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1.
T. E. Maselko 《Journal of Mathematical Sciences》1993,64(3):953-956
In the context of an analog of the
k
—model the problem of the stress-strain state of a shallow cylindrical shell with a nonthrough longitudinal crack is reduced to a system of singular integral equations that is solved by the small-parameter method. For a shell under an internal pressure we study the dependence of the opening of the crack on the geometric and physico-mechanical parameters of the shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 66–70. 相似文献
2.
Using an analog of the δ
c
-model, we have obtained a solution of the problem of the stress-strain state of an elastoplastic orthotropic shell, having
an arbitrary curvature, with a surface crack. Here, additional constraints on the elastic parameters of the material are not
imposed. Furthermore, we have studied the dependence of the length of the plastic zone and surface-crack opening on the level
of load, the shell and crack geometrical parameters, and the mechanical properties of the material. 相似文献
3.
We solve the thermoelastic problem for a plane with a rectilinear heat-conducting crack whose conductivity depends on its opening. By modeling the crack as a thin inclusion of variable thickness we reduce the problem to a system of singular integrodifferential equations for the potential densities of the temperature field. We study the behavior of the unknown functions at the ends of the contour of integration and, using a numerical-iteration method, we also determine the solution of the problem. We find an approximate asymptotic solution in the case of a weakly conducting crack.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 54–58. 相似文献
4.
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
5.
On the basis of an analog of the Leonov—Panasyuk—Dugdale -model and with the use of the initial equations of the general moment theory of shells the article deals with the limit equilibrium of a closed infinite cylindrical shell which has a transverse blind crack. On the basis of the generalized dislocation method the problem is reduced to a system of two singular integral equations whose solution is constructed with a view to the conditions of finiteness of the stresses in the vicinity of the crack. For a shell uniformly tensioned at infinity the article investigates the dependence of the dimension of the plastic zone and of the crack opening on the external load.Lvov. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 83–86, 1990. 相似文献
6.
N. P. Lazarev 《Journal of Applied and Industrial Mathematics》2013,7(1):78-88
Under study is the nonlinear equilibrium problem for an elastic Timoshenko-type shallow shell containing a through crack. Some boundary conditions in the form of inequalities are imposed on the curve defining the crack. We establish the unique solvability of the variational statement of the nonlinear problem of the equilibrium of a shell. We prove that, for sufficient smoothness of the solution, the initial variational statement is equivalent to the differential formulation of the problem. We deduce the boundary conditions on the inner boundary that describes the crack. In the case of the zero opening of the crack, we prove the local infinite differentiability of the solution function with additional assumptions on the functions defining the curvatures of the shell and the external loads. 相似文献
7.
P. M. Kushnir 《Journal of Mathematical Sciences》2001,107(1):3671-3679
Using the method of generalized problems of conjugation, for a piecewise homogeneous cylindrical shell with a longitudinal crack we develop a system of integral equations (some of which are singular) for functions of displacement jumps and their derivatives on the line of the crack and on the surfaces of separation of dissimilar component shells. The particular features of application of the method proposed to the case of a nonthrough crack are analyzed with due regard for plastic zones near its front and, also, for determining the redistribution of residual and temperature stresses, caused by the presence of a crack. The numerical analysis of the problem is performed, and certain relationships between the coefficients of intensity of efforts, moments, opening of the crack, and its size and distance to the surface of separation are established. 相似文献
8.
We propose a mathematical model that makes it possible to reduce the problem of the stressed state and limit equilibrium of
a cylindrical anisotropic elastoplastic shell with internal crack to a system of nonlinear singular integral equations with
discontinuous functions on the right-hand sides. We construct an algorithm for numerical solution of such systems together
with the conditions of plasticity and boundedness of stresses near the crack. For a transversally isotropic shell, we carry
out a numerical analysis of the dependence of the opening of the internal crack front on the load and geometric and mechanical
parameters.
Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences L'viv. Translated from
Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 111–116, April–June, 1998 相似文献
9.
I. Yu. Khoma 《Journal of Mathematical Sciences》1998,92(5):4133-4135
On the basis of a generalized theory constructed using the Fourier-series expansion of the unknowns in Legendre polynomials
of the thickness coordinate we give a representation of the general solution of the equilibrium equations of a transversally
isotropic spherical shell for an arbitrary approximation. On this basis we study the problem of the stressed state of a shallow
spherical shell with a circular cavity on whose boundary surface there are tangential stresses varying nonlinearly over the
thickness.
Bibliography: 3 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 19–24. 相似文献
10.
By using the method of mechanical quadratures we reduce the resolvent integral equation for the problem of an infinite elastic
space with a rectangular crack to a system of linear algebraic equations. We give the results of numerical experiments in
varying the stress intensity factor on one side of the crack in the case of tension in the direction perpendicular to the
plane of the crack.
One figure. Bibliography: 5 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 24–28. 相似文献
11.
We study the problem for a spherical shell weakened by thermally insulated slits. Using the two-dimensional Fourier transform
and the elements of the theory of distributions, we obtain the resolvent systems of singular integral equations. We carry
out numerical studies of the influence of the geometric parameters of the shell and the slits on the values of the coefficients
of intensity of the forces and moments. Three figures. Bibliography: 5 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 75–81. 相似文献
12.
R. Z. Stasyuk 《Journal of Mathematical Sciences》1996,81(6):3073-3075
Using the Rice-Levy line spring model we find an approximate solution of the problem of elastic balance of a closed infinite
circular cylindrical shell weakened by a periodic system of longitudinal interior cracks of identical length. The stress intensity
factors are found at the center of a crack for various numbers of cracks with various parameters.
Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995. 相似文献
13.
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
14.
G. M. Ulitin 《Journal of Mathematical Sciences》1995,74(4):1185-1187
We consider the vibrations of a conical shell filled with a fluid. We obtain a system of differential equations that describes
the interaction of a variable volume of fluid with the shell. We solve the problem of determining the natural frequencies
for a completely full shell. We obtain a formula for computing the fundamental frequency as a function of the geometric parameters
of the shell. One figure. Bibliography: 4 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 85–88, 1991. 相似文献
15.
We have solved the problem of determining the stressed state of an elastoplastic isotropic shell of arbitrary curvature with
a through crack with regard for material hardening. We have obtained a system of singular integral equations and solved it
numerically by the method of mechanical quadratures. We have also studied the influence of material hardening on the general
characteristics of the stressed state. 相似文献
16.
By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface. 相似文献
17.
In this paper, the blood flow problem is considered in a blood vessel, and a coupling system of Navier–Stokes equations and linear elastic equations, Navier–Lame equations, in a cylinder with cylindrical elastic shell is given as the governing equations of the problem. We provide two finite element models to simulating the three-dimensional Navier–Stokes equations in the cylinder while the asymptotic expansion method is used to solving the linearly elastic shell equations. Specifically, in order to discrete the Navier–Stokes equations, the dimensional splitting strategy is constructed under the cylinder coordinate system. The spectral method is adopted along the rotation direction while the finite element method is used along the other directions. By using the above strategy, we get a series of two-dimensional-three-components (2D-3C) fluid problems. By introduce the S-coordinate system in E3 and employ the thickness of blood vessel wall as the expanding parameter, the asymptotic expansion method can be established to approximate the solution of the 3D elastic problem. The interface contact conditions can be treated exactly based on the knowledge of tensor analysis. Finally, numerical test shows that our method is reasonable. 相似文献
18.
The problem of the limiting equilibrium of a closed cylindrical shell with evenly spaced longitudinal cuts, stated in the context of the analogy with the k-model of Leonov-Panasyuk-Dagdeil, is reduced to a system of singular integral equations. An algorithm is constructed for the numerical solution of this system. For a shell under internal pressure we study the influence of the number of cuts, the magnitude of the applied load, and the length of a cut on the opening of its ends. Two figures. Bibliography: 4 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 50–55. 相似文献
19.
We give the statement and solution of the problem of limiting equilibrium of a spherical shell weakened by a surface crack. We study the dependence of the separation of the edges of the crack on the geometric and physical parameters of the shell. 相似文献
20.
L. F. Vakhlaeva V. A. Krys'ko A. S. Saninskii N. S. Surova 《Journal of Mathematical Sciences》1992,62(1):2583-2586
The finite difference method is used to obtain a solution of a nonlinear static problem for a laminated inclined rectangular shell in a plane acted on by a force load and a temperature field. The approximating system of nonlinear equations is obtained using an approximation of the equation of variations or systems of differential equations.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 86–89. 相似文献