TY  - EJOU
AU  - Fernandes, M.T.C.  Araújo 
AU  - Cardoso, C.O.  
AU  - Mansur, W.J.  

TI  - An adaptive load stepping algorithm for path-dependent problems based on estimated convergence rates
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2017
VL  - 113
IS  - 3
SN  - 1526-1506

AB  - A new adaptive (automatic) time stepping algorithm, called RCA (Rate of Convergence Algorithm) is presented. The new algorithm was applied in nonlinear finite element analysis of path-dependent problems. The step size is adjusted by monitoring the estimated convergence rate of the nonlinear iterative process. The RCA algorithm is relatively simple to implement, robust and its performance is comparable to, and in some cases better than, the automatic load incrementaion algorithm existent in commercial codes. Discussions about the convergence rate of nonlinear iterative processes, an estimation of the rate and a study of the parameters of the RCA algorithm are presented. To show the capacity of the algorithm to adjust the increment size, detailed discussions based on results for different limit load analyses are presented. The results obtained by RCA algorithm are compared with those by ABAQUS®, one of the most powerful nonlinear FEA (Finite Element Analysis) commercial software, in order to verify the capability of RCA algorithm to adjust the increment size along nonlinear analyses.
KW  - Rate of convergence
KW  -  nonlinear
KW  -  automatic
KW  -  load incrementation
KW  -  limit load

DO  - 10.3970/cmes.2017.113.341