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1.
E. Sanchez‐Palencia We derive a linearized prestressed elastic shell model from a nonlinear Kirchhoff model of elastic plates. The model is given in terms of displacement and micro‐rotation of the cross‐sections. In addition to the standard membrane, transverse shear, and flexural terms, the model also contains a nonstandard prestress term. The prestress is of the same order as flexural effects; hence, the model is appropriate when flexural effects dominate over membrane ones. We prove the existence and uniqueness of the solutions by Lax–Milgram theorem and compare solution with the solution of the standard shell model via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
2.
The mathematical problem of the plane shear buckling form (BF) of sandwich plates and plates homogeneous across the thickness
in pure shear is considered. The solution to this problem is compared with the solution to the problem of a flexural BF which
is realized in these plates with the formation of oblique waves. It is established that, in the case of plates homogeneous
across the thickness, the critical loads corresponding to the plane shear BF are maximum for isotropic ones. In real one-layer
structural elements manufactured both of isotropic homogeneous and orthotropic composite materials, these critical loads cannot
be reached since they exceed considerably the critical loads for the flexural BFs with oblique waves. The critical loads corresponding
to the two BFs are comparable only for relatively thick plates. However, the plane shear BF can be realized in sandwich plates
earlier than the flexural one even if the plates are thin.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 215–228, 2000. 相似文献
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The linearized problems on the stability of a circular sandwich ring of symmetric structure under an axially symmetric temperature field inhomogeneous across the core thickness are stated and analytical solutions to them are given. The first problem deals with the mixed flexural buckling form (BF) of the ring as a whole, realized as a result of buckling in one of the load-carrying layers due to formation of precritical pressure stresses in the layer. The second problem considers purely shear BFs when one load-carrying layer is rotated relative to the other. The deformation processes for the load-carrying layers are described by the Kirchhoff-Love model, and for the core of arbitrary thickness - by two models, namely by the equations of the plane problem of elasticity theory and by the model of a transversely soft layer of arbitrary thickness (the same equations simplified by the assumption of zero circumferential normal stresses). Within the frames of the first model adopted for the core, the shear BF is theoretically possible but practically unrealizable, since the mixed flexural BF arises earlier than the shear BF. 相似文献
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V. N. Paimushin V. A. Ivanov S. A. Lukankin A. A. Bushkov 《Mechanics of Composite Materials》2004,40(6):461-472
A solution to the problem on the stability according to the flexural buckling mode is given for a cylindrical sandwich shell with a transversely soft core of arbitrary thickness. The shell is under the action of a temperature field inhomogeneous across the thickness, and its end faces are fastened in such a way (in the axial direction, the face sections of the external layer are fixed, but of the internal one are free) that an inhomogeneous subcritical stress-strain state arises in the shell across the thickness of its layers. It is shown that, under such conditions, the buckling mode of the shell is mixed flexural. To reveal and investigate this mode, equations of subcritical equilibrium and stability of a corresponding degree of accuracy are needed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 715–730, November–December, 2004. 相似文献
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A method is presented for determining the flexural strength of composites from tests on pinned specimens in axial compression. This scheme is close to the so-called Euler buckling model, but the load is applied eccentrically, and the bar is bent practically from the beginning of loading. An analytical model is proposed for calculating the flexural stress in longitudinal flexure of a thin bar in the case of large displacements. The problem is solved in elliptic integrals of the first and second kinds. The analytical model shows an excellent agreement with experiments. The results obtained are compared with experimental tension data. A device is also designed for testing composite bars in longitudinal flexure. The method offered has an obvious advantage over the conventional three- or four-point bending — the gage zone in this scheme is far away from the loading zone of the test specimen. 相似文献
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V. N. Paimushin V. A. Ivanov S. N. Bobrov T. V. Polyakova 《Mechanics of Composite Materials》2000,36(3):185-192
The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement.
The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse
compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with
more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining
parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the
most efficient from the weight viewpoint.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 317–328, May–June, 2000. 相似文献
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O. G. Gurtovyi 《Mechanics of Composite Materials》1999,35(6):487-494
Continual models of deformation of thick layered plates, where the general order of resolving equations does not depend on the number of layers, are constructed with account of the specific character of the unflexural and flexural deformation caused by the symmetric and antisymmetric components of bilateral loads and temperature. Account of the load decomposition during the process of refining a certain reasonable initial solution, consisting in the analytical iterative integration, makes it possible to obtain rather precise continual approximations of stresses and displacements over the transverse coordinate and thus to revise the known continual models.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 743–756, November–December, 1999. 相似文献
11.
Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates 总被引:1,自引:0,他引:1
The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening,
are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse
of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control
beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer
(CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also
applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution
if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 667–686, September–October, 2007. 相似文献
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Resonance methods for determining the complex shear moduli of orthotropic composites 总被引:1,自引:1,他引:0
V. S. Ekel’chik 《Mechanics of Composite Materials》2007,43(6):487-502
A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural
and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented. The errors in
the computed values of dynamic shear moduli caused by inaccuracies in the experimental determination of resonance frequencies
are examined. A new variant of the resonance method is developed, which permits one to find three complex shear moduli of
a composite from the resonant frequencies and the damping of torsional vibrations of three rods oriented along three symmetry
axes of the material. For computing the moduli in the case of an overdetermined system, an algorithm of nonlinear optimization
based on the least-squares method is recommended. From the results obtained it follows that, for determining the interlaminar
shear moduli with a necessary accuracy, the rods must be sufficiently thick. It is shown that a good agreement alone between
calculated and experimental frequencies of flexural and torsional vibrations of rods does not ensure a reliable determination
of the moduli of interlaminar shear if experiments are carried out on wide test specimens cut out from a thin plate. Recommendations
are given for the choice of geometrical sizes of test specimens for resonance experiments.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 721–744, November–December, 2007. 相似文献
14.
The results of a theoretical and experimental research project on the use of an innovative technique for strengthening concrete
beams are presented. A spacer element is inserted between the tension side of a beam and the composite material to increase
its lever arm and to enhance the over all stiffness of the strengthened beam. The main aim of this exploratory project was
to increase the ultimate failure load of strengthened beam specimens, whilst guaranteeing acceptable over all deflections
at the serviceability limit states. This resulted into a significant reduction in the amount of FPR required and in a better
utilization of the materials employed. A preliminary theoretical study was carried out to investigate the effect of Young’s
modulus, failure strain, and thickness of the element to be used as a spacer in order to determine the best possible candidate
material. Three tests on 2.5-m-long beams were carried out, and different anchorage techniques were used to try and prevent
the debonding of the strengthening system. The results from this pilot study are very promising, as the strengthening system
ensures an adequate initial stiffness along with an improved ultimate flexural capacity.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 403–416, May–June, 2008. 相似文献
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V. N. Paimushin V. A. Ivanov S. A. Lukankin A. A. Bushkov 《Mechanics of Composite Materials》2004,40(4):309-330
Problems on buckling modes (BMs) are considered for a spherical sandwich shell with thin isotropic external layers and a transversely soft core of arbitrary thickness in a centrosymmetric temperature field inhomogeneous across the shell thickness. For their statement, the two-dimensional equations of the theory of moderate bending of thin Kirchhoff–Love shells are used for the external layers, with regard for their interaction with the core; for the core, maximum simplified geometrically nonlinear equations of thermoelasticity theory, in which a minimum number of nonlinear summands is retained to correctly describe its pure shear BM, are utilized. An exact analytical solution to the problem on initial centrosymmetric deformation of the shell is found, assuming that the temperature increments in the external layers are constant across their thickness. It is shown that the three-dimensional equations for the core, linearized in the neighborhood of the solution, can be integrated along the radial coordinate and reduced to two two-dimensional differential equations, which supplement the six equations that describe the neutral equilibrium of the external layers. It is established that the system of eight differential equations of stability, upon introduction of new unknowns in the form of scalar and vortical potentials, splits into two uncoupled sets of equations. The first of them has two kinds of solutions, by which the pure shear BM is described at an identical value of the parameter of critical temperature. The second system describes a mixed flexural BM, whose realization, at definite combinations of determining parameters of the shell and over wide ranges of their variation, is possible for critical parameters of temperature by orders of magnitude exceeding the similar parameter of shear BM. 相似文献
16.
One of the greatest challenges in structural engineering nowadays is the strengthening, upgrading, and retrofitting of existing
structures. The use of fibre-reinforced polymers (FRPs) bonded to the tension face of a structural member is an attractive
technique in this field of application. The strengthening of reinforced concrete structures by means of an externally bonded
reinforcement (EBR) is achieved by gluing a FRP laminate to the concrete substrate. For an efficient utilization of the FRP
EBR systems, an effective stress transfer is required between the FRP and concrete. The paper discusses the bond behaviour
between a FRP and concrete in the case of flexural strengthening of continuous beams. With respect to this type of beams,
only a few studies have been reported, though continuous members often occur in concrete constructions. The structural behaviour
of statically indeterminate elements is typically characterized by redistributions of the internal forces. These distributions
are related to the nonlinear deformations of the beams and has also a distinct influence on the bond behaviour between the
FRP and concrete.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 389–402, May–June, 2008. 相似文献
17.
Experimentally determined resonant frequencies and damping of flexural and torsional vibrations of rod-type rectangular test
specimens made of an orthotropic GFRP fabric with different ratios of cross-sectional sizes are used for calculating six principal
complex elastic and shear moduli. The application of the classical theories of flexural and torsional vibrations, the theory
of flexural vibrations of a Timoshenko beam, and a refined theory of torsional vibrations of free-free orthotropic rods is
analyzed. 相似文献
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A.T. Il’ichev 《Journal of Applied Mathematics and Mechanics》2008,72(3):323-330
The spectral stability of compression solitons in non-linear elastic rods with respect to perturbations of the flexural mode of the oscillations of the rod is investigated. The system of equations of the isotropic theory of elasticity, taking account of the non-linear corrections corresponding to the interaction being studied, is used to describe the interaction of longitudinal and flexural waves in the rod. This system of equations describes long longitudinal-flexural waves of small but finite amplitude. It is shown that trapped flexural modes exist, which propagate together with a compression soliton. It is established that these modes, which are the least stable, do not increase with time. 相似文献
20.
A. K. Arnautov 《Mechanics of Composite Materials》2005,41(5):467-476
A method is presented for determining the flexural strength of unidirectional composites from three-point bending tests at
large deflections. An analytical model is proposed for calculating the flexural stress in testing thin bars in the case of
large deflections. The model takes into account the changes in the support reactions at bar ends and in the span of the bar
caused by its deflection. In the model offered, the influence of transverse shear and the friction at supports are neglected.
The problem is solved in elliptic integrals of the first and second kind. The results obtained are compared with experimental
tension data. The method elaborated for calculating flexural stresses has an obvious advantage over the conventional engineering
procedure, because the calculation accuracy of the stresses increases considerably in the case of large deflections.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 691–704, September–October, 2005. 相似文献