共查询到20条相似文献,搜索用时 15 毫秒
1.
E. A. Karabut V. V. Pukhnachev 《Journal of Applied Mechanics and Technical Physics》2008,49(4):568-579
The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated
in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional
problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient
on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary,
which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour,
the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface
shape.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008. 相似文献
2.
D. N. Sheidakov 《Journal of Applied Mechanics and Technical Physics》2007,48(4):547-555
The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional
equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one
to separate variables in the linearized equilibrium equations are specified on the lateral surfaces. For three particular
models of incompressible materials, the critical curves are constructed and the instability region is determined in the plane
of the loading parameters (the multiplicities of elongations of the plate material in the unperturbed equilibrium state).
The numerical results show that for thin plates loaded by tensile stresses, the size and shape of the instability region depend
only slightly on the relation among the length, width, and thickness of the plate. Based on the results obtained, a simple
approximate stability criterion is proposed for an elastic plate under tensile loads.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 94–103, July–August, 2007. 相似文献
3.
D. Ieşan 《International Journal of Solids and Structures》2011,48(3-4):573-583
This paper is concerned with the linear theory of porous Cosserat elastic solids. We study the equilibrium of a cylindrical bar which is subjected to resultant forces and resultant moments on the ends, to body loads and to surface tractions on the lateral surface. The Almansi problem, where the body loads and the surface loading on the lateral surface are polynomials in the axial coordinate, is considered. The bar is made of an inhomogeneous and isotropic material whose constitutive coefficients are independent of the axial coordinate. The problem is reduced to the study of two-dimensional problems. The results are used to study two practical applications concerning the deformation of a circular rod. It is shown that a uniform pressure on the lateral surface produces an extension, a uniform change of the porosity, and a plane deformation. The bending by terminal couples produces a non-uniform variation of the porosity and a microrotation of the material particles. 相似文献
4.
The two-dimensional equations of a nonlinearly elastic ‘flexural’ shell have been recently identified and justified by V.
Lods and B. Miara, by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear
elasticity. These equations can be recast as a minimization problem for a ‘two-dimensional energy’ over a manifold of ‘admissible
deformations’. The stored energy function is a quadratic expression in terms of the exact difference between the curvature
tensor of the deformed middle surface and that of the undeformed one; the admissible deformations are those that preserve
the metric of the undeformed middle surface and satisfy boundary conditions of clamping or of simple support. We establish
here that this minimization problem has at least one solution.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
A variable cross-section bar is considered. The bar is not uniform in length. The bar axis through the mass centers of all
cross sections is a straight line. The bar is compressed by a longitudinal force applied to the mass center of the boundary
cross section. The stability loss of the straight-line shape of the bar’s equilibrium is discussed when a curved shape is
also possible. Approximate analytical formulas are obtained for the critical compressive force when four types of end fixing
are used for a periodically nonuniform bar. The numerical results obtained by these formulas are compared with the known exact
solutions to the stability equation for a bar whose cross section is stepwise variable and whose nonuniformity consists of
only one period (the limiting case). 相似文献
6.
We present an exact solution for the postbuckling configurations of beams with fixed–fixed, fixed–hinged, and hinged–hinged
boundary conditions. We take into account the geometric nonlinearity arising from midplane stretching, and as a result, the
governing equation exhibits a cubic nonlinearity. We solve the nonlinear buckling problem and obtain a closed-form solution
for the postbuckling configurations in terms of the applied axial load. The critical buckling loads and their associated mode
shapes, which are the only outcome of solving the linear buckling problem, are obtained as a byproduct. We investigate the
dynamic stability of the obtained postbuckling configurations and find out that the first buckled shape is a stable equilibrium
position for all boundary conditions. However, we find out that buckled configurations beyond the first buckling mode are
unstable equilibrium positions. We present the natural frequencies of the lowest vibration modes around each of the first
three buckled configurations. The results show that many internal resonances might be activated among the vibration modes
around the same as well as different buckled configurations. We present preliminary results of the dynamic response of a fixed–fixed
beam in the case of a one-to-one internal resonance between the first vibration mode around the first buckled configuration
and the first vibration mode around the second buckled configuration. 相似文献
7.
This paper considers the problem of steady two-dimensional boundary layer flow of a micropolar fluid near an oblique stagnation
point on a fixed surface with Navier’s slip condition. It is shown that the governing nonlinear partial differential equations
admit similarity solutions. The resulting nonlinear ordinary differential equations are solved numerically using the Keller
box method for some values of the governing parameters. It is found that the flow characteristics depend strongly on the micropolar
and slip parameters. 相似文献
8.
The Stroh formalism is extended to provide a new class of three-dimensional solutions for the generally anisotropic elastic material that have polynomial dependence on x3, but which have quite general form in x1,x2. The solutions are obtained by a sequence of partial integrations with respect to x3, starting from Stroh's two-dimensional solution. At each stage, certain special functions have to be introduced in order to satisfy the equilibrium equation. The method provides a general analytical technique for the solution of the problem of the prismatic bar with tractions or displacements prescribed on its lateral surfaces. It also provides a particularly efficient solution for three-dimensional boundary-value problems for the half-space. The method is illustrated by the example of a half-space loaded by a linearly varying line force. 相似文献
9.
G. V. Druzhinin N. M. Bodunov 《Journal of Applied Mechanics and Technical Physics》1999,40(4):712-718
A numerical-analytical method based on approximation by harmonic or biharmonic functions is proposed for solving a mixed two-dimensional
problem of elasticity theory. This method allows one to decrease the geometric dimensionality of the boundary-value problem
by reducing it to minimization of the boundary residual. The resultant approximate analytical solution satisfies all equations
of elasticity theory.
Kazan’ State Technical University, Kazan’ 420111. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40,
No. 4, pp. 179–185, July–August, 1999. 相似文献
10.
S. V. Levyakov 《Journal of Applied Mechanics and Technical Physics》1998,39(4):624-627
The problem of loading of a thin-walled elastic pipe (a toroidal shell) by external pressure is examined in a geometrically
nonlinear formulation. A numerical algorithm is used to study the nonlinear deformation of the shell and the stability of
its equilibrium states when its cross section has undergone a significant change in shape. Results are presented from a determination
of the critical stresses of curvilinear pipes with allowance for moments in the subcritical state. These results are compared
with the approximate solution.
Chaplygin Siberian Aviation Institute, Novosibirsk 630051. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika,
Vol. 39, No. 4, pp. 162–166, July–August, 1998. 相似文献
11.
Holm Altenbach Victor A. Eremeyev Leonid P. Lebedev Leonardo A. Rendón 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(3):217-227
Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility
relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression
for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral
problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic
form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented. 相似文献
12.
N. M. Minazetdinov 《Journal of Applied Mechanics and Technical Physics》2009,50(3):540-545
A method is proposed for determining the shape of the anode-article boundary for a given shape of the cathode-tool in plane
problems of the theory of dimensional electrochemical machining of metals. Under the assumptions used, the boundary of the
anode-article is divided into the working zone, where metal dissolution occurs, and an adjacent zone, where the treatment
(dissolution) is terminated. The initial problem is reduced to a problem of a fictitious plane-parallel potential flow of
an ideal fluid with a nonlinear condition on the free surface. The point of separation of the fictitious flow from the solid
boundary corresponds to the point separating these two zones of the anode boundary. The Brillouin-Will condition of smooth
separation is imposed at the separation point to construct a closed system of equations determining the problem solution.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 214–220, May–June, 2009. 相似文献
13.
This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs
from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogenous force constants.
Instead, it starts with an interatomic potential, possibly with infinite range as appropriate for situations with electrostatics,
and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force
constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution
of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing
the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit
symmetry. It is then extended to the anharmonic problem using modified Newton–Raphson iteration. The method is demonstrated
for model problems motivated by domain walls in ferroelectric materials.
相似文献
14.
A. V. Babkin S. V. Ladov V. M. Marinin S. V. Fedorov 《Journal of Applied Mechanics and Technical Physics》1999,40(4):571-580
The results of physicomathematical modeling obtained within the framework of continuum mechanics by numerical solution of
the two-dimensional axisymmetric nonstationary problem of the dynamic deformation of a compressed elastoplastic bar of variable
section are presented. Dependences of the quantitative characteristics of stretching and breakup of a shaped-charge jet (the
coefficients of ultimate and inertial elongation and the number of individual elements formed in breakup) on the jet parameters
and the jet material properties are revealed by calculations. The calculated dependences are compared with experimental data
for plastically failing jets of copper and niobium, and the character of the dependences is explained from the physical viewpoint.
Bauman Moscow State Technical University, Moscow 107005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol.
40, No. 4, pp. 25–35, July–August, 1999. 相似文献
15.
Yu. A. Bogan 《Journal of Applied Mechanics and Technical Physics》2006,47(2):221-228
A complete potential theory is constructed for the first boundary-value problem in the two-dimensional anisotropic theory
of elasticity (the force vector is specified on the boundary) in a bounded domain on a plane with a Lyapunov boundary.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 85–94, March–April, 2006. 相似文献
16.
P. Balakumar 《Theoretical and Computational Fluid Dynamics》1997,9(2):103-119
Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the
full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order
compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette
flow is stable at all Reynolds numbers when the Couette velocity component σ2 exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the
combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ2. It is found that, for small σ2, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds
number gradually increases with increasing σ2. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with
an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ2 values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ2. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases
slowly up to σ2∼ 0.2 and remains constant until σ2∼ 0.58. Beyond σ2 > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear
equilibrium solutions do not exist beyond a critical σ2 value of about 0.59.
Received: 26 November 1996 and accepted 12 May 1997 相似文献
17.
Xiaoguang Zhong 《Journal of Elasticity》1995,41(1):39-72
Using the continuum mechanical model of solid-solid phase transitions of Abeyaratne and Knowles, this paper examines the large time dynamical behavior of a phase boundary. The problem studied concerns a semi-infinite elastic bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. Interaction between the phase boundary and the elastic waves generated by an impact at the end of the bar and subsequent reflections is studied in detail, and an exact solution of the dynamical problem, which is governed by a nonlinear resursive formula, is obtained. It is shown that the phase boundary reaches a new equilibrium state for large time. Numerical calculations based on the recursive formula are carried out to illustrate analytical results.Address after August 15, 1995: Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA24061, USA. 相似文献
18.
Nonlocal generalizations of Burgers’ equation were derived in earlier work by Hunter (Contemp Math, vol 100, pp 185–202. AMS, 1989), and more recently by Benzoni-Gavage and Rosini (Comput Math Appl 57(3–4):1463–1484, 2009), as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage (Differ Integr Equ 22(3–4):303–320, 2009) under an appropriate stability condition originally pointed out by Hunter. The same stability condition has also been shown to be necessary for well-posedness in Sobolev spaces in a previous work of the authors in collaboration with Tzvetkov (Benzoni-Gavage et al. in Adv Math 227(6):2220–2240, 2011). In this article, we show how the verification of Hunter’s stability condition follows from natural stability assumptions on the original hyperbolic boundary value problem, thus avoiding lengthy computations in each particular situation. We also show that the resulting amplitude equation has a Hamiltonian structure when the original boundary value problem has a variational origin. Our analysis encompasses previous equations derived for nonlinear Rayleigh waves in elasticity. 相似文献
19.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(5):699-709
The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex
plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class
of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions
on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation
of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows.
An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known
approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998. 相似文献
20.
O. R. Kuznetsov 《Mechanics of Solids》2008,43(1):86-99
We consider thin-walled right-angle closed prismatic shells with rigid contour of the transverse cross-section. Such shells underlie the schemes used in the analysis of various thin-walled spatial structures. The use of nonlinear physical and geometric relations in the computations permits numerically obtaining the strength margin of the corresponding structures. In the present paper, we propose methods for obtaining a boundary value problem and analyzing such shells with nonlinear factors taken into account; the problem is presented as a system of linear differential equations with variable coefficients. We show that, within the approach proposed, this boundary value problem has a fixed structure independent of the special form of nonlinearity. The entire variety of problems of static analysis of right-angle prismatic shells with nonlinear factors taken into account can be reduced to solving this boundary value problem. Methods for taking a specific nonlinearity into account are treated as various methods for obtaining expressions for the variable coefficients in the matrices of the boundary value problem. We present methods for solving this boundary value problem numerically; these methods are independent of the specific form of the nonlinearity. 相似文献