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Computational Mechanics
Published in: Computational Mechanics 2/2016

01-08-2016 | Original Paper

On path-following methods for structural failure problems

Authors: Andjelka Stanić, Boštjan Brank, Jože Korelc

Published in: Computational Mechanics | Issue 2/2016

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Abstract

We revisit the consistently linearized path-following method that can be applied in the nonlinear finite element analysis of solids and structures in order to compute a solution path. Within this framework, two constraint equations are considered: a quadratic one (that includes as special cases popular spherical and cylindrical forms of constraint equation), and another one that constrains only one degree-of-freedom (DOF), the critical DOF. In both cases, the constrained DOFs may vary from one solution increment to another. The former constraint equation is successful in analysing geometrically nonlinear and/or standard inelastic problems with snap-throughs, snap-backs and bifurcation points. However, it cannot handle problems with the material softening that are computed e.g. by the embedded-discontinuity finite elements. This kind of problems can be solved by using the latter constraint equation. The plusses and minuses of the both presented constraint equations are discussed and illustrated on a set of numerical examples. Some of the examples also include direct computation of critical points and branch switching. The direct computation of the critical points is performed in the framework of the path-following method by using yet another constraint function, which is eigenvector-free and suited to detect critical points.
previous article A size-dependent constitutive modelling framework for localised failure analysis
next article A Full Dynamic Compound Inverse Method for output-only element-level system identification and input estimation from earthquake response signals

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Appendix
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Metadata
Title
On path-following methods for structural failure problems
Authors
Andjelka Stanić
Boštjan Brank
Jože Korelc
Publication date
01-08-2016
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 2/2016
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-016-1294-y

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