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The limit elastic state of an infinitely large half-plane under the action of concentrated vertical and horizontal forces has been considered. The gradient yield condition specifying the elasto-plastic material yielding initial moment at non-uniform stress state is used as the limit state criterion. The analytical expressions allowing to interpret the result in the singular point have been derived.

The limiting elastic state of a beam with large curvature under pure and transverse bending is considered. The gradient plasticity condition which determines the yield onset in an inhomogeneous stress state is applied as a criterion of the ultimate state. The analytical expressions for calculating the corresponding stresses and loads are obtained.

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Relevant objective of this article is elaboration of methods of efficient determination of the dynamic characteristics of the materials both within the framework of well-known and classical models as well as within the advanced ones in the context of interaction with the environment under the impact of external dynamic loads. In the present work free and forced oscillations are studied with a help of spectral methods what allows to compare theoretical results with experimental data, obtained by other authors. The key point of the work is theoretical determination of the proper functions of the oscillatory system, its frequency characteristic using Green’s function. We examine longitudinal oscillations, caused by the substitute load, which provokes oscillations of a sound spectrum. Univariate character of the task is determined by the linearity organization of the longitudinal oscillations of a beam. The oscillations are modeled with a help of the substitute load, which is a subject to Dirac impulse function, which belongs to a class of generalized functions. The obtained solution makes it possible to use the proposed approach in order to determine frequency characteristics in the acoustic spectrum, taking into account that the oscillations are included in a full frequency spectrum and can be used for an adequate valuation of the possibility of the appearance of resonance phenomena.