An Augmented Lagrange Method to Solve Large Deformation Three-Dimensional Contact Problems

2010 ◽  
Author(s):  
M. Tur ◽  
J. Albelda ◽  
E. Giner ◽  
J.E. Tarancón
Keyword(s):  
Large Deformation ◽  
Three Dimensional ◽  
Contact Problems ◽  
Lagrange Method ◽  
Augmented Lagrange Method

scholarly journals Sensitivity Analysis for Frictional Contact Problems with Large Deformation.

1999 ◽  
Vol 65 (637) ◽  
pp. 1859-1866
Author(s):  
Xian CHEN ◽  
Kazuhiro NAKAMURA ◽  
Masahiko MORI ◽  
Toshiaki HISADA
Keyword(s):  
Sensitivity Analysis ◽  
Large Deformation ◽  
Frictional Contact ◽  
Contact Problems

scholarly journals A note on embeddings for the Augmented Lagrange Method

2010 ◽  
Vol 20 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Gemayqzel Bouza-Allende ◽  
Jurgen Guddat
Keyword(s):  
Augmented Lagrangian ◽  
Equality Constraints ◽  
Embedding Problem ◽  
Lagrange Method ◽  
Parametric Problem ◽  
Nonlinear Programs ◽  
Augmented Lagrange Method ◽  
Quadratic Perturbation ◽  
Lagrangian Embedding

Nonlinear programs (P) can be solved by embedding problem P into one parametric problem P(t), where P(1) and P are equivalent and P(0), has an evident solution. Some embeddings fulfill that the solutions of the corresponding problem P(t) can be interpreted as the points computed by the Augmented Lagrange Method on P. In this paper we study the Augmented Lagrangian embedding proposed in [6]. Roughly speaking, we investigated the properties of the solutions of P(t) for generic nonlinear programs P with equality constraints and the characterization of P(t) for almost every quadratic perturbation on the objective function of P and linear on the functions defining the equality constraints.

A virtual element method for frictional contact including large deformations

2019 ◽  
Vol 36 (7) ◽  
pp. 2133-2161 ◽  
Author(s):  
Peter Wriggers ◽  
Wilhelm T. Rust
Keyword(s):  
Large Deformation ◽  
Contact Problems ◽  
Stable Node ◽  
Virtual Element Method ◽  
Polygonal Mesh ◽  
Content Type ◽  
Polygonal Elements ◽  
Virtual Element ◽  
Adaptively Adjusting ◽  
Element Method

Purpose This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies. Design/methodology/approach Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding. Findings The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples. Originality/value This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

On the Singularities in Fracture and Contact Mechanics

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Fazil Erdogan ◽  
Murat Ozturk
Keyword(s):  
Contact Mechanics ◽  
Integral Equations ◽  
Mixed Boundary ◽  
Complex Function ◽  
Three Dimensional ◽  
Contact Problems ◽  
Cauchy Kernel ◽  
Square Root ◽  
Complex Function Theory ◽  
Graded Materials

Generally, the mixed boundary value problems in fracture and contact mechanics may be formulated in terms of integral equations. Through a careful asymptotic analysis of the kernels and by separating nonintegrable singular parts, the unique features of the unknown functions can then be recovered. In mechanics and potential theory, a characteristic feature of these singular kernels is the Cauchy singularity. In the absence of other nonintegrable kernels, Cauchy kernel would give a square-root or conventional singularity. On the other hand, if the kernels contain, in addition to a Cauchy singularity, other nonintegrable singular terms, the application of the complex function theory would show that the solution has a non-square-root or unconventional singularity. In this article, some typical examples from crack and contact mechanics demonstrating unique applications of such integral equations will be described. After some remarks on three-dimensional singularities, the key examples considered will include the generalized Cauchy kernels, membrane and sliding contact mechanics, coupled crack-contact problems, and crack and contact problems in graded materials.

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