Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

A new fixed-point algorithm for hardening plasticity based on non-linear mixed variational inequalities

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.672 ◽

2003 ◽

Vol 57 (1) ◽

pp. 83-102 ◽

Cited By ~ 5

Author(s):

P. Venini ◽

R. Nascimbene

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Fixed Point Algorithm ◽

Non Linear ◽

Mixed Variational Inequalities

Download Full-text

An Eccentric Barycentric fixed Point Algorithm

Mathematics of Operations Research ◽

10.1287/moor.2.4.343 ◽

1977 ◽

Vol 2 (4) ◽

pp. 343-359 ◽

Cited By ~ 6

Author(s):

Willard I. Zangwill

Keyword(s):

Fixed Point ◽

Fixed Point Algorithm

Download Full-text

Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

Applied Sciences ◽

10.3390/app11104637 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4637

Author(s):

Gildas Yaovi Amouzou ◽

Azzeddine Soulaïmani

Keyword(s):

Fixed Point ◽

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Numerical Algorithms ◽

Constitutive Law ◽

Layer By Layer ◽

Implementation Framework ◽

Fixed Point Algorithm ◽

Tangent Matrix

Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.

Download Full-text