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1.
Mahir Sayir 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1968,19(2):185-219
Summary I. This report on thin-walled circular cylindrical shells of ideal-plastic material obeying the exact Tresca yield condition consists of two main parts. In the first part a general method of solution for exact collapse loads for 1° rigid-plastic material, 2° axially symmetrical loading, 3° radial load and axial load constant or piecewise constant over the shell length is illustrated by a number of examples. The case of a ring force previously treated byG. Eason [7] is generalised by inclusion of axial loading and admission of various end conditions. For the case of a distributed radial load and an axial load exact solutions are given. 相似文献
2.
M. Sayir 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1966,17(2):353-360
Summary In this report the circular cylindrical shell of rigid-plastic material obeying the exact Tresca yield condition is considered and the basic stress and velocity equations are integrated for the case where the axially symmetrical, distributed, radial load is constant or piecewise constant over the shell length and the axial load is constant. No special assumption is made for the boundary conditions or the shell length. The velocity field thus obtained is independent of the Tresca yield condition and can be used for every other yield criterion. Two examples are numerically solved and the exact collapse loads thus obtained are compared with approximate solutions. 相似文献
3.
O. G. Gurtovyi 《Mechanics of Composite Materials》2000,36(3):193-198
A phenomenological yield condition for quasi-brittle and plastic orthotropic materials with initial stresses is suggested.
All components of the yield tensor are determined from experiments on uniaxial loading. The reliability estimates of the criterion
suggested is discussed. For a plastic material without initial stresses, the given condition transforms into the Marin—Hu
criterion. The defining equations of the deformation theory of plasticity with isotropic and “anisotropic” hardening, associated
with the yield condition suggested, are obtained. These equations are used as the basis for a highly accurate nonclassical
continuous model for nonlinear deformation of thick sandwich plates. The approximations with respect to the transverse coordinate
take into account the flexural and nonflexural deformations in transverse shear and compression. The high-order approximations
allow us to model the occurrence of layer delamination cracks by introducing thin nonrigid interlayers without violating the
continuity concept of the theory.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. pp. 329–340, May–June, 2000. 相似文献
4.
A. E. Mironov I. A. Taimanov 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):169-184
We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve
becomes singular. We show that when the curve is reducible and all its irreducible components are rational curves, the construction
procedure reduces to solving systems of linear equations and to simple computations with elementary functions. We also demonstrate
how well-known coordinate systems, such as polar coordinates, cylindrical coordinates, and spherical coordinates in Euclidean
spaces, fit in this scheme.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 255, pp. 180–196. 相似文献
5.
Jean-Michel Roquejoffre Violaine Roussier-Michon 《Annali di Matematica Pura ed Applicata》2009,188(2):207-233
Bistable reaction–diffusion equations are known to admit one-dimensional travelling waves which are globally stable to one-dimensional
perturbations—Fife and McLeod [7]. These planar waves are also stable to two-dimensional perturbations—Xin [30], Levermore-Xin
[19], Kapitula [16]—provided that these perturbations decay, in the direction transverse to the wave, in an integrable fashion.
In this paper, we first prove that this result breaks down when the integrability condition is removed, and we exhibit a large-time
dynamics similar to that of the heat equation. We then apply this result to the study of the large-time behaviour of conical-shaped
fronts in the plane, and exhibit cases where the dynamics is given by that of two advection–diffusion equations.
相似文献
6.
G. Teters 《Mechanics of Composite Materials》2006,42(4):347-352
The multicriteria optimization of the structure and geometry of a laminated cylindrical shell under the action of external
pressure and longitudinal thermal stresses is considered. From the known monolayer properties of the composite and the given
values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite
are determined. The criteria to be optimized — the critical external pressure and thermal stresses — depend on two variable
parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal
subdomain are found.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 495–502, July–August, 2006. 相似文献
7.
G. Teters 《Mechanics of Composite Materials》2009,45(2):153-158
The multicriteria optimization of the structure and geometry of a multilayer cylindrical shell under the action of external
torque and longitudinal thermal stresses is considered. From known monolayer properties of the composite and given values
of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined.
The criteria to be optimized — the critical external torque and thermal stresses — depend on two variable parameters and temperature.
In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 223–230, March–April, 2009. 相似文献
8.
V. G. Zhitnyaya 《Journal of Mathematical Sciences》1995,76(3):2431-2434
We solve the problem of antiplane deformation for an infinite isotropic massif with a curvilinear cavity in which a harmonic
shear wave is propagating.
The solution of the problem, which is based on the application of the theory of functions of a complex variable, is reduced
to finding unknown constants from a system of linear algebraic equations. Numerical results are given for a circular cavity.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 115–119. 相似文献
9.
We consider the problem of distention of a thin circular cylindrical shell of finite length weakened by a circular slit. On
the basis of the complex equations of the theory of cylindrical shells we construct a solution that makes it possible to take
account of the influence of the boundaries of the hole and the faces. Using the method of boundary collocations and taking
account of the conditions for single-valuedness of the displacements, we reduce the problem to a system of linear algebraic
equations. We study numerically the behavior of the membrane stresses as the boundaries of the hole and the faces are moved
closer together.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 45–48. 相似文献
10.
A. F. Kregers G. A. Teters Yu. G. Melbardis A. Zh. Lagzdin' 《Mechanics of Composite Materials》1996,32(5):431-438
In a numerical example of compromise optimization by computerized mathematical modeling (2000 realizations) for a known deterministic
solution, in the case of an isotropic spatially reinforced porous composite, certain scatter characteristics of the optimal
solution have been established, namely four standard deviations and six coefficients of linear correlation for four properties—density,
modulus of elasticity, thermal conductivity, and linear thermal expansion coefficient. Of the 17 input data (parameters of
the composite components), 10 are stochastic, the others deterministic. An equation is presented for the four-dimensional
hyperellipsoid of normal distribution with numerical values of the coefficients, as well as all invariants and roots of the
characteristic equation, the matrix of direction cosines of the principal axes of the hyperellipsoid, and the lengths of the
principal semiaxes, depending on the dimensionality of the scattering region and the assigned probability P. The four-dimensional
hyperellipsoid has been projected onto three-dimensional space and then onto a plane. A section of the scattering region has
been constructed.
Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh
Materialov, No. 5, pp. 625–635, September–October, 1996. 相似文献
11.
G. S. Sharov 《Theoretical and Mathematical Physics》1997,113(1):1263-1276
In this paper, consideration is given to a baryon model in which three material points (quarks) are pairwise connected by
relativistic strings forming a curvilinear triangle. For this model, we found and studied classical solutions corresponding
to a uniform rotation of the system in a plane about the center of mass. Along with the simplest state—a rotating curvilinear
triangle with smooth sides—there can be more complicated configurations characterized by the motion, at the velocity of light,
of some interior massless points of the string. In the limit, the closed string takes the form of a rotating hypocycloid as
the quark masses tend to zero.
The possibility of describing baryon states on Regge trajectories with the help of the above-mentioned solutions is analyzed.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 68–84, October, 1997. 相似文献
12.
V. M. Akhundov 《Mechanics of Composite Materials》2007,43(2):159-172
Equations for a round cylinder weakly reinforced with systems of yarns and subjected to large tensile, inflation, and torsional
deformations are presented. Since the degree of filling is small, the model of uniaxial stress state is assumed. The fibers
are aligned with spirals on cylindrical surfaces and with radii in the transverse and meridional sections of the cylinder.
The equations are obtained in the macroscopically unidimensional statement for the case of cylindrically symmetric strains.
Numerical results are given for twisted hollow rubber cylinders reinforced with polymer yarns in the axial and radial directions.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 237–256, March–April, 2007. 相似文献
13.
V. L. Kulakov Yu. M. Tarnopol’skii D. D. Mungalov A. I. Beyle 《Mechanics of Composite Materials》2000,36(3):199-206
The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices
of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided
composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging.
The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and
by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP)
and aramid (AFRP) epoxy plastics.
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).
Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000. 相似文献
14.
The stability problem is solved for cylindrical shells made of a laminated composite whose directions of layer reinforcement
are not aligned with coordinate axes of the shell midsurface. Each layer of the composite is modeled by an anisotropic material
with one plane of symmetry. The resolving functions of the mixed variant of shell theory are approximated by trigonometric
series satisfying boundary conditions. The stability of the shells under axial compression, external pressure, and torsion
is investigated. A comparison with calculation data obtained within the framework of an orthotropic body model is carried
out. It is shown that this model leads to considerably erroneous critical loads for some structures of the composites.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 651–662, September–October, 2005. 相似文献
15.
R. Z. Stasyuk 《Journal of Mathematical Sciences》1996,79(6):1439-1440
We study the elastic equilibrium of a closed infinite circular cylindrical shell with a system of surface cracks of identical
length and depth. We use the method of singular integral equations together with the modeling of solid matter in the plane
of a part-through crack by irregularly distributed “line springs”. We conduct a numerical analysis of the variation of the
relative stress intensity factor at the center of a crack as a function of the parameters of a crack and the number of cracks.
We study cracks located on both the interior and exterior surface of the shell.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 63–65. 相似文献
16.
Abstract. We present algorithms for constructing a hierarchy of increasingly coarse Morse—Smale complexes that decompose a piecewise
linear 2-manifold. While these complexes are defined only in the smooth category, we extend the construction to the piecewise
linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse—Smale complexes
by canceling pairs of critical points in order of increasing persistence. 相似文献
17.
A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of
symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions
not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external
pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the
shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites
with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections.
This fact is important from the practical point of view.
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007. 相似文献
18.
For a Wiener field with an arbitrary finite number of parameters, we construct the law of the iterated logarithm in the functional
form. We consider the problem for random fields of a certain type to reside within curvilinear boundaries without assuming
that the Cairoli—Walsh condition is satisfied.
Donetsk University, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 883–894, July, 1997. 相似文献
19.
The Riemann–Silberstein–Majorana–Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix
formalism. Within the squaring procedure we construct four types of formal solutions of the Maxwell equations on the base
of scalar D’Alembert solutions. General problem of separating physical electromagnetic solutions in the linear space λ0Ψ0 + λ1Ψ1 + λ2Ψ2 + λ3Ψ3 is investigated, the Maxwell equations reduce to a new form including parameters λ
a
. Several particular cases, plane waves and cylindrical waves, are considered in detail. Possible extension of the technique
to a curved space–time models is discussed. 相似文献
20.
The representation of order conditions for general linear methods formulated using an algebraic theory by Butcher, and the
alternative using B-series by Hairer and Wanner for treating vector initial value problems in ordinary differential equations
are well-known. Each relies on a recursion over rooted trees; yet tractable forms—for example, those which may be solved to
yield particular methods—often are obtained only after extensive computation. In contrast, for Runge–Kutta methods, tractable
forms have been used by various authors for obtaining methods. Here, the corresponding recursion formula for two-step Runge–Kutta
methods is revised to yield tractable forms which may be exploited to derive such methods and to motivate the selection of
efficient algorithms in an obvious way. The new recursion formula is utilized in a MAPLE code. 相似文献