New trends in free boundary problems and new mathematical tools together
with broadening areas of applications have led to attempts at presenting
the state of art of the field in a unified way. In this monograph we
focus on formal models representing contact problems for elastic and
elastoplastic plates and shells. New approaches open up new fields for
research. For example, in crack theory a systematic treatment of
mathematical modelling and optimization of problems with cracks is
required. Similarly, sensitivity analysis of solutions to problems
subjected to perturbations, which forms an important part of the problem
solving process, is the source of many open questions. Two aspects of
sensitivity analysis, namely the behaviour of solutions under
deformations of the domain of integration and perturbations of surfaces
seem to be particularly demanding in this context. On writing this book
we aimed at providing the reader with a self-contained study of the
mathematical modelling in mechanics. Much attention is given to
modelling of typical constructions applied in many different areas.
Plates and shallow shells which are widely used in the aerospace
industry provide good exam- ples. Allied optimization problems consist
in finding the constructions which are of maximal strength (endurance)
and satisfy some other requirements, ego weight limitations.
Mathematical modelling of plates and shells always requires a reasonable
compromise between two principal needs. One of them is the accuracy of
the de- scription of a physical phenomenon (as required by the
principles of mechanics).
