A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics

Nonlinear solution schemes;nonlinear finite element analysis;incremental-iterative procedure;Newton-Raphson method;displacement\rcontrol method;arc-length control method;work control method;generalized displacement control method;orthogonal residual procedure

Leon, Sofia ; Paulino ; Glaucio H.

关键词: Nonlinear solution schemes;    nonlinear finite element analysis;    incremental-iterative procedure;    Newton-Raphson method;    displacement\rcontrol method;    arc-length control method;    work control method;    generalized displacement control method;    orthogonal residual procedure;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/18353/Leon_Sofia.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

A library of nonlinear solution schemes including load, displacement, arc-length, work, generalizeddisplacement, and orthogonal residual control are cast into a unified framework forsolving nonlinear finite element systems. Each of these solution schemes differs in the use ofa constraint equation for the incremental-iterative procedure. The governing finite elementequations and constraint equation for each solution scheme are combined into a single matrixequation, which characterizes the unified approach. This theoretical model leads naturally toan effective object-oriented implementation and potential for integration into a finite elementanalysis code. Using this framework, the strengths and weaknesses of the various solutionschemes are examined through several numerical examples.