{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18353"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18353","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics","abstract":"A library of nonlinear solution schemes including load, displacement, arc-length, work, generalized displacement, and orthogonal residual control are cast into a unified framework for solving nonlinear finite element systems. 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. 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Using this framework, the strengths and weaknesses of the various solution schemes are examined through several numerical examples.","abstract_has_math":false,"creators":["Leon, Sofia"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Paulino, Glaucio H."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-14T22:47:14Z","date_published":"2011-01-14T22:47:14Z","updated_at":"2026-07-22T22:25:11Z","subjects":["Nonlinear solution schemes","nonlinear finite element analysis","incremental-iterative procedure","Newton-Raphson method","displacement control method","arc-length control method","work control method","generalized displacement control method","orthogonal residual procedure"],"languages":["en"],"rights":["Copyright 2010 Sofia E. 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