A non-local solution is obtained here in the theory of cracks, which depends on scale parameter elasticity. The gradient constructed as a regular inhomogeneous Helmholtz equation, where function right side equation singular classical solution. An assertion proved that allows us to propose new for displacements and stresses at crack tip through vector harmonic potential, determines by Papkovich-Neuber representation. One goals this work definition representation plane problem elasticity...

In the present work, we aim to estimate effective storage and loss moduli of bristled fiber composite material (modified composites), where surfaces fibers are radially grown or coated with nanostructures such as nanowires, nanorods, carbon nanotubes (fuzzy fiber). We use Eshelby integral formula, which plays a fundamental role in micromechanics materials especially gradient models that allow one describe scale effects. two-phase system, an formula framework generalized self-consistent...

The problem of improved simulation ultrathin rods, arising because the need explaining known experimental data about a substantial dependence flexural rigidity such structures on their thickness when becomes commensurable with characteristic parameters material microstructure, is discussed. In order to simulate effects in theory thin rods gradient theories are used. question whether really implement scale that result modification effective properties considered. analysis made using correct...

In this work, we study gas flow through shale matrix consisting of a microporous inorganic material and nanoporous organic (kerogen). We apply multiscale analysis to mass balance equations taking into account such processes as desorption from nanopores in kerogen, diffusion, filtration. As result, get macroscopic initial boundary-value problem with effective coefficients. The coefficients are determined the solution on representative elementary volume (REV or periodicity cell). They...

In the paper, a two-level scheme is substantiated for representing solutions thermoviscoelasticity equations with fast oscillating coefficients corresponding to structurally inhomogeneous viscoelastic medium nonlinear characteristics. contrast traditional approach based on classical method of asymptotic homogenization, here, in analysis equations, additional dependences material characteristics temperature and spatial coordinates are taken into account. To this end, homogenization procedure...

The problem of designing a sandwich flat panel consisting bearing layers, corrugated Z-shaped rigid filler, heat-insulating and heat-shielding external coating is considered. made provided static mechanical strength with account for thermal protection requirements under the conditions stationary nonstationary effects. Models construction mechanics, physics, mechanics composite materials are used to formulate explicit analytical relations determining geometry parameters layers comprising...

A homogenization procedure was implemented to carry out a multiscale asymptotic analysis of Brinkman's filtration fluid in rigid porous media. As result we obtained averaged macroscopic equations with the components effective permeability tensor as coefficients. The derivation reduced solution periodic boundary problems unit cell. In order solve this problem have developed an analytical-numerical method based on approximation by series shape functions that exactly satisfied interface...

Abstract New efficient analytic‐numerical method for solving elliptic boundary‐value problems in 2D and 3D complex‐shaped domains is presented. The case of with rounded cones considered detail.

The asymptotic averaging technique is used to solve the equations describing filtration of viscous compressible barotropic substance in a medium with periodic structure pores. As equation motion, we consider generalization Brinkman case possible unsteady flow fluid, which takes into account nonlinear effects related dependence viscosity and friction coefficients on pressure. effective permeability tensor found course solution periodicity cell corresponding problems their subsequent...

In this paper, we apply the method of asymptotic homogenization in parametric space order to determine thermo-viscoelastic properties materials composed cylindrical fibers surrounding by an intermediate layer separating them from viscoelastic matrix. We use Maxwell model viscoelasticity. The volumetric fraction and physical can vary. There is a possibility contrast between fibers, layer, Our approach allows us treat temperature as parameter study response mechanical characteristics on change...

The optimization problem of a measuring network on coastal seawater areas is actually<br>for the countries with advanced line subject to influence flows, ebbs and wind<br>fluxes, including Russia. optimal location devices tracing a<br>level water surface in area Northern sea, adjoining Wilhelmshaven port the<br>Jade river bay at northern coast Germany considered.