A formulation based on the localized Lagrange multipliers for solving 3D frictional contact problems using the BEM

2008 ◽  
pp. 391-400
Keyword(s):  
Lagrange Multipliers ◽  
Frictional Contact ◽  
Contact Problems

A Partitioned Formulation for FEM/BEM Coupling in Contact Problems Using Localized Lagrange Multipliers

2014 ◽  
Vol 618 ◽  
pp. 23-48
Author(s):  
Jose A. González ◽  
K.C. Park ◽  
Ramon Abascal
Keyword(s):  
Finite Element Method ◽  
Lagrange Multipliers ◽  
Frictional Contact ◽  
State Of The Art ◽  
Contact Problems ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Numerical Techniques ◽  
Strongly Coupled ◽  
Software Modularity

This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids using classical Lagrangemultipliers. These methods tend to generate strongly coupled systems that require a deep knowledgeof the discretization characteristics on each side of the contact zone complicating the process ofmixing different numerical techniques. In this work a displacement contact frame is inserted betweenthe FE and BE interface meshes, discretized and finally connected to the contacting substructuresusing LLMs collocated at the mesh-interface nodes. This methodology will provide a partitionedformulation which preserves software modularity and facilitates the connection of non-matching FEand BE meshes.

Dual Weighted Residual Error Control for Frictional Contact Problems

2015 ◽  
Vol 15 (3) ◽  
pp. 391-413 ◽  
Author(s):  
Andreas Rademacher ◽  
Andreas Schröder
Keyword(s):  
Lagrange Multipliers ◽  
Error Control ◽  
Frictional Contact ◽  
Contact Problems ◽  
Residual Error ◽  
Contact Forces ◽  
Processing Step ◽  
Discretization Schemes ◽  
Adaptive Schemes ◽  
Error Method

AbstractIn this paper goal-oriented error control based on the dual weighted residual error method (DWR) is applied to frictional contact problems. The derivation of DWR error controls is done for arbitrary discretization schemes via the introduction of some discrete Lagrange multipliers describing the residual of the discretization. The discrete Lagrange multipliers may be provided by a reconstruction in a post-processing step or by a discretization of a mixed formulation in which they are directly available. The error controls are defined for user-defined functionals (the quantities of interest) which measure the error of the displacement field as well as the normal and tangential contact forces. Numerical experiments confirm the applicability of the estimates within adaptive schemes.

Elastoplastic Frictional Contact Study on Interference Fits of Compressor

2011 ◽  
Vol 211-212 ◽  
pp. 535-539
Author(s):  
Ai Hua Liao
Keyword(s):  
Stress Distribution ◽  
Contact Stress ◽  
Frictional Contact ◽  
Contact Problems ◽  
Boundary Problems ◽  
Interference Fit ◽  
Parametric Variational Principle ◽  
Design And Manufacturing ◽  
Contact Stress Distribution ◽  
Fit Tolerance

The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The FE parametric quadratic programming (PQP) method which was developed based on the parametric variational principle (PVP) was used for the analysis of stress distribution of 3D elastoplastic frictional contact of impeller-shaft sleeve-shaft. The solution of elastoplastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. The effect of fit tolerance, rotational speed and the contact stress distribution on the contact stress was discussed in detail in the numerical computation. The study play a referenced role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers.

scholarly journals CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA
Keyword(s):  
Lagrange Multipliers ◽  
Variational Equation ◽  
Small Deformation ◽  
Contact Problems ◽  
Point Theory ◽  
The Body ◽  
Elastic Materials ◽  
Weak Formulation ◽  
Nonlinearly Elastic ◽  
Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

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
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