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Applications of a self‐adaptive algorithm to non‐linear finite element analysis
Author(s) -
Lee Sang H.,
Hsieh Steve S.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620320509
Subject(s) - finite element method , bisection method , algorithm , convergence (economics) , computer science , inertia , adaptive algorithm , process (computing) , stiffness matrix , stiffness , mathematical optimization , matrix (chemical analysis) , mathematics , engineering , physics , structural engineering , classical mechanics , economics , economic growth , operating system , materials science , composite material
A self‐adaptive algorithm has been developed and implemented for the implicit time integration of non‐linear finite element analysis. In this algorithm, a proper time increment for the next time step is estimated based on the deformation pattern at the preceding step. The iteration process for the equalibrium employs expeditious methods such as quasi‐Newton updates and line searches as well as an adaptive stiffness matrix update strategy for efficiency. Convergence difficulties induced from inadequate prediction of step size or the change in non‐linearities are tackled by the bisection method. These procedures were also successfully applied to static problems by ignoring the damping and the inertia forces. The objective of this paper is to demonstrate the applicability and the effectiveness of the adaptive algorithm in a wide spectrum of non‐linear problems. Six example problems are illustrated, some of which are rather novel. As demonstrated in this paper, the self‐adaptive algorithm implemented in MSC/NASTRAN is proving to be versatile, accurate and efficient.