Lecture Notes in Engineering: A Boundary Element Method for Two-Dimensional Contact Problems

by Ghodratollah Karami

Overview

The Boundary Element Method (BEM) has been established as a powerful numerical tool for the analysis of continua in recent years. The method is based on an attempt to transfer the governing differential equations into integral equations over the boundary. Thus, the discretization scheme or the introduction of any approximations must be done over the boundary. This book presents a BEM for two-dimensional elastic, thermo­ -elastic and body-force contact problems. The formulation is implemented for the general case of contact with various fric­ tional conditions. The analysis is limited to linear elasto­ statics and small strain theory. Following a review of the basic nature of contact problems, the analytical basis of the direct formulation of the BEM method is described. The numerical implementation employs three-noded isoparametric line elements for the representation of the boundary of the bodies in contact. Opposite nodal points in equi-Iength element-pairs are defined on the two surfaces in the area which is expected to come into contact under an increasing load. The use of appropriate contact IV conditions enables the integral equations for the two bodies to be coupled together. To find the proper contact dimensions and the contact load a combined incremental and iterative approach is utilised. With this approach, the loads are applied progressively, and the sliding and adhering portion of the contact region is established for each load increment using an iterative procedure. A coulomb type of friction law is assumed.

Product Details

ISBN-13:	9783540515623
Publisher:	Springer Berlin Heidelberg
Publication date:	09/18/1989
Series:	Lecture Notes in Engineering , #51
Edition description:	Softcover reprint of the original 1st ed. 1989
Pages:	243
Product dimensions:	6.69(w) x 9.53(h) x 0.02(d)

Table of Contents

Content.- 1. Introduction.- References.- 2. The Contact Problem.- 2.1 Analytical Treatment of Contact.- 2.2 Numerical Treatment of Contact.- 2.3 General Description of Contact Problems.- 2.4 Interface Boundary Conditions.- 2.5 Load Increment Method.- References.- 3. Formulation of the Boundary Element Method.- 3.1 Intorduction.- 3.2 Governing Equation of Elastostatics.- 3.3 Derivation of the Integral Equation.- 3.4 Integral Equations for Dispacements and Stresses at Interior Points.- 3.5 The Boundary Integral Equation.- 3.6 The Boundary Integral Equation for Contact Problems.- 3.7 Final Remarks.- References.- 4. The Numerical Solution to Boundary Element Method.- 4.1 Review of Various Numerical Formulations.- 4.2 Parametric Representation of Geometry and Functions.- 4.3 Numerical Formulation of Boundary Integral Equations.- 4.4 Evaluation of Equation Coefficients.- 4.5 Formation of Coefficient Matrix of the Equations.- 4.6 Treatment of Boundary Conditions.- 4.7 Treatment of Contact Conditions.- 4.8 Solution to the System of Equations.- 4.9 Stresses at the Boundary.- 4.10 Stresses and Displacements at Interior Points.- 4.11 Calculation of Forces on Every Boundary Element.- 4.12 Modified Load Increment Factor for Parabolic Elements.- 4.13 Final Remarks.- References.- 5. Application of the Bem to Hertzian Type Contact Problems.- 5.1 Two-dimensional Hertzian Contact.- 5.2 Two-dimensional Hertzian Modelling-Contact of Rollers.- 5.3 Determination of the External Load.- References.- 6. Application of Bem to Non-Hertzian Contact Problems.- 6.1 Introduction.- 6.2 Elastic Punch on an Elastic Foundation.- 6.3 Connecting Rod.- 6.4 Turbine Blade Root Fastenings.- 6.5 A Circular Inclusion in an Infinite Plate.- References.- 7. Application of Bem to Thermo-Elastic Body-Force Contact Problems.- 7.1 Governing Equations.- 7.2 Analytical Treatment.- 7.3 Numerical Treatment.- 7.4 Body-Force Contact Examples.- 7.5 Thermo-Elastic Contact Examples.