All Outputs (5)

Asymptotic strategy for matching homogenized structures. Conductivity problem (2018)
Journal Article
Kolpakov, A. G., Andrianov, I. V., & Prikazchikov, D. A. (2018). Asymptotic strategy for matching homogenized structures. Conductivity problem. Quarterly Journal of Mechanics and Applied Mathematics, 71(4), 519-535. https://doi.org/10.1093/qjmam/hby017

The paper is concerned with application of the homogenization theory to bodies containing macroinhomogeneities or bodies, parts of which cannot be homogenized (partial homogenization). This situation arises, in particular, for problems of joining hom... Read More about Asymptotic strategy for matching homogenized structures. Conductivity problem.

Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space (2018)
Journal Article
Khajiyeva, L., Prikazchikov, D., & Prikazchikova, L. (2018). Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space. Mechanics Research Communications, 92, 49-53. https://doi.org/10.1016/j.mechrescom.2018.07.006

The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic half-space, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the p... Read More about Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space.

Free vibrations of nonlocally elastic rods (2018)
Journal Article
Mikhasev, G., Avdeichik, E., & Prikazchikov, D. (2019). Free vibrations of nonlocally elastic rods. Mathematics and Mechanics of Solids, 24(5), 1279-1293. https://doi.org/10.1177/1081286518785942

Several of the Eringen’s nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in case of free longitudinal vibrations of a nanorod, for various types of boundary... Read More about Free vibrations of nonlocally elastic rods.

Justification and refinement of Winkler-Fuss hypothesis (2018)
Journal Article
Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2018). Justification and refinement of Winkler-Fuss hypothesis. Zeitschrift für Angewandte Mathematik und Physik, 69, Article 80. https://doi.org/10.1007/s00033-018-0974-1

Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that... Read More about Justification and refinement of Winkler-Fuss hypothesis.

Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane (2018)
Journal Article
Nobili, A., & Prikazchikov, D. A. (2018). Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane. European Journal of Mechanics - A/Solids, 70, 86-94

We develop an explicit asymptotic model for the Rayleigh wave field arising in case of stresses prescribed on the surface of an orthorhombic elastic half-plane. The model consists of an elliptic equation governing the behaviour within the half-plane,... Read More about Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane.