Michel

Dear Prof. Jean Sir,

For my case, when i define force criteria only solution converge after long iteration for only few steps but converge after few steps if i define both or all three energy, displacement and force criteria. I define small displacement criteria and tried for solution but the problem still remains in force vs displacement loop, which is fluctuating. I attached my force vs disp. plot of RC frame structure under monotonic loading using BFGS. 

Best Regards,

Chandani