Book,
Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (Studies in Applied and Numerical Mathematics)
Society for Industrial and Applied Mathematics, (Jul 14, 1995)
Abstract
The contact of one deformable body with another lies at the heart of almost
every mechanical structure. Here, in a comprehensive treatment, two of the
field's leading researchers present a systematic approach to contact problems.
Using variational formulations, Kikuchi and Oden derive a multitude of
results, both for classical problems and for nonlinear problems involving
large deflections and buckling of thin plates with unilateral supports, dry
friction with nonclassical laws, large elastic and elastoplastic deformations
with frictional contact, dynamic contacts with dynamic frictional effects, and
rolling contacts. This method exposes properties of solutions obscured by
classical methods, and it provides a basis for the development of powerful
numerical schemes.
Among the novel results presented here are algorithms for contact problems
with nonlinear and nonlocal friction, and very effective algorithms for
solving problems involving the large elastic deformation of hyperelastic
bodies with general contact conditions. Includes detailed discussion of
numerical methods for nonlinear materials with unilateral contact and
friction, with examples of metalforming simulations. Also presents algorithms
for the finite deformation rolling contact problem, along with a discussion of
numerical examples.
Contents
Introduction; Signorini's Problem; Minimization Methods and Their Variants;
Finite Element Approximations; Orderings, Trace Theorems, Green's Formulas and
Korn's Inequalities; Signorini's Problem Revisited; Signorini's Problem for
Incompressible Materials; Alternate Variational Principles for Signorini's
Problem; Contact Problems for Large Deflections of Elastic Plates; Some
Special Contact Problems with Friction; Contact Problems with Nonclassical
Friction Laws;Contact Problems Involving Deformations and Nonlinear Materials;
Dynamic Friction Problems; Rolling Contact Problems; Concluding Comments.
Tags
- 35j87-nonlinear-elliptic-variational-inequalities
- 74m15-contact-mechanics-of-deformable-solids
- 74s05-finite-element-methods-for-solid-mechanics
