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. [DOI: 10.1115/1.4006992]
We present an object-oriented framework, named DOOLINES, for non-linear static and dynamic analyses of slender marine structures which often appear in offshore structures employed in the petroleum and gas industries as, among others, flexible risers, steel catenary risers, umbilicals, floating hoses, and mooring lines. DOOLINES allows the rapid development of tailored, modular, reusable and extensible large-size systems, being itself extensible. These properties, along with the ease of use of our framework, are assessed by means of case studies. Code examples are provided.
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