𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Variational and quasi-variational inequalities in mechanics

✍ Scribed by Alexander S. Kravchuk, Pekka J. Neittaanmäki

Book ID
127419210
Publisher
Springer
Year
2007
Tongue
English
Weight
4 MB
Series
Solid Mechanics and Its Applications
Edition
1
Category
Library
ISBN
1402063776

No coin nor oath required. For personal study only.

✦ Synopsis

The essential aim of the present book is to consider a wide set of problems arising in the mathematical modelling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities, and the transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.

Important new results concern contact problems with friction. The Coulomb friction law and some others are considered, in which relative sliding velocities appear. The corresponding quasi-variational inequality is constructed, as well as the appropriate iterative method for its solution. Outlines of the variational approach to non-stationary and dissipative systems and to the construction of the governing equations are also given.

Examples of analytical and numerical solutions are presented. Numerical solutions were obtained with the finite element and boundary element methods, including new 3D problems solutions.

📜 SIMILAR VOLUMES

[Advances in Mechanics and Mathematics]
[Advances in Mechanics and Mathematics] Variational Inequalities and Frictional Contact Problems Volume 31 || Dual Formulations of Quasi-Variational Inequalities
✍ Capatina, Anca 📂 Article 📅 2014 🏛 Springer International Publishing 🌐 German ⚖ 202 KB

Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide

Generalized quasi-variational hemi-varia
Generalized quasi-variational hemi-variational inequalities
✍ Zhenhai Liu 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 261 KB

This paper is devoted to the existence of solutions for generalized quasi-variational hemi-variational inequalities with multivalued, discontinuous pseudomonotone operators. We obtain results which generalize and extend previously known theorems.