Nonsmooth/Nonconvex Mechanics

PREFACE

P . D. Panagiotopoulos was born in 1950 in Thessaloniki.
At the age of 40 he had already achieved distinction in nearly everything that for us, common human beings that we are, were to remain just longing or dream for our whole life: for him it was the normal march.
At the age of 24 years he obtained his Doctorate, at 28 years he became a Reader, at 28 years he was elected Full Professor in Thessaloniki University, at 35 Ordinarius at the University of Aachen, at 38 Corresponding Member of the Hellenic National Academy in Athens and finally at 39 Full Member of the Academia Europaea in London.
P. Panagiotopoulos or better Panagis, as he was known to his friends, enjoyed a meteoric rise in his career. His glimmer did not die away with his premature passing. He is to be remembered.
However the most important element of his existence was not his excellent scientific personality but his character: He was full of humanity, sentimental, gentle-natured, sweet. Ready to help, to support, and also to forgive.
It could be said that Gabriel Garcia Marquez met Panagis when he wrote that there is no day without expressions of love and care to friends, colleagues, collaborators.
He was not looking down on us because of scorn, but to offer help to reach his level.
I think that the following few words can be considered the epitaph on Panagis memory:
“The defunct, who lies here, was man of courage and confidence in himself. He made probably mistakes, never lost his fighting spirit or getting fatalist. He spared his passion and energy, mental and spiritual, to serve the science and society.”

Ων οι Θεοί φιλούσιν, αποθνήσκει νέος
Who is by Gods beloved, dies young.

INTRODUCTION

When developing a theory in Mechanics, convenient assumptions are usually adopted; for instance, ‘smoothness’ of all energy functions involved is the requirement, so that all necessary derivatives exist and are continuous functions. However, nature is not smooth: nonsmoothness and nonconvexity arise in a plethora of problems of Mechanics and Engineering along with the need to investigate more realistic i.e. complicated applications. Due to technical ramifications of the corresponding modelling and computation tools, the transition from Smooth into Nonsmooth Mechanics took several decades while several researchers from the science of Mathematics started, since years, the development of effective methods as well as their theoretical investigation. In the same time, researchers in Mechanics and Engineering realized the efficiency of these tools for the treatment of complicated phenomena and real-life problems. Today Nonsmooth/Nonconvex Mechanics has become a well-established scientific branch with exciting prospects of application into Engineering Mechanics, Structural Engineering and Engineering in general.
Within this scope, the Department of Civil Engineering of the Aristotle University of Thessaloniki, pursuing the promotion of original, high level research in various areas of Nonsmooth Mechanics, organized the International Conference on Nonsmooth/Nonconvex Mechanics with Applications in Engineering held at the Aristotle University of Thessaloniki (A.U.Th.), Thessaloniki, Greece, July 5-6, 2002. The International Conference on Nonsmooth/Nonconvex Mechanics with Applications in Engineering is dedicated to the memory of the late Professor Panagiotis (Panos) D. Panagiotopoulos, one of the pioneers of the field who made a plethora of fundamental contributions into the field of Nonsmooth Mechanics and is beyond any doubt considered as one of its fathers.
The research works presented at this International Conference have been assembled in the present Proceedings volume composed of four parts: in the first part, research works on topics from Nonsmooth Analysis, Optimization and Variational Methods are presented; the second part contains works dealing with problems of Nonsmooth Mechanics, Contact Analysis and Elasticity Theory. The third part of the book is devoted to topics from the field of Nonsmooth Dynamics and to certain topics of Control Theory, whereas the last part concerns relevant applications in Engineering problems. In this sense, the Proceedings of the International Conference on Nonsmooth/Nonconvex Mechanics reflect the state-of-the-art of this scientific area.
The papers of the present book correspond to the oral presentations of the participants who supported this scientific event enthusiastically. We would like to thank all the authors for their contributions and all the colleagues for their assistance during the preparation of this volume. Particular thanks are due to Professor Dr.-Ing. habil. G.E. Stavroulakis (Ioannina and Braunschweig) for many valuable discussions and Dipl.Ing. C. Efstathiadis (Thessaloniki) for his support to the preparation of the present volume. Without their assistance, the preparation of the present volume would have, most probably, been impossible.