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Numerical methods for unilateral problems in solid mechanics. (English) Zbl 0873.73079
Ciarlet, P. G. (ed.) et al., Finite element methods (part 2), numerical methods for solids (part 2). Amsterdam: North-Holland (ISBN 0-444-81794-8). Handbook of Numerical Analysis 4, 313-485 (1995).
The purpose is to survey the numerical analysis of variational inequalities, which stem from solid mechanics. The work comprises six chapters.
In chapter I we consider elliptic second order problems, where the unknown is a single real scalar function in a given domain of an \(n\)-dimensional space \(\mathbb{R}^n\), \(n=2,3\). Using simple models, we illustrate the primal, mixed and dual variational formulations. Approximations of the above-mentioned problems are studied in chapter II.
Chapter III contains an analysis of the one-sided contact of elastic bodies, both without friction and with friction of Coulomb’s type. An extension of the contact problems to some elasto-plastic bodies is presented in chapter IV. From various mathematical models of elasto-plastic bodies we choose the perfect plasticity and plasticity with strain hardening. Both existence problems and approximations via finite-element methods are studied in chapter V.
The final chapter VI is devoted to the bending of elastic plates with unilateral obstacles either on the boundary or in the interior of the domain occupied by the plate.
For the entire collection see [Zbl 0864.65001].

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
49J40 Variational inequalities