Contact in Structural Mechanics
A Weighted Residual Approach
1. Auflage Juni 2024
288 Seiten, Hardcover
Wiley & Sons Ltd
Contact in Structural Mechanics treats the problem of contact in the context of large deformations and the Coulomb friction law. The proposed formulation is based on a weak form that generalizes the classical principle of virtual powers in the sense that the weak form also encompasses all the contact laws. This formulation is thus a weighted residue method and has the advantage of being amenable to a standard finite element discretization.
This book provides the reader with a detailed description of contact kinematics and the variation calculus of kinematic quantities, two essential subjects for any contact study. The numerical resolution is carried out in statics and dynamics. In both cases, the derivation of the contact tangent matrix - an essential ingredient for iterative calculation - is explained in detail. Several numerical examples are presented to illustrate the efficiency of the method.
1 Introduction to Contact Problems in Structural Mechanics 1
2 Contact Kinematics 23
3 Sthenics of Contact 37
4 The Constitutive Law 39
5 Contact Laws 45
6 Strong Formulation of the Contact Problem 51
7 Weak Formulation of the Contact Problem 55
8 Matrix Equations of the Contact Problem 69
9 Solution of the Quasi-static Contact Problem 109
10 Numerical Examples of Quasi-static Contact 157
11 Solution of the Dynamic Contact Problem 197
12 Numerical Examples of Dynamic Contact 213
Appendix A: Variations of Kinematic Quantities 239
References 247
Index 257
