PREFACE

The studies of contact interaction in the mechanics of deformable solids have been carried out since late 19th century, starting from the works of Winkler (1867), Hertz (1881), and Boussinesq (1885). These studies have been further developed by specialists in the mechanics of deformable solids as well as in structural mechanics, bases and foundations. Thousands of papers on this topic have been published, most of their authors using simplifying assumptions of theoretical modeling on a flat or axially symmetrical stressed state of a base under a punch (a foundation model). It is seen from the detailed analysis of references found in literature that mathematical modeling of essentially spatial contact interaction is in its early stage. The existing methods for the calculation of complex-shaped foundations are, as a rule, based on a bed coefficient hypothesis. This results in the introduction of empirical coefficients into the calculation methods, thus restricting the range of their application. In the recent years more attention is paid to finite-element approach to mathematical modeling of spatial contact interaction of foundations with bases. However, in such studies the dimensionality of the algebraic analogue of the contact problem sharply increases and the problem must be restricted to a number of partial problems – for example, by imposing restrictions to shape and size of both the foundations themselves and the soil massifs around the foundations, by considering loads in assumption of existence of symmetry axes or planes in the calculation scheme etc. Such studies are rather rare and lack proper consideration of loads of general spatial type (horizontal, vertical forces and moments) and the possibility of their combined action. And extremely rare are studies where the complex shape of various foundations, applied in industrial and civil engineering, is fully taken into account and theoretically based calculations are made. Creation of new progressive foundation structures and solution of current problems of geotechnical engineering result in more complicated problems to be solved and in the increasing accuracy of the calculation results. The mathematical description of the problems has become so complicated that traditional methods are no longer suitable for their solution. The lack of reliable mathematical methods to a certain extent retards elaboration and implementation of new foundation structures in engineering. Hence, the development of boundary element method (BEM), a relatively new trend in structural mechanics, based on boundary integral equations, seems to be quite promising from the point of view of both theory and application as