Efficient and reliable accelerated constant stiffness algorithms for the solution of non‐linear problems

Chang-New Chen

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The paper relates to a secant‐relation‐based acceleration method used to improve the modified Newton‐Raphson scheme in which the constant stiffness matrix formed at the first iteration step is adopted to make incremental predictions for all iteration steps. An accelerator defined by minimizing a certain globally defined system error is used to scale the incremental response vector obtained by the modified Newton‐Raphson prediction in iteratively updating the response vector. The performance of acceleration is dependent on the method used to evaluate the system error. A consistent approach of evaluating the system error leads to obtaining a consistent accelerator. Another approach evaluates the system error less consistently, which results in obtaining a less consistent accelerator. Numerical results of non‐linear finite element analyses will be presented to show the effectiveness of this approach and to demonstrate the conclusion made by theoretical investigation regarding the convergency performances of the two accelerators proposed.

Original languageEnglish
Pages (from-to)481-490
Number of pages10
JournalInternational Journal for Numerical Methods in Engineering
Volume35
Issue number3
DOIs
Publication statusPublished - 1992 Jan 1

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Accelerator
Particle accelerators
Nonlinear Problem
Stiffness
Newton-Raphson
Iteration
Nonlinear Finite Element
Evaluate
Prediction
Stiffness matrix
Stiffness Matrix
Updating
Numerical Results
Dependent
Demonstrate

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

Cite this

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Efficient and reliable accelerated constant stiffness algorithms for the solution of non‐linear problems. / Chen, Chang-New.

In: International Journal for Numerical Methods in Engineering, Vol. 35, No. 3, 01.01.1992, p. 481-490.

Research output: Contribution to journalArticle

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