Open Access

ARTICLE

An adaptive load stepping algorithm for path-dependent problems based on estimated convergence rates

M.T.C. Araújo Fernandes¹, C.O. Cardoso², W.J. Mansur³

1 Civil Engineering Department/COPPE/Federal University of Rio de Janeiro, Ilha do Fundão, P.B. 68506, 21945-970 Rio de Janeiro, RJ, Brazil
2 Petrobras/Cenpes, Av. Horácio Macedo, 950, Ilha do Fundão, 21941-915 Rio de Janeiro,RJ, Brazil
3 Corresponding author, Civil Engineering Department/COPPE/Federal University of Rio de Janeiro, Ilha do Fundão, P.B. 68506, 21945-970 Rio de Janeiro, RJ, Brazil, webe@coc.ufrj.br

Computer Modeling in Engineering & Sciences 2017, 113(3), 325-342. https://doi.org/10.3970/cmes.2017.113.341

Abstract

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.

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Keywords

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