Contact Problems in Elasticity A Study of Variational Inequalities and Finite Element Methods azw3 网盘 高速 下载地址大全 免费

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 new 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.

Front Matter pp. i-xiii 1. Introduction pp. 1-17 2. Signorini's Problem pp. 19-30 3. Minimization Methods and Their Variants pp. 31-54 4. Finite Element Approximations pp. 55-73 5. Orderings, Trace Theorems, Green's Formulas, and Korn's Inequalities pp. 75-110 6. Signorini's Problem Revisited pp. 111-172 7. Signorini's Problem for Incompressible Materials pp. 173-199 8. Alternate Variational Principles for Signorini's Problem pp. 201-239 9. Contact Problems for Large Deflections of Elastic Plates pp. 241-265 10. Some Special Contact Problems with Friction pp. 267-306 11. Contact Problems with Nonclassical Friction Laws pp. 307-367 12. Contact Problems Involving Deformations and Nonlinear Materials pp. 369-408 13. Dynamic Friction Problems pp. 409-449 14. Rolling Contact Problems pp. 451-469 Back Matter pp. 471-495

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