Journal ArticleDOI
A fast incremental/iterative solution procedure that handles "snap-through"
TLDR
In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.About:
This article is published in Computers & Structures.The article was published on 1981-06-01. It has received 1581 citations till now. The article focuses on the topics: Iterative method & Deflection (engineering).read more
Citations
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A plastic-damage model for concrete
TL;DR: In this article, a constitutive model based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete is presented, which uses a new yield criterion which matches experimental data quite well and it accounts for both elastic and plastic stiffness degradations effects.
Journal ArticleDOI
Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues
Giulio Alfano,M. A. Crisfield +1 more
TL;DR: In this paper, a finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law, where the principles of linear elastic fracture mechanics are indirectly used by equating the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination.
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Simulation of strain localization: a reappraisal of the cosserat continuum
TL;DR: In this paper, the governing field equations are regularized by adding rotational degrees of freedom to the conventional translational degree of freedom, and the convergence of the load-deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone is demonstrated.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
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An incremental approach to the solution of snapping and buckling problems
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.
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Quasi-Newton Methods, Motivation and Theory
John E. Dennis,Jorge J. Moré +1 more
TL;DR: In this paper, an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton''s method for general and gradient nonlinear systems of equations is made, and references are given to ample numerical justification; here we give an overview of many of the important theoretical results.
Journal ArticleDOI
The solution of nonlinear finite element equations
TL;DR: In this article, a quisi-Nowton method was proposed to solve nonlinear finite element equations, and initial tests of its application to both material and geometric nonlinearities are discussed.