scholarly journals On the formulation of closest-point projection algorithms in elastoplasticity-part II: Globally convergent schemes

2001 ◽  
Vol 53 (2) ◽  
pp. 331-374 ◽  
Author(s):  
A. Pérez-Foguet ◽  
F. Armero
Keyword(s):  
Projection Algorithms ◽  
Globally Convergent ◽  
Closest Point Projection ◽  
Point Projection

scholarly journals New Double Projection Algorithm for Solving Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lian Zheng
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Projection Algorithm ◽  
Iterative Sequence ◽  
Local Error ◽  
Projection Algorithms ◽  
Local Error Bound ◽  
Globally Convergent

We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient.

scholarly journals Elastic-Plastic Numerical Analysis of Tunnel Stability Based on the Closest Point Projection Method Considering the Effect of Water Pressure

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Zhan-ping Song ◽  
Ten-tian Yang ◽  
An-nan Jiang
Keyword(s):  
Rock Mass ◽  
Numerical Analysis ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Surrounding Rock ◽  
Tunnel Stability ◽  
Elastic Plastic ◽  
Closest Point Projection ◽  
Point Projection

To study the tunnel stability at various static water pressures and determine the mechanical properties and deformation behavior of surrounding rock, a modified effective stress formula was introduced into a numerical integration algorithm of elastic-plastic constitutive equation, that is, closest point projection method (CPPM). Taking the effects of water pressure and seepage into account, a CPPM-based formula was derived and a CPPM algorithm based on Drucker-Prager yield criterion considering the effect of pore water pressure was provided. On this basis, a CPPM-based elastic-plastic numerical analysis program considering pore water pressure was developed, which can be applied in the engineering of tunnels and other underground structures. The algorithm can accurately take the effects of groundwater on stability of surrounding rock mass into account and it can show the more pronounced effect of pore water pressure on stress, deformation, and the plastic zone in a tunnel. The stability of water flooding in Fusong tunnel was systematically analyzed using the developed program. The analysis results showed that the existence of groundwater seepage under tunnel construction will give rise to stress redistribution in the surrounding rock mass. Pore water pressure has a significant effect on the surrounding rock mass.

scholarly journals Solving Reynolds lubrication equations using closest point projection method

2020 ◽  
pp. 1-32 ◽  
Author(s):  
Elizaveta Vyacheslavovna Zipunova ◽  
Evgeny Borisovich Savenkov
Keyword(s):  
Projection Method ◽  
Closest Point Projection ◽  
Point Projection

scholarly journals Cosserat Elastoplastic Finite Elements for Masonry Structures

2014 ◽  
Vol 624 ◽  
pp. 131-138 ◽  
Author(s):  
Michele Godio ◽  
Ioannis Stefanou ◽  
Karam Sab ◽  
Jean Sulem
Keyword(s):  
Finite Elements ◽  
Projection Algorithm ◽  
Elastic Plates ◽  
Discrete Elements ◽  
Backward Euler ◽  
Out Of Plane ◽  
Evolution Laws ◽  
Definition Of ◽  
Closest Point Projection ◽  
Point Projection

A Finite Elements formulation previously developed for Cosserat elastic plates, has been extended herein to the elastoplastic framework. Material non-linearities are taken into account through the implementation of a backward-Euler closest-point-projection algorithm, for which the definition of non-smooth yield loci and non-associated plastic potentials and evolution laws is made possible. An existing homogenized elastic constitutive model and a set of yield criteria for the out-of-plane behaviour of block-masonry are implemented in the code and their validity is discussed based on the comparison with Discrete Elements simulations. The comparison is carried out in both the static and the dynamic regime.

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