共查询到16条相似文献,搜索用时 15 毫秒
1.
L. F. Fatullaeva 《Mechanics of Composite Materials》2007,43(6):513-520
The limiting state of a multilayer eccentric ring made of a nonlinearly elastic material and subjected to a uniform external
pressure is investigated. The topicality and importance of the problem are connected with the search for reserves of savings
in materials, with a simultaneous in crease in the load-carrying capacity of structures. Since rings often must have walls
of varying thickness, their critical buckling force is determined as a function of a parameter considering this fact. In solving
the problem, the geometric nonlinearity is also taken into account.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 761–770, November–December, 2007. 相似文献
2.
The buckling in stability of a long multilayer linearly viscoelastic shell, composed of different materials and loaded with
a uniformly distributed external pressure of given intensity, is investigated. By neglecting the influence of fastening of
its end faces, the initial problem is reduced to an analysis of the loss of load-carrying capacity of a ring of unit width
separated from the shell. The new problem is solved by using a mixed-type variational method, allowing for the geometric nonlinearity,
together with the Rayleigh-Ritz method. The creep kernels are taken exponential with equal indices of creep. As an example,
a three-layer ring with a structure symmetric about its midsurface is considered, and the effect of its physicomechanical
and geometrical parameters, as well as of wave formation, on the critical time of buckling in stability of the ring is determined.
It is found that, by selecting appropriate materials, more efficient multilayer shell-type structural members can be created.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 617–628, September–October, 2007. 相似文献
3.
V. S. Pakosh 《Journal of Mathematical Sciences》1999,96(1):2911-2915
Using the generalized dynamic theory of bending of plates, which takes account of the compliance of the material to transverse shear strains, we obtain an approximate solution of the problem of the dynamic stressed state of a composite plate with rigidly fixed edges subject to an impact load. We exhibit the contribution of the physico-mechanical and geometric parameters of the plate to the magnitude of the computed stresses and their time variation for different coefficients of internal dissipation of mechanical energy.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 129–133. 相似文献
4.
S. M. Vereshchaka 《Mechanics of Composite Materials》2007,43(4):345-358
Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing
a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial
contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is
allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear
moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic
plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in
the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the
magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations
for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers.
It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in
calculating their buckling stability.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007. 相似文献
5.
E. A. Aliyev 《Mechanics of Composite Materials》2007,43(6):521-534
Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability
(TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic
(viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered,
and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection)
of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are
obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form
perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations
is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the
stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and
the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time
is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 771–788, November–December, 2007. 相似文献
6.
7.
Within the frame work of the three-dimensional linearized theory of stability of deformable bodies (TLTSDB), the near-surface
buckling instability of a system consisting of a half-plane (substrate), a viscoelastic bond layer, and an elastic covering
layer is suggested. The equations of the TLTSDB are obtained from the three-dimensional geometrically non linear equations
of viscoelasticity theory by using the boundary-form perturbation technique. By employing the Laplace transform, a method
for solving the problem is developed. It is supposed that the covering layer has an insignificant initial imperfection. The
stability of the system is considered lost if the imperfection starts to increase and grows indefinitely. Numerical results
for the critical compressive force and the critical time are presented.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 517–530, July–August, 2006. 相似文献
8.
A. P. Markeev 《Regular and Chaotic Dynamics》2008,13(2):96-129
Basic investigation techniques, algorithms, and results are presented for nonlinear oscillations and stability of steady rotations
and periodic motions of a rigid body, colliding with a rigid surface, in a uniform gravity field.
相似文献
9.
S. S. Ganji D. D. Ganji H. Babazadeh N. Sadoughi 《Mathematical Methods in the Applied Sciences》2010,33(2):157-166
The scope of this paper is evaluating an oscillation system with nonlinearities, using a periodic solution called amplitude–frequency formulation, such as the motion of a rigid rod rocking back. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. We are to compare the solutions results of this method with the exact ones in order to validate the approach and assess the accuracy of the solutions. This method has a distinguished feature, which makes it simple to use and agree with the exact solutions for various parameters. Moreover, it is perceived that with one‐step iteration high accuracy of the solution will be achieved. We may apply the results of the solution to explain some of the practical physical problems. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
V. N. Paimushin 《Mechanics of Composite Materials》1999,35(6):465-470
The main stages of development of the stability theory of sandwich structural elements are considered. The mechanism of their stability loss is revealed using the experimental data and theoretical solutions obtained on the basis of refined statements of problems. A classification of all possible forms of stability loss is given within the limits of continuum representation of load-bearing layers and the core of these structures.Center for Study of Dynamics and Stability, Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 707–716, November–December, 1999. 相似文献
11.
研究一类具功能反应的食饵—捕食系统:x=xg(x)-yφ(x),y=y(-d+eφ(x))在g(x)=a-bx~m,φ(x)=cx~θ及m=θ=1/n,n>2为正整数情形下,分析了该系统的平衡点性态,并得到了系统在正平衡点外围的极限环的不存在性,存在性与唯一性的相关条件. 相似文献
12.
讨论了一类非定常经济系统的Lyapunov稳定性,给出了经济系统稳定和渐进稳定的充分条件和稳定的必要条件,同时得到与系统稳定性有关的临界积累率的解析表达式.结果可为经济政策的制定提供理论依据. 相似文献
13.
刘会茹 《数学的实践与认识》2017,(12):263-268
讨论了企业投资系统的Lyapunov稳定性,得到了企业投资系统渐进稳定的充分条件和稳定的必要条件,并给出了企业投资系统的临界积累率的表达式,这个问题的研究对于促进我国经济高速、稳定持续增长具有重要的理论意义和现实指导价值. 相似文献
14.
Marié Grobbelaar‐Van Dalsen 《Mathematical Methods in the Applied Sciences》2012,35(2):228-237
In this paper, we are concerned with a model for the magneto–elastic interactions of a three‐dimensional elastic body and a two‐dimensional flexible plate, which is attached to the flat flexible part of the surface of the body. Both the solid body and the plate are permeated by magnetic fields. The mathematical model is analyzed from the point of view of existence and uniqueness and stabilization.It turns out that, in the presence of the magnetic fields in the solid and the plate, strong stabilization can be achieved under viscous damping in the plate in one direction that is determined by the nature of the primary magnetic fields in the body and the plate. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
The torsional oscillations are studied of a solid of revolution under the action of elastic torque inside a container with a viscous incompressible fluid. We prove the asymptotic stability of the static equilibrium. We use the two approaches: the direct Lyapunov and linearization methods. The global asymptotic stability is established using a one-parameter family of Lyapunov functionals. Then small oscillations are studied of the fluid-solid system. The linearized operator of the problem of a solid oscillating in a fluid can be realized as an operator matrix obtained by appending two scalar rows and two columns to the Stokes operator. This operator is therefore a two-dimensional bordering of the Stokes operator and inherits many properties of the latter; in particular, the spectrum is discrete. The eigenvalue problem for the linearized operator is reduced to solving a dispersion equation. Inspection of the equation shows that all eigenvalues lie inside the right (stable) half-plane. Basing on this, we justify the linearization. Using an abstract theorem of Yudovich, we prove the asymptotic stability in a scale of function spaces, the infinite differentiability of solutions, and the decay of all their derivatives in time. 相似文献
16.
In this paper, we study the following critical fractional Schrödinger–Poisson system where is a small parameter, and , is the fractional critical exponent for 3‐dimension, has a positive global minimum, and are positive and have global maximums. We obtain the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials and Q as the concentration position of these ground state solutions as . Moreover, we consider some properties of these ground state solutions, such as convergence and decay estimate. 相似文献