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Models and Analysis of Quasistatic Contact

2004-09-16 Science
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Release : 2004-09-16
Genre : Science
Kind : eBook
Book Rating : 155/5 ( reviews)

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Book Synopsis Models and Analysis of Quasistatic Contact by : Meir Shillor

Download or read book Models and Analysis of Quasistatic Contact written by Meir Shillor. This book was released on 2004-09-16. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 925/5 ( reviews)

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Book Synopsis Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity by : Weimin Han

Download or read book Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity written by Weimin Han. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Índice: Function spaces and their properties; Introduction to finite difference and finite element approximations; Variational inequalities; Constitutive relations in solid mechanics; Background on variational and numerical analysis in contact mechanics; Contact problems in elasticity; Bilateral contact with slip dependent friction; Frictional contact with normal compliance; Frictional contact with normal damped response; Other viscoelastic contact problems; Frictionless contact with dissipative potential; Frictionless contact between two viscoplastic bodies; Bilateral contact with Tresca's friction law; Other viscoelastic contact problems; Bibliography; Index.

Analysis of Geometrically Non-linear Models for Contact with Dry Friction

2008
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Release : 2008
Genre :
Kind : eBook
Book Rating : 058/5 ( reviews)

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Book Synopsis Analysis of Geometrically Non-linear Models for Contact with Dry Friction by : Florian Schmid

Download or read book Analysis of Geometrically Non-linear Models for Contact with Dry Friction written by Florian Schmid. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This work establishes a mathematical existence theory for solutions of some quasi-static models in contact mechanics with dry friction. The models are finite dimensional and friction is modeled according to Coulomb's law. The main focus is on the geometric non-linearity which is due to the curved obstacle surface.

Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity

Mathematics
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Genre : Mathematics
Kind : eBook
Book Rating : 339/5 ( reviews)

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Book Synopsis Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity by : Weimin Han

Download or read book Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity written by Weimin Han. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to a mathematical theory of contact problems involving deformable bodies. It covers mechanical modeling, mathematical formulations, variational analysis, and the numerical solution of the associated formulations. The authors give a complete treatment of some contact problems by presenting arguments and results in modeling, analysis, and numerical simulations. Variational analysis of the models includes existence and uniqueness results of weak solutions,as well as results of continuous dependence of the solution on the data and parameters. Also discussed are links between different mechanical models.

Analysis of a Quasi-variational Contact Problem Arising in Thermoelasticity

2020
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Release : 2020
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Book Synopsis Analysis of a Quasi-variational Contact Problem Arising in Thermoelasticity by : Amal Alphonse

Download or read book Analysis of a Quasi-variational Contact Problem Arising in Thermoelasticity written by Amal Alphonse. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling is determined by the thermal displacement of the mould that depends in turn on the membrane through the contact region. The two models considered are a stationary (or elliptic) model and an evolutionary (or quasistatic) one. For the first model, we prove the existence of weak solutions by solving an elliptic quasi-variational inequality coupled to elliptic equations. By exploring the fine properties of the variation of the contact set under non-degenerate data, we give sufficient conditions for the existence of regular solutions, and under certain contraction conditions, also a uniqueness result. We apply these results to a series of semi-discretised problems that arise as approximations of regular solutions for the evolutionary or quasistatic problem. Here, under certain conditions, we are able to prove existence for the evolutionary problem and for a special case, also the uniqueness of time-dependent solutions.

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