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The stress–strain state in the alveolar bone crest is analyzed over a wide range of stiffness ratios between the bone and
the primary strut of the subperiosteal implant. Recommendations on the rational design of subperiosteal implants are given

Content Type Journal ArticlePages 1-7DOI 10.1007/s10778-012-0510-5Authors
A. N. Chuiko, Kharkiv State University of Food Technology and Trade, 333 Klochkovskaya St., Kharkov, Ukraine 61061I. A. Shinchukovskii, Bogomolets National Medical University, 13 T. Shevchenko Av., Kyiv, Ukraine 01601A. V. Oleinik, Bogomolets National Medical University, 13 T. Shevchenko Av., Kyiv, Ukraine 01601V. A. Kutsenko, Kharkiv State University of Food Technology and Trade, 333 Klochkovskaya St., Kharkov, Ukraine 61061A. S. Alymbaev, Akhunbaev Kyrgyz State Medical Academy, 92 Akhunbaeva St., Bishkek, Kyrgyzstan 720020

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials
are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized
by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the
equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises or Schleicher–Nadai criteria,
and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations
relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage
and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied

Content Type Journal ArticlePages 1-49DOI 10.1007/s10778-012-0504-3Authors
L. P. Khoroshun, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057E. N. Shikula, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

The model of a fracture process zone near the tip of a mode I crack in a nonlinear elastic body is proposed. Using the numerical
solution of an appropriate boundary-value problem, the effect of the fracture process zone on a crack opening displacement
is examined

Content Type Journal ArticlePages 1-10DOI 10.1007/s10778-011-0499-1Authors
A. A. Kaminsky, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057E. E. Kurchakov, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

An algorithm for the identification of a stationary linear system from sampled data on a transient process is presented. The
algorithm allows the original problem to be decomposed into two problems: finding the roots of the characteristic polynomial
and determining the amplitudes of the respective modes. A special objective function permits increasing the accuracy of identification

Content Type Journal ArticlePages 1-7DOI 10.1007/s10778-011-0501-yAuthors
V. B. Larin, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057A. S. Apostolyuk, National Technical University of Ukraine “KPI”, 37 Pobedy Av., Kyiv, Ukraine 03056

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

Edge effects in a laminated composite with two isotropic components under uniaxial compression are studied. Grid equations
are derived using a modified variational difference method. Numerical results are analyzed

Content Type Journal ArticlePages 1-7DOI 10.1007/s10778-011-0494-6Authors
Yu. V. Kokhanenko, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

The natural frequencies and modes of a flexible elastic ring fixed at one point are determined numerically by solving an eigenvalue
problem for the differential operator of the equation of its motion. The ring models a large circular antenna that slowly
expands under zero gravity. Bending and torsional vibrations in a plane perpendicular to the antenna plane are studied

Content Type Journal ArticlePages 1-9DOI 10.1007/s10778-011-0500-zAuthors
A.E. Zakrzhevskii, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057V. S. Khoroshilov, M. K. Yangel’ State Design Office “Yuzhnoe”, 3 Krivorozhskaya St., Dnepropetrovsk, Ukraine 490008

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

It is proved that fractional exponential hereditary kernels of nonlinear viscoelasticity can be used to evaluate creep strains
and stress relaxation. A nonlinear theory of viscoelasticity with time-independent nonlinearity described as a nonlinear curve
of instantaneous elastoplastic deformation is used. The calculated results are validated against experimental data on the
viscoelastic deformation of laminated and unidirectional fibrous composites and their components under the conditions of constant
stresses, complete unloading, incremental loading, pure torsion, and constant strains

Content Type Journal ArticlePages 1-8DOI 10.1007/s10778-011-0498-2Authors
V. P. Golub, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

A method for determining the natural frequencies and modes of ribbed shallow shells with rectangular planform on an elastic
foundation is developed. The method takes into account the discrete arrangement of the ribs. A shallow spherical shell with
square planform is considered as example to analyze the effect of the number of ribs and the Winkler and Pasternak coefficients
of subgrade reaction on the natural frequencies and modes. It is recommended to take into account the discrete arrangement
of ribs when they are few

Content Type Journal ArticlePages 1-6DOI 10.1007/s10778-011-0496-4Authors
P. Z. Lugovoi, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057N. Ya. Prokopenko, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

The perturbation method (small-parameter method) is used to analyze the propagation of a cylindrical wave in a quadratic nonlinear
hyperelastic material described by the classical Murnaghan model. The exact representation of the first-order solution in
terms of squared Hankel functions of zero and first orders and their product is derived. A simplification of the new solution
is considered

Content Type Journal ArticlePages 1-6DOI 10.1007/s10778-011-0493-7Authors
J. J. Rushchitsky, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095

The theory of long-term damage is generalized to particulate composite materials with physically nonlinear components. The
damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized
by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between
the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to
be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated.
Algorithms of calculating the time dependence of are developed. The effect on the nonlinearity of the matrix on the damage
and macrodeformation curves is examined

Content Type Journal ArticlePages 1-9DOI 10.1007/s10778-011-0490-xAuthors
L. P. Khoroshun, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057E. N. Shikula, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine 03057

Journal International Applied MechanicsOnline ISSN 1573-8582Print ISSN 1063-7095