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1.
L. I. Shkutin 《Journal of Applied Mechanics and Technical Physics》1999,40(4):757-762
A nonlinear deformation model for a rod with rigid cross sections is proposed. A complete system of local incremental equations,
a variational equation equivalent to this system, and an equation of virtual work are formulated. Numerical analysis of the
deformation of a ring transmission is performed.
Institute of Computer Modeling, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya
Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 229–235, July–August, 1999. 相似文献
2.
The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized.
A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von
Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance
equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations.
The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed 相似文献
3.
A structural theory of short-term microdamage is proposed for a two-component laminated composite with microdamageable reinforcement
and physically nonlinear matrix. The basis of the theory is the stochastic elasticity equations of a laminated composite with
a porous reinforcement. Microvolumes in the reinforcement material meet the Huber-Mises failure criterion. The damaged-microvolume
balance equation for the reinforcement is derived. This equation and the equations relating macrostresses and macrostrains
of a laminated composite with porous reinforcement and physically nonlinear matrix constitute a closed-form system of equations.
This system describes the coupled processes of physically nonlinear deformation and microdamage occurring in different composite
components. Algorithms for computing the microdamage-macrostrain relationships and deformation diagrams are developed. Uniaxial
tension curves are plotted for a laminated composite with linearly hardening matrix
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 3–12, December 2005. 相似文献
4.
The structural theory of short-term microdamage is generalized to a laminated composite with a microdamageable matrix and
physically nonlinear reinforcement. The basis for the generalization is the stochastic elasticity equations of a laminated
composite with a porous matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume
balance equation for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a laminated
composite with porous matrix and physically nonlinear reinforcement constitute a closed-form system of equations. This system
describes the coupled processes of physically nonlinear deformation and microdamage occurring in different composite components.
Algorithms for computing the microdamage-macrostrain relationships and deformation diagrams are developed. Uniaxial tension
curves are plotted for a laminated composite with linearly hardening reinforcement
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 47–56, November 2005. 相似文献
5.
A structural theory of short-term microdamage is proposed for a fibrous composite with physically nonlinear matrix and microdamaged
reinforcement. The theory is based on the stochastic elasticity equations of a fibrous composite with porous fibers. Microvolumes
of the fiber material are damaged in accordance with the Huber-Mises failure criterion. A balance equation for damaged microvolumes
in the reinforcement is derived. This equation together with the equations relating macrostresses and macrostrains of a fibrous
composite with porous reinforcement and physically nonlinear matrix constitute a closed-form system. This system describes
the coupled processes of physically nonlinear deformation and microdamage that occur in different components of the composite.
Algorithms are proposed for computing the dependences of microdamage on macrostrains and macrostresses on macrostrains. Uniaxial
tension curves are plotted for a fibrous composite with a linearly hardening matrix
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 3–13, February 2006. 相似文献
6.
V. V. Kuznetsov S. V. Levyakov 《Journal of Applied Mechanics and Technical Physics》2007,48(5):755-765
A refined geometrically nonlinear formulation of a thin-shell finite element based on the Kirchhoff-Love hypotheses is considered.
Strain relations, which adequately describe the deformation of the element with finite bending of its middle surface, are
obtained by integrating the differential equation of a planar curve. For a triangular element with 15 degrees of freedom,
a cost-effective algorithm is developed for calculating the coefficients of the first and second variations of the strain
energy, which are used to formulate the conditions of equilibrium and stability of the discrete model of the shell. Accuracy
and convergence of the finite-element solutions are studied using test problems of nonlinear deformation of elastic plates
and shells.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 160–172, September–October, 2007. 相似文献
7.
The structural theory of short-term microdamage is generalized to a fibrous composite with a microdamageable matrix and physically
nonlinear fibers. The basis for the generalization is the stochastic elasticity equations of a fibrous composite with a porous
matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation
for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a fibrous composite
with porous matrix and physically nonlinear fibers constitute a closed-form system of equations. This system describes the
coupled processes of physically nonlinear deformation and microdamage occurring in different components of the composite.
Algorithms for computing the microdamage-macrostrain and macrostress-macrostrain relationships are developed. Uniaxial tension
curves are plotted for a fibrous composite with linearly hardening fibers
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 38–47, January 2006. 相似文献
8.
M. A. Abdou 《Nonlinear dynamics》2008,52(1-2):1-9
In this paper, the Exp-function method with the aid of the symbolic computational system Maple is used to obtain the generalized
solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, (2+1)-dimensional
Konopelchenko–Dubrovsky equations, the (3+1)-dimensional Jimbo–Miwa equation, the Kadomtsev–Petviashvili (KP) equation, and
the (2+1)-dimensional sine-Gordon equation. It is shown that the Exp-function method, with the help of symbolic computation,
provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics. 相似文献
9.
A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative
properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected
by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme
are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids,
and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive
equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation
rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic
deformations of the material and deformations of elements of the medium at the structural level.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009. 相似文献
10.
11.
In this paper the post-critical behavior of beam columns with variable mass and stiffness properties subjected to follower
forces arbitrarily distributed along their length in the presence of damping (both internal and external) is investigated
using a complete nonlinear dynamic analysis. Although the static nonlinear analysis is more economical in computational cost,
it is associated only with the loss of local stability via flutter or divergence. Thus, the nonlinear dynamic analysis is
adopted in order to examine the global stability of the system. The governing equations of hyperbolic type are derived in
terms of the displacements by considering (a) nonlinear response including the axial deformation, (b) nonlinear response excluding
the axial deformation and (c) linear response. Moreover, as the cross-sectional properties of the beam vary along its axis,
the resulting coupled nonlinear differential equations have variable coefficients. Their solution is achieved using the analog
equation method (AEM) of Katsikadelis. Besides its accuracy and effectiveness, this method overcomes the shortcoming of a
possible FEM solution which may experience a lack of convergence. The problems treated in this investigation include beam
columns with various load distributions, such as constant, linear and parabolic. Some of the conclusions detected in studying
the nonlinear dynamic stability of Beck’s column with variable cross section (Katsikadelis and Tsiatas, Nonlinear dynamic
stability of damped Beck’s column with variable cross section. Int. J. Non-linear Mech. 42, 164–171, 2007), are also valid for the case of distributed loads. The important, however, finding is that the post-critical response under
distributed loads depends on the law of distribution of mass and stiffness properties, which may lead also to explosive flutter
(unbounded amplitude), in contrast to Beck’s column (end-tip load) where the motion is always bounded. 相似文献
12.
S. B. Kozitskii 《Journal of Applied Mechanics and Technical Physics》2000,41(3):429-438
The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the
neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau
equation, a Newell-Whitehead-type equation, and an equation of the ϕ4 type, respectively, were obtained. Analytic expressions for the coefficients of these equations and their various asymptotic
forms are presented. In the case of Hopf bifurcation for low and high frequencies, the amplitude equation reduces to a perturbed
nonlinear Shroedinger equation. In the high-frequency limit, structures of the type of “dark” solitons are characteristic
of the examined physical system.
Pacific Ocean Institute, Vladivostok 690041. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3,
pp. 56–66, May–June, 2000. 相似文献
13.
V. V. Chekhov 《International Applied Mechanics》2011,46(10):1147-1153
A tensor–matrix FEM equation describing large-strain deformation is derived. The equation is simplified and modified to describe
the deformation of incompressible materials. The results of test analysis are presented 相似文献
14.
We extend our result Nakanishi and Schlag in J. Differ. Equ. 250(5):2299–2333, 2011) to the non-radial case, giving a complete classification of global dynamics of all solutions with energy that is at most
slightly above that of the ground state for the nonlinear Klein–Gordon equation with the focusing cubic nonlinearity in three
space dimensions. 相似文献
15.
The structural theory of short-term damage is used to study the coupled processes of deformation and microdamage of a physically
nonlinear material in a combined stress state. The basis for the analysis is the stochastic elasticity equations for a physically
nonlinear porous medium. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure
criterion. The balance equation for damaged microvolumes is derived and added to the macrostress-macrostrain relations to
produce a closed-form system of equations. It describes the coupled processes of nonlinear deformation and microdamage of
the porous material. Algorithms are developed for calculating the dependence of microdamage on macrostresses and macrostrains
and plotting stress-strain curves for a homogeneous material under either biaxial normal loading or combined normal and tangential
loading. The plots are analyzed depending on the type of stress state
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 30–39, November 2006. 相似文献
16.
17.
A constitutive equation for polymer solutions and melts is obtained on the basis of the dynamics of noninteracting dumbbells
moving in a nonlinear anisotropic fluid. The equation obtained is used to describe nonlinear effects under conditions of simple
shear and steady-state flow in a circular tube and for the numerical investigation of a flow in a finite cylinder with a rotating
end face.
Barnaul. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–13, January–February,
2000. 相似文献
18.
The dynamics and stability of the high-speed fiber spinning process with spinline flow-induced crystallization and neck-like deformation have been studied using a simulation model equipped with governing equations of continuity, motion, energy, and crystallinity, along with the Phan-Thien–Tanner constitutive equation. Despite the fact that a simple one-phase model was incorporated into the governing equations to describe the spinline crystallinity, as opposed to the best-known two-phase model [Doufas et al. J Non-Newton Fluid Mech, 92:27–66, 2000a]; [Kohler et al. J Macromol Sci Phys, 44:185–202, 2005] that treats amorphous and crystalline phases separately in computing the spinline stress, the simulation has successfully portrayed the typical nonlinear characteristic of the high-speed spinning process called neck-like spinline deformation. It has been found that the criterion for the neck-like deformation to occur on the spinline is for the extensional viscosity to decrease on the spinline, so that the spinning is stabilized by the formation of the spinline neck-like deformation. The accompanying linear stability analysis explains this stabilizing effect of the spinline neck-like deformation, corroborating a recent experimental finding [Takarada et al. Int Polym Process, 19:380–387, 2004].This paper was presented at the 2nd Annual European Rheology Conference 2005 on April 21–23, 2005, in Grenoble, France. 相似文献
19.
C. W. Lim S. K. Lai B. S. Wu W. P. Sun Y. Yang C. Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):411-431
An analytical approach is developed for the nonlinear oscillation of a conservative, two-degree-of-freedom (TDOF) mass-spring
system with serial combined linear–nonlinear stiffness excited by a constant external force. The main idea of the proposed
approach lies in two categories, the first one is the transformation of two nonlinear differential equations of a two-mass
system using suitable intermediate variables into a single nonlinear differential equation. Another is the treatment a quadratic
nonlinear oscillator (QNO) by the modified Lindstedt–Poincaré (L-P) method presented recently by the authors. The first-order
and second-order analytical approximations for the modified L-P method are established for the QNOs with satisfactory results.
After solving the nonlinear differential equation, the displacements of two-mass system can be obtained directly from the
governing linear second-order differential equation. Unlike the common perturbation method, the modified L-P method is valid
for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical
expressions valid for small as well as large amplitudes of oscillation. In short, this new approach yields extended scope
of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to
the previous approaches such as the perturbation and classical harmonic balance methods. Two examples of nonlinear TDOF mass-spring
systems excited by a constant external force are selected and the approximate solutions are verified with the exact solutions
derived from the Jacobi elliptic function and also the numerical fourth-order Runge–Kutta solutions. 相似文献
20.
D. A. Khodzhaev B. Kh. Éshmatov 《Journal of Applied Mechanics and Technical Physics》2007,48(6):905-914
The problem of vibrations of a viscoelastic plate with concentrated masses is studied in a geometrically nonlinear formulation.
In the equation of motion of the plate, the action of the concentrated masses is taken into account using Dirac δ-functions.
The problem is reduced to solving a system of Volterra type ordinary nonlinear integrodifferential equations using the Bubnov-Galerkin
method. The resulting system with a singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature
formulas. The effect of the viscoelastic properties of the plate material and the location and amount of concentrated masses
on the vibration amplitude and frequency characteristics is studied. A comparison is made of numerical calculation results
obtained using various theories.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007. 相似文献