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Gives a complete and rigorous presentation of the mathematical
study of the expressions - hemivariational inequalities - arising
in problems that involve nonconvex, nonsmooth energy functions. A
theory of the existence of solutions for inequality problems
involving monconvexity and nonsmoothness is established.
Gives a complete and rigorous presentation of the mathematical
study of the expressions - hemivariational inequalities - arising
in problems that involve nonconvex, nonsmooth energy functions. A
theory of the existence of solutions for inequality problems
involving monconvexity and nonsmoothness is established.
Nonsmooth energy functions govern phenomena which occur frequently
in nature and in all areas of life. They constitute a fascinating
subject in mathematics and permit the rational understanding of yet
unsolved or partially solved questions in mechanics, engineering
and economics. This is the first book to provide a complete and
rigorous presentation of the quasidifferentiability approach to
nonconvex, possibly nonsmooth, energy functions, of the derivation
and study of the corresponding variational expressions in
mechanics, engineering and economics, and of their numerical
treatment. The new variational formulations derived are illustrated
by many interesting numerical problems. The techniques presented
will permit the reader to check any solution obtained by other
heuristic techniques for nonconvex, nonsmooth energy problems. A
civil, mechanical or aeronautical engineer can find in the book the
only existing mathematically sound technique for the formulation
and study of nonconvex, nonsmooth energy problems. Audience: The
book will be of interest to pure and applied mathematicians,
physicists, researchers in mechanics, civil, mechanical and
aeronautical engineers, structural analysts and software
developers. It is also suitable for graduate courses in nonlinear
mechanics, nonsmooth analysis, applied optimization, control,
calculus of variations and computational mechanics.
Nonsmooth energy functions govern phenomena which occur frequently
in nature and in all areas of life. They constitute a fascinating
subject in mathematics and permit the rational understanding of yet
unsolved or partially solved questions in mechanics, engineering
and economics. This is the first book to provide a complete and
rigorous presentation of the quasidifferentiability approach to
nonconvex, possibly nonsmooth, energy functions, of the derivation
and study of the corresponding variational expressions in
mechanics, engineering and economics, and of their numerical
treatment. The new variational formulations derived are illustrated
by many interesting numerical problems. The techniques presented
will permit the reader to check any solution obtained by other
heuristic techniques for nonconvex, nonsmooth energy problems. A
civil, mechanical or aeronautical engineer can find in the book the
only existing mathematically sound technique for the formulation
and study of nonconvex, nonsmooth energy problems. Audience: The
book will be of interest to pure and applied mathematicians,
physicists, researchers in mechanics, civil, mechanical and
aeronautical engineers, structural analysts and software
developers. It is also suitable for graduate courses in nonlinear
mechanics, nonsmooth analysis, applied optimization, control,
calculus of variations and computational mechanics.
The fields of boundary integral equations and of inequality
problems, or more gen erally, of nonsmooth mechanics, have seen, in
a remarkably short time, a considerable development in mathematics
and in theoretical and applied mechanics. The engineering sciences
have also benefited from these developments in that open problems
have been attacked succesfully and entirely new methodologies have
been developed. The contact problems of elasticity is a class of
problems which has offered many open questions to deal with, both
to the research workers working on the theory of boundary integral
equations and to those working on the theory of inequality
problems. Indeed, the area of static and dynamic contact problems
could be considered as the testing workbench of the new
developments in both the inequality problems and in the boundary
integral equations. This book is a first attempt to formulate and
study the boundary integral equations arising in inequality contact
problems. The present book is a result of more than two decades of
research and teaching activity of the first author on boundary
integral equations and, of the second author, on inequality
problems, as well as the outgrowth of seminars and courses for a
variety of audiences in the Technical University of Aachen, the
Aristotle University of Thessa loniki, the Universities of Bochum,
of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio
de Janeiro etc."
In a remarkably short time, the field of inequality problems has
seen considerable development in mathematics and theoretical
mechanics. Applied mechanics and the engineering sciences have also
benefitted from these developments in that open problems have been
treated and entirely new classes of problems have been formulated
and solved. This book is an outgrowth of seven years of seminars
and courses on inequality problems in mechanics for a variety of
audiences in the Technical University of Aachen, the Aristotle
University of Thessaloniki, the University of Hamburg and the
Technical University of Milan. The book is intended for a variety
of readers, mathematicians and engineers alike, as is detailed in
the Guidelines for the Reader. It goes without saying that the work
of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating
and developing the theory of inequality problems has considerably
influenced the present book. I also wish to acknowledge the helpful
comments received from C. Bisbos, J. Haslinger, B. Kawohl, H.
Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also
due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally
diligent work in the preparation of the fmal figures. Many thanks
are also due to T. Finnegan and J. Gateley for their friendly
assistance from the linguistic standpoint. I would also like to
thank my editors in Birkhiiuser Verlag for their cooperation, and
all those who helped in the preparation of the manuscript.
1 Introductory Material.- 2 The Direct and Indirect B.I.E.M. for
Bilateral Problems.- 3 Boundary Integral Formulations for Some
Special Elastostatic B.V.Ps.- 4 On the Numerical Implementation of
Boundary Element Equations.- 5 Extension to Dynamic Problems.- 6
Dynamic Interaction Problems.- 7 B.I. Formulations for the
Signorini-Fichera Inequality Problem.- 8 Mathematical Study of the
B.I. Formulations of the Signorini-Fichera B.V.P..- 9 Boundary
Integral Formulation of the Frictional Unilateral Contact B.V.P..-
10 Boundary Integral Formulations for the Monotone Multivalued
Boundary Conditions.- 11 Elastodynamic Unilateral Problems. A
B.I.E. Approach.- 12 Nonconvex Unilateral Contact Problems.- 13
Miscellanea.- References.
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