Nonlinear-elastic patterns of dents on surfaces

In the monograph, special variants of the reductive theory of perturbations are developing, which allow you to bring three-dimensional dynamic equations of nonlinear theory of elasticity for plates, layered medium and shells to more simple: two-dimensional and one-dimensional models. The first orders of such the theory are reduced to traditional equations for plates and shells. New substantially nonlinear models have been obtained, which correctly take into account the boundary conditions on the surfaces of the samples, the interaction of longitudinal and transverse modes of material deformation, geometric and physical nonlinearity of the medium, changes in the inertial properties of deformable surfaces due to local changes of their curvature. On this basis, patterns from dents and new types of solitons are analytically described, which are formed on the surfaces of the listed systems on the initial (nonlinear-elastic) stage of change of their form.
The monograph is addressed to researchers, graduate students and students of universities of relevant specialties