Contact Problems in Elasticity. A Study of Variational Inequalities and Finite Element Methods

Description

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.