Contact in Structural Mechanics

A Weighted Residual Approach

Contact in Structural Mechanics

Anh Le van, University of Nantes, France.

ISBN : 9781786309068

Publication Date : May 2024

Hardcover 280 pp

165.00 USD



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.
2. Contact Kinematics.
3. Sthenics of Contact.
4. The Constitutive Law.
5. Contact Laws.
6. Strong Formulation of the Contact Problem.
7. Weak Formulation of the Contact Problem.
8. Matrix Equations of the Contact Problem.
9. Solution of the Quasi-static Contact Problem.
10. Numerical Examples of Quasi-static Contact.
11. Solution of the Dynamic Contact Problem.
12. Numerical Examples of Dynamic Contact.

About the authors/editors

Anh Le van is Professor of Structural Mechanics in the Faculty of Science and Technology, University of Nantes, France. His research at the Research Institute in Civil and Mechanical Engineering (GeM) focuses on membrane structures and, more specifically, on contact and bifurcation problems in these structures.