A unified library of nonlinear solution schemes

Sofie E. Leon, Glaucio H. Paulino, Anderson Pereira, Ivan F.M. Menezes, Eduardo N. Lages

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


Nonlinear problems are prevalent in structural and continuum mechanics, and there is high demand for computational tools to solve these problems. Despite efforts to develop efficient and effective algorithms, one single algorithm may not be capable of solving any and all nonlinear problems. A brief review of recent nonlinear solution techniques is first presented. Emphasis, however, is placed on the review of load, displacement, arc length, work, generalized displacement, and orthogonal residual control algorithms, which are unified into a single framework. Each of these solution schemes differs in the use of a constraint equation for the incremental-iterative procedure. The governing finite element equations and constraint equation for each solution scheme are combined into a single matrix equation, which characterizes the unified approach. This conceptual model leads naturally to an effective object-oriented implementation. Within the unified framework, the strengths and weaknesses of the various solution schemes are examined through numerical examples.

Original languageEnglish (US)
Article number040803
JournalApplied Mechanics Reviews
Issue number4
StatePublished - 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering


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