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1.
On the basis of the Timoshenko kinematic hypothesis for shells we give a formulation of the problem of studying the stress-strain
state of orthotropic plates and shells weakened by a combined stress concentrator (a hole with two symmetric cracks extending
to its edge).
We propose a method of solving such problems on the basis of the finite-element method. To simulate the singularity of the
stresses and displacements in a neighborhood of the tip of a crack we apply special finite elements with degenerate faces
and nodes displaced by 1/4 the length of an edge. The stress intensity factors are found in terms of the displacements of
the nodes of such elements.
We give the results of computation of the concentration coefficients and the stress intensity factors for spherical and cylindrical
shells loaded by internal pressure and for a cylindrical shell and a plate under the action of a distending load with various
concentrators: a circular hole, an isolated crack, and a combined concentrator.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 48–54. 相似文献
2.
T. V. Shopa 《Journal of Mathematical Sciences》2010,170(6):721-733
We consider the problem of natural vibrations of a hingedly supported transversally isotropic cylindrical panel with a circular
hole. The deformation of the shell is described by modified equations of the Timoshenko theory of shells. The numerical solution
of the problem is constructed by the indirect method of boundary integral equations based on the sequential representation
of Green functions. 相似文献
3.
Stress state of a composite shell with a sizable opening 总被引:1,自引:0,他引:1
The stress-strain state of a nonshallow cylindrical shell of a composite material is investigated. The shell is weakened by a circular hole and loaded with internal pressure. For solving the problem, the variational-difference method is used. The calculations are carried out for an orthotropic shell with a sizable hole, with account of the reduced shear stiffness of the material.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 49–56, January–February, 2005. 相似文献
4.
M. M. Nikolishin 《Journal of Mathematical Sciences》1997,86(2):2547-2551
In the context of an analog of the Leonov-Panasyuk-Dagdeil model we consider the problem of limit equilibrium of a nonshallow
transversally isotropic cylindrical shell weakened by a nonthrough surface longitudinal crack. Based on the equations that
take account of the initial stresses, we reduce the problem to a system of two singular integral equations with unknown limits
of integration. We carry out a numerical analysis of the dependence of the opening of the edges of the crack on the load and
the geometric and physico-mechanical parameters of the shell.
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 31–36. 相似文献
5.
E. V. Altukhov 《Journal of Mathematical Sciences》1997,86(6):3089-3094
We obtain homogeneous solutions of the equations of the three-dimensional theory of elasticity for transtropic plates on whose
planar faces the normal stress and tangential displacements are zero. We study the problem of the stress state of a transtropic
layer with a cylindrical cavity. Bibliography: 5 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 3–12. 相似文献
6.
本文导出了分析计及横向剪变形的浅壳小孔应力集中问题的简化方程.对浅球壳和圆柱壳带一小圆孔的情况,获得了方程的级数形式通解.对均匀内压作用下的圆柱壳,求得了小圆孔边上应力集中系数的近似显式解,并计算了数值结果. 相似文献
7.
We consider a problem of wedging of an elastic wedge by a rigid plate along an edge crack that is located on the axis of symmetry
of the wedge and reaches its vertex. The detachment of the crack faces from the surfaces of the plate is taken into account.
Using the Wiener–Hopf method, we obtain an analytic solution of the problem. The size of the detachment zone, the stress intensity
factor, the distribution of stresses on the line of continuation of the crack and in the contact domain, and circular displacements
of the crack faces are determined. 相似文献
8.
Using the operator method we reduce the system of resolvent differential equations for a transvers ally isotropic cylindrical shell that takes account of the deformations caused by physicochemical processes to a single equation of tenth order. We construct the Green's function of this equation for the case of an infinite shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 80–84. 相似文献
9.
B. D. Drobenko V. I. Astashkin I. I. Chupik A. P. Bukalov 《Journal of Mathematical Sciences》1996,79(6):1431-1433
We use the finite-element method to study the problem of determining the temperature field and the evolution of the phase-state
regions in a hollow cylindrical casting. Using weighted discrepancies we reduce the problem to solving systems of ordinary
differential equations. We give a model solution of a specific problem and detailed analysis of the results.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 55–57. 相似文献
10.
Eleni Bisognin Vanilde Bisognin Mauricio Sepúlveda Octavio Vera 《Journal of Computational and Applied Mathematics》2008,220(1-2):290-321
We consider the initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of Korteweg–de Vries (KdV)-type modelling strong interactions between internal solitary waves. Finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed. We prove a global existence and uniqueness for strong solutions for the coupled system of equations of KdV-type as well as the exponential decay of small solutions in asymptotically cylindrical domains. Finally, we present a numerical scheme based on semi-implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems. 相似文献
11.
The problem on vertical oscillations of a circular die with a plane base that freely lies on an elastic half-space and contains a cylindrical cavity, whose axis is perpendicular to the plane of the base of the die and passes through its center, is considered. The problem is formulated in the form of paired integral equations that are related to integral Weber transforms. The paired equations are reduced to an equivalent Fredholm equation of the second kind. Some results of numerical calculations of amplitude-frequency characteristics of oscillations of the die are given. A comparative analysis with a known solution of an analogous problem for a continuous elastic half-space is given.Translated from Dinamicheskie Sistemy, No. 8, pp. 30–36, 1989. 相似文献
12.
Yu. M. Gnativ 《Journal of Mathematical Sciences》1996,81(6):3076-3079
We study the stressed state of a thin cylindrical shell with a circular neck loaded by a constant internal pressure. We start
from the equations obtained using Reissner's variational principle applying expansions of the components of the stress tensor
and the displacement vector with respect to the coordinates along the normal to the base surface of the shell.
Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995. 相似文献
13.
根据修正的Timoshenko理论,在几何非线性中考虑了剪切变形和转动惯量,对黏弹性圆柱壳的动力稳定性进行了研究.根据Bubnov-Galerkin法,结合基于求积公式的数值方法,将问题简化为求解具有松弛奇异核的非线性积分-微分方程的问题.针对物理-力学和几何参数在大范围内的变化,研究壳体的动力特性,显示了材料的黏弹性对圆柱壳动力稳定性的影响.最后,比较了通过不同的理论得到的结果. 相似文献
14.
Norbert Gorenflo 《Integral Equations and Operator Theory》1998,32(2):180-198
The problem of solving the three-dimensional Helmholtz equation in the exterior of a circular disk is considered where radially symmetric Dirichlet data on the disk are assumed to be prescribed. This problem for example arises in the scattering of plane (sound) waves at an infinite plane screen with a circular aperture if the direction of the incident wave is normal to the screen, as well as in the process of diffusion through a circular hole. By applying the factorization technique developed in [N. GORENFLO, M. WERNER,Solution of a finite convolution equation with a Hankel kernel by matrix factorization, SIAM J. Math. Anal., 28 (1997), pp. 434–451] to the disk problem an equivalent ordinary differential equation is derived, whose solution leads directly to the solution of the disk problem. This differential equation belongs to a class of ordinary differential equations which are of higher complexity than the standard ordinary differential equations of mathematical physics. The examination of this new class of differential equations therefore is motivated. 相似文献
15.
Dan Archdeacon C. Paul Bonnington Nathaniel Dean Nora Hartsfield Katherine Scott 《Journal of Graph Theory》2001,38(1):42-64
A graph is outer‐cylindrical if it embeds in the sphere so that there are two distinct faces whose boundaries together contain all the vertices. The class of outer‐cylindrical graphs is closed under minors. We give the complete set of 38 minor‐minimal non‐outer‐cylindrical graphs, or equivalently, an excluded minor characterization of outer‐cylindrical graphs. We also give the obstruction sets under the related topological ordering and Y Δ‐ordering. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 42–64, 2001 相似文献
16.
To solve the boundary-value problem for cylindrical orthotropic shell with sizeable rectangular hole we suggest analytical and numerical method of finite bodies. For determination of the stress state of orthotropic thin-walled cylinder we use a systemof equations that exactly satisfies the equilibrium equations of orthotropic cylindrical shell. Representation of the solutions is divided into basic and self-equilibrium state. For some loads of a shell we build the basic stress state. We obtain a countable number of resolving functions that exactly satisfy the equations of a shell and describe the self-equilibrium stress state. We develop the algorithm of the analytical and numerical solutions of boundary-value problem based on approximation of the stress state of a shell by finite sum of resolving functions and propose a universal way of reduction of all conditions of the contact parts of the enclosure and the boundary conditions to minimize the generalized quadratic forms. We establish criteria under which the construction of approximate solutions coincides with the exact one. 相似文献
17.
Parametric resonance of a functionally graded (FG) cylindrical thin shell with periodic rotating angular speeds subjected to thermal environment is studied in this paper. Taking account of the temperature-dependent properties of the shell, the dynamic equations of a rotating FG cylindrical thin shell based upon Love's thin shell theory are built by Hamilton's principle. The multiple scales method is utilized to obtain the instability boundaries of the problem with the consideration of time-varying rotating angular speeds. It is shown that only the combination instability regions exist for a rotating FG cylindrical thin shell. Moreover, some numerical examples are employed to systematically analyze the effects of constant rotating angular speed, material heterogeneity and thermal effects on vibration characteristics, instability regions and critical rotating speeds of the shell. Of great interest in the process is the combined effect of constant rotating angular speed and temperature on instability regions. 相似文献
18.
A. R. Snitser 《Journal of Mathematical Sciences》1996,82(3):3439-3443
We study the problem of the torsional oscillations of a plane disk-shaped die coupled with the upper boundary of a multilayer
elastic base containing a vertical cylindrical cavity whose axis is perpendicular to the interface of the layers. The problem
is stated as paired integral equations connected with the Weber integral transforms. To couple the solutions in the layers
we use the method of initial parameters, which makes it possible to express the stress-strain state in any layer in terms
of the solution of a Fredholm integral equation of second kind, to which the paired equations reduce. We exhibit an algorithm
for numerical implementation of the problem.
Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 55–61. 相似文献
19.
V. M. Shopa B. N. Polevoi I. I. Popadyuk V. I. Tusevich 《Journal of Mathematical Sciences》1993,63(3):398-401
We propose a method of determining the contact pressures between the shells in a packet under the influence of nonlinear internal and constant external pressure. Using the equations of the general moment theory of shells we determine the stress-deformed state of a packet of finite cylindrical shells taking account of frictional forces on the contacting surfaces. One table. Bibliography: 10 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 94–98. 相似文献
20.
We study the problem of nonstationary deformation of a system of imbedded cylindrical shells under the action of an internal
compression wave. The rigorous method of solution we apply makes it possible to obtain a system of Volterra integral equations
with retarded arguments in the deflections of the shells. We give the results of computations for the case of a linear source
and a source of finite size with limiting hardness properties.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 60–66. 相似文献