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.

scholarly journals Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM

2017 ◽  
Vol 11 (1) ◽  
pp. 896-905
Author(s):  
Zhu Chaolei ◽  
Gao Qian ◽  
Hu Zhiqiang ◽  
Lin Gao ◽  
Lu Jingzhou
Keyword(s):  
Mathematical Programming ◽  
Differential Equations ◽  
Cantilever Beam ◽  
Frictional Contact ◽  
Double Cantilever Beam ◽  
Contact Problems ◽  
Contact Forces ◽  
Contact Conditions ◽  
Good Convergence ◽  
Practical Engineering

Introduction: The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering. Method: The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Complementary Problem, etc. Result: In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations. Conclusion The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

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.

Linear Complementary Formulations Involving Frictional Contact for Elasto-Plastic Deformable Bodies

1997 ◽  
Vol 64 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Maocheng Li ◽  
Desong Sha ◽  
K. K. Tamma
Keyword(s):  
Frictional Contact ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Contact Problems ◽  
Tangential Direction ◽  
Normal Direction ◽  
Contact Forces ◽  
Contact Boundary ◽  
Normal Contact

In the present study, an incremental variational inequality is described for frictional contact problems with material non linear behavior assumed to be elasto-plastic for the contacting bodies. On the contacting boundaries, the constraint conditions include noninterpenetration along the normal direction of the contact boundary and Coulomb friction law in the sliding direction. After numerical discretization using the finite element method, an effective linear complementary formulation is then established with two unknown variables and two complementary variables for each contact nodal pair. The proposed developments permit a reduced number of unknown variables which are chosen as the gap function for the normal direction and the norm of the incremental sliding displacements for the tangential direction; and the complementary variables are taken as the normal contact forces and slack variables in the tangential directions. The resulting linear complementary equations are then solved employing an explicit Conjugate Gradient Based Projection (CGBP) method in conjunction with a generalized Newton-Raphson iteration procedure to account for the material nonlinear behavior. The methodology is valid for three-dimensional frictional contact representations; however, for purposes of illustration of the proposed approaches, attention is confined to applications involving two-dimensional static elasto-plastic problems under small deformation. Numerical examples are presented which clearly show that the developments satisfy the problem physics and contact conditions with features to include high accuracy and reduced computational costs.

Goal Oriented Error Control for Frictional Contact Problems in Metal Forming

2012 ◽  
Vol 504-506 ◽  
pp. 987-992
Author(s):  
Heribert Blum ◽  
Andreas Rademacher ◽  
Andreas Schröder
Keyword(s):  
Finite Element ◽  
Metal Forming ◽  
Error Control ◽  
Frictional Contact ◽  
A Posteriori Error Estimates ◽  
Contact Problems ◽  
Posteriori Error ◽  
Weighted Residual Method ◽  
Contact Conditions ◽  
Element Discretization

In this note, techniques for goal oriented error control of finite element discretizations are proposed for frictional contact problems. The finite element discretization is based on a mixed method, where Lagrange multipliers are introduced to capture the geometrical and frictional contact conditions. A posteriori error estimates for user-defined, probably non-linear quantities of interest are derived using the dual weighted residual method (DWR). Numerical results substantiate the applicability of the presented techniques to the simulation of metal forming processes.

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.

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