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1.
It is considered a heat conduction in a layer made of two conductors distributed in the form of laminas with varied thicknesses.
Macroscopic (averaged) properties of the layer are continuously “transversally” graded across its thickness (TGL layer), cf.
Fig. 1. The aim of the paper is to present and apply an averaged model of the heat conduction, obtained within the tolerance
averaging technique, discussed in the book edited by Woźniak et al. (Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach, Łódź, Wydawnictwo Politechniki Łódzkiej, 2008). It is shown that the proposed model describes the microstructural effect on the heat conduction of the TGL layer. Moreover,
results obtained within this model are compared to results by the higher order theory (cf. Aboudi et al., Composites B, 30:777–832,
1999). 相似文献
2.
The aim of the contribution is to formulate a macroscopic mathematical model describing the dynamic behaviour of a certain composite thin plates. The plates are made of two-phase stratified composites with a smooth and a slow gradation of macroscopic properties along the stratification. The formulation of mathematical model of these plates is based on a tolerance averaging approach (Woźniak, Michalak, Jędrysiak in Thermomechanics of microheterogeneous solids and structures, 2008). The presented general results are illustrated by analysis of the natural frequencies for two cases of plates: a plate band and an annular plate. The spatial volume fractions of the two different isotropic homogeneous components are optimized so as to maximize or minimize the first natural frequency of the plate under consideration. 相似文献
3.
Physically and geometrically nonlinear deformation of conical shells with an elliptic hole 总被引:1,自引:1,他引:0
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2008,44(2):174-181
The elastoplastic state of conical shells weakened by an elliptic hole and subjected to finite deflections is studied. The
material of the shells is assumed to be isotropic and homogeneous; the load is constant internal pressure. The problem is
formulated and a technique for numerical solution with allowance for physical and geometrical nonlinearities is proposed.
The distribution of stresses, strains, and displacements along the hole boundary and in the zones of their concentration is
studied. The solution obtained is compared with the solutions of the physically and geometrically nonlinear problems and a
numerical solution of the linear elastic problem. The stress-strain state around an elliptic hole in a conical shell is analyzed
considering both nonlinearities
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 69–77, February 2008. 相似文献
4.
Ahmet Birinci Fatma Birinci Fevzi L. Cakiroglu Ragip Erdol 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(9):997-1005
The elastostatic plane problem of an infinite elastic layer with an internal crack is considered. The elastic layer is subjected
to two different loadings, (a) the elastic layer is loaded by a symmetric transverse pair of compressive concentrated forces
P/2, (b) it is loaded by a symmetric transverse pair of tensile concentrated forces P/2. The crack is opened by an uniform internal pressure p
0 along its surface and located halfway between and parallel to the surfaces of the elastic layer. It is assumed that the effect
of the gravity force is neglected. Using an appropriate integral transform technique, the mixed boundary value problem is
reduced to a singular integral equation. The singular integral equation is solved numerically by making use of an appropriate
Gauss–Chebyshev integration formula and the stress-intensity factors and the crack opening displacements are determined according
to two different loading cases for various dimensionless quantities. 相似文献
5.
O. G. Dashko 《International Applied Mechanics》2007,43(10):1100-1106
An uncoupled stress problem for an unbounded elastic soft ferromagnetic body with a spherical cavity in a magnetic field uniform
at infinity is solved. The stresses, displacements, and magnetic quantities in the body are determined. The features of stress
distribution over the body and its boundary surface are studied
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 42–48, October 2007. 相似文献
6.
多孔饱和半空间上弹性圆板垂直振动的积分方程 总被引:5,自引:0,他引:5
应用新的方法求解多孔饱和固体的动力基本方程-Biot波动方程,首先把Biot波动方程化为仅有土骨架位移和孔隙水压力的偏微分方程组,并且逐次解耦方法(不引入位移势函数)求解此偏微分方程组,然后按混合边值条件建立多孔饱和半空间上弹性圆板垂直振动的对偶积分方程,用Abel变换化对偶积分方程为第二类Fredholm积分方程。文中考虑两种孔隙流体的表面边界条件:(a)半空间表面(包括圆板与半空间的接触面)是 相似文献
7.
Vladimir Kobelev 《Meccanica》2006,41(6):653-660
Failure of a composite is a complex process accompanied by irreversible changes in the microstructure of the material. Microscopic
mechanisms are known of the accumulation of damage and failure of the type of localized and multiple ruptures of the fibers
delamination along interphase boundaries, and also mechanisms associated with fracture of fibers. In this work, we propose
a mathematical model of the local mechanism of failure of a composite material randomly reinforced with a system of short
fibers. We implement the Cosserat moment model of crack tip for filament material, reinforced with whiskers or in fiber- reinforced
polycrystalline materials. It is assumed that the angular distribution of the fibers is isotropic and the elastic characteristics
of the fibers are considerably higher than the elastic constants of the matrix. We implement the homogenization procedure
for the effective Cosserat constants similarly to the effective elastic constants. The singular solution in the vicinity of
the crack tip in the Cosserat moment model is found. Using this solution, we examine the bending stresses in the filaments
due to effective moment stresses in the material. The constructed model describes the phenomenon of fracture of the fibers
occurring during crack propagation in those composites. The following assumptions are used as the main hypotheses for the
micromechanical model. The matrix contains a nucleation crack. When the load is increased the crack grows and its boundary
comes into contact with the reinforcing fibers. A further increase of the stress causes bending of the fiber. When~the fiber
curvature reaches a specific critical value, the fiber ruptures. If the stress at infinity is given, the fibers no longer
delay the development of failure during crack propagation The degree of bending distortion of the fiber in the vicinity of
the boundary of the crack is determined by the moment model of the material. The necessity to take into account the moment
stresses in the failure theory of the reinforced material was stressed in [Muki and Sternberg (1965) Zeitschrift f angew Math
und Phys 16:611–615; Garajeu and Soos (2003) Math Mech Solids 8(2):189–218; Ostoja-Starzewski et al (1999) Mech Res Commun
26:387–396]. The moment Cosserat stresses were accounted also for inhomogeneous biomechanical materials by Buechner and Lakes
(2003) Bio Mech Model Mechanobiol 1: 295–301. We should also mention the important methodological studies [Sternberg and Muki
(1967) J Solids Struct 1:69–95; Atkinson and Leppington (1977) Int J Solids Struct 13: 1103–1122] concerned with the moment
stresses in homogeneous fracture mechanics. 相似文献
8.
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2008,44(7):802-809
The elastoplastic state of cylindrical shells with a circular hole is studied considering finite deflections. The material
of the shells is isotropic and homogeneous; the load is axial tension. The distribution of stresses, strains, and displacements
along the hole boundary and in the zone of their concentration is studied by solving a doubly nonlinear problem. The data
obtained are compared with the solutions of the physically and geometrically nonlinear problems and a numerical solution of
the linear elastic problem
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 101–109, July 2008. 相似文献
9.
The elastoplastic state of thin cylindrical shells weakened by a curvilinear (circular) hole is analyzed considering finite
deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The
distributions of stresses (strains, displacements) along the hole boundary and in the zone of their concentration are studied.
The results obtained are compared with solutions that account for physical (plastic strains) or geometrical (finite deflections)
nonlinearity alone and with a numerical linear elastic solution. The stress-strain state around a circular hole is analyzed
for different geometries in the case where both nonlinearities are taken into account
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 115–123, December, 2006. 相似文献
10.
Yongbin Zhang 《Theoretical and Computational Fluid Dynamics》2009,23(4):239-254
Boundary film shear elastic modulus effect is analyzed in a hydrodynamic contact. The contact is one-dimensional composed
of two parallel plane surfaces, which are, respectively, rough rigid with rectangular micro projections in profile periodically
distributed on the surface and ideally smooth rigid. The whole contact is consisted of cavitated area and hydrodynamic area.
The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the
contact. Analysis is thus carried out for a micro Raleigh bearing in this contact. The hydrodynamic contact in this micro
Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones.
In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact
interface, while the film does not slip at the lower contact surface due to the shear stress capacity large enough at the
film–contact interface. In boundary film area, the viscosity, density and shear elastic modulus of the film are varied across
the film thickness due to the film–contact interactions, and their effective values are used in modeling, which depend on
the film thickness. The analytical approach proposed by Zhang (J Mol Liq 128:60–64, 2006) and Zhang et al. (Int J Fluid Mech
Res 30:542–557, 2003) is used for boundary film area. In fluid film area, the film does not slip at either of the contact
surfaces, and the shear elastic modulus of the film is neglected. Conventional hydrodynamic analysis is used for fluid film
area. The present paper presents the theoretical analysis and a typical solution. It is found that for the simulated case
the boundary film shear elastic modulus effects on the mass flow through the contact, the overall film thickness of the contact
and the carried load of the contact are negligible but the boundary film shear elastic modulus effect on the local film thickness
of the contact may be significant when the boundary film thickness is on the 1 nm scale and the contact surfaces are elastic.
In Part II will be presented detailed results showing boundary film shear elastic modulus effects in different operating conditions.
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11.
The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite.
The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are
formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed.
The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is
studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations)
or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic
problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear
factors
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005. 相似文献
12.
A. N. Guz 《International Applied Mechanics》2011,47(2):121-168
Major results on the mechanics of crack propagation in materials with initial (residual) stresses are analyzed. The case of
straight cracks of constant width that propagate at a constant speed in a material with initial (residual) stresses acting
along the cracks is examined. The results were obtained, based on linearized solid mechanics, in a universal form for isotropic
and orthotropic, compressible and incompressible elastic materials with an arbitrary elastic potential in the cases of finite
(large) and small initial strains. The stresses and displacements in the linearized theory are expressed in terms of analytical
functions of complex variables when solving dynamic plane and antiplane problems. These complex variables depend on the crack
propagation rate and the material properties. The exact solutions analyzed were obtained for growing (mode I, II, III) cracks
and the case of wedging by using methods of complex variable theory, such as Riemann–Hilbert problem methods and the Keldysh–Sedov
formula. As the initial (residual) stresses tend to zero, these exact solutions of linearized solid mechanics transform into
the respective exact solutions of classical linear solid mechanics based on the Muskhelishvili, Lekhnitskii, and Galin complex
representations. New mechanical effects in the dynamic problems under consideration are analyzed. The influence of initial
(residual) stresses and crack propagation rate is established. In addition, the following two related problems are briefly
analyzed within the framework of linearized solid mechanics: growing cracks at the interface of two materials with initial
(residual) stresses and brittle fracture under compression along cracks 相似文献
13.
V. D. Bondar' 《Journal of Applied Mechanics and Technical Physics》2000,41(3):547-555
The averaged rotations and other mechanical parameters at finite plane strains of an elastic material, which are characterized
by a linear relation between the Cauchy stresses and the Almansi strains, are studied. The form of the elastic potential is
determined. The displacement problem is reduced to a boundary-value problem for complex potentials, which is solved in terms
of Cauchy-type integrals for the specified boundarys displacements. The results obtained are compared with the linear solution.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 3, pp. 187–196, May–June, 2000. 相似文献
14.
A boundary-element scheme is proposed for the numerical determination of the stress-strain state of a three-dimensional composite
body, which is an elastic inclusion of arbitrary shape perfectly bonded to an infinite elastic matrix. The scheme involves
the reduction of the original problem to six boundary integral equations for the components of interfacial displacements and
forces and the boundary-element parametrization and discretization of these equations using generalized Gaussian integrals
and topological maps with regularizing Jacobians. Numerical results are obtained for a cylindrical inclusion with rounded
ends in a matrix subject at infinity to constant forces acting along this fiber. The influence of the length-to-radius ratio
of the fiber and the ratio of the elastic moduli of the matrix and fiber on the stresses is examined
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 27–35, April 2007. 相似文献
15.
The stress-strain state of an incompressible cylindrical elastic body with antiplane strain under the action of potential
forces and surface loading constant along the body is considered in a nonlinear formulation in actual variables. The stresses
are expressed via the pressure and independent strains, the pressure is expressed via the force and elastic potentials, and
nonlinear boundary-value problems are posed for strains (and displacements). Various methods for solving these problems are
developed. For the nonlinear equations obtained, some analytical solutions containing free parameters are given, which can
be used as a basis for solving particular problems.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 93–101, November–December, 2006. 相似文献
16.
S. Itou 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(1):53-62
Summary Transient stresses around two parallel cracks in an infinite elastic medium are investigated in the present paper. The shape
of the cracks is assumed to be square. Incoming shock stress waves impinge upon the two cracks normal to tzheir surfaces.
The mixed boundary value equations with respect to stresses and displacements are reduced to two sets of dual integral equations
in the Laplace transform domain using the Fourier transform technique. These equations are solved by expanding the differences
in the crack surface displacements in a double series of a function that is equal to zero outside the cracks. Unknown coefficients
in the series are calculated using the Schmidt method. Stress intensity factors defined in the Laplace transform domain are
inverted numerically to the physical space. Numerical calculations are carried out for transient dynamic stress intensity
factors under the assumption that the shape of the upper crack is identical to that of the lower crack.
Received 2 February 2000; accepted for publication 10 May 2000 相似文献
17.
The paper addresses a problem of plane elasticity for a doubly connected body with outer and inner boundaries in the form
of regular polygons with a common center and parallel sides. The neighborhoods of the vertices of the inner boundary are unknown
equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center. It is assumed that this elastic
body is inserted into a hole of a rigid body, with the hole boundary coinciding with the outer boundary of the elastic body.
Absolutely smooth rigid punches with rectilinear bases are pressed into all the rectilinear sections of the inner polygonal
boundary of the elastic body. There is no friction between the elastic and rigid bodies. The unknown arcs are free from external
stresses. Complex variable theory is used to determine the unknown arcs and the stress state of the elastic body
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 110–118, March 2006. 相似文献
18.
Summary An interface crack with an artificial contact zone at the right-hand side crack tip between two piezoelectric semi-infinite
half-planes is considered under remote mixed-mode loading. Assuming the stresses, strains and displacements are independent
of the coordinate x
2, the expression for the displacement jumps and stresses along the interface are found via a sectionally holomorphic vector
function. For piezoceramics of the symmetry class 6 mm and for electrically permeable crack faces, the problem is reduced
to a combined Dirichlet-Riemann boundary value problem which can be solved analytically. Further, analytical expressions for
the stresses, electrical displacements, derivatives of elastic displacement jumps, stress and electrical intensity factors
are found at the interface. Real contact zone lengths and the well-known oscillating solution are derived from the obtained
solution as well. Analytical relationships between the fracture-mechanical parameters of various models are found, and recommendations
are suggested concerning the application of numerical methods to the problem of an interface crack in the discontinuity area
of a piezoelectric bimaterial.
Received 16 March 1999; accepted for publication 31 May 1999 相似文献
19.
Hamdy M. Youssef Amnah H. Al-Harby 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(9):675-687
In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing
equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech
26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state
space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained
is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and
ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques.
Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters. 相似文献
20.
Yongbin Zhang 《Theoretical and Computational Fluid Dynamics》2009,23(4):255-269
The present paper is the subsequent research of the first part (Theor Comput Fluid Dyn, 2009). It investigates the boundary
film shear elastic modulus effect in a hydrodynamic contact in different operating conditions. The hydrodynamic contact is
one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular micro projections
in profile periodically distributed on the surface and ideally smooth rigid. The whole contact consists of cavitated area
and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically
distributed in the contact. The hydrodynamic contact in a micro Raleigh bearing consists of boundary film area and fluid film
area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact
surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower
contact surface due to the shear stress capacity of the film–contact interface large enough. In boundary film area, the viscosity,
density, and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions,
and their effective values are used in modeling which depends on the film thickness. In fluid film area, the film does not
slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. It is found from the simulation
results that the boundary film shear elastic modulus influences are normally negligible on the mass flow through the contact,
the carried load of the contact and the overall film thickness of the contact, and the boundary film shear elastic modulus
would normally influence the local film thickness in an elastic contact when the local film thickness is on the film molecule
diameter scale. It is also found that the boundary film shear elastic modulus effect has the tendency of being increased with
the reduction of the width of a micro contact. It is increased with the reduction of the boundary film–contact interfacial
shear strength or with the increase of the critical boundary film thickness, while it is strongest at certain values of the
contact surface roughness, the width ratio of fluid film area to boundary film area, and the lubricant film shear elastic
modulus.
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