Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.