Solution of discrete nonlinear equation systems resulting from the finite element method using a global secant relaxation based accelerated iteration procedure

Chang-New Chen

研究成果: Chapter

摘要

A global secant relaxation(GSR)-based accelerated iteration scheme can be used to carry out the incremental/iterative solution of various nonlinear finite element problems. This computation procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation. Moreover, this method can efficiently accelerate the convergency of the iterative computation. This incremental/iterative analysis can consistently be carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behaviour of a structure under certain external cause, if the constant stiffness is used. Consequently, this method can widely be used to solve general nonlinear problems. Mathematical procedures of Newton-Raphson techniques in finite element methods for nonlinear finite element problems are summarized. These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results obtained by using various accelerated modified Newton- Raphson methods are used to study the convergency performances of these techniques for material nonlinearity problems and deformation nonlinearity problems, separately.

原文English
主出版物標題Computational Engineering
主出版物子標題Design, Development and Applications
發行者Nova Science Publishers, Inc.
頁面131-149
頁數19
ISBN(電子)9781536117011
ISBN(列印)9781611228069
出版狀態Published - 2012 一月 1

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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