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An application of the arc length method involving concrete cracking
Author(s) -
Foster Stephen
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330204
Subject(s) - arc (geometry) , arc length , convergence (economics) , cracking , line (geometry) , finite element method , newton's method , constant (computer programming) , scheme (mathematics) , stability (learning theory) , computer science , algorithm , mathematics , mathematical optimization , structural engineering , materials science , engineering , mathematical analysis , geometry , composite material , nonlinear system , physics , quantum mechanics , machine learning , economics , programming language , economic growth
To overcome numerical difficulties in highly non‐linear materials Crisfield 6 proposed a solution procedure involving the use of a constant arc length solution scheme with line searches and accelerations. This paper uses the arc length method with line searches to increase the stability and substantially reduce the cpu time required for convergence in the finite element modelling of reinforced concrete. The arc length method is compared with the modified Newton–Raphson solution scheme and it was found that substantial savings in computer resources are obtained by using the arc length method. On difficult iterations the use of line searches is shown to lead to substantial improvement, with the best results occurring when using a slack tolerance of ψ = 0.8.