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1.
The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite.
The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are
formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed.
The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is
studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations)
or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic
problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear
factors
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005. 相似文献
2.
I. S. Chernyshenko E. A. Storozhuk F. D. Kadyrov 《International Applied Mechanics》2007,43(5):512-518
The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal
pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities.
The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration
is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear,
and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with
allowance for nonlinear factors
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 46–54, May 2007. 相似文献
3.
The elastoplastic state of thin cylindrical shells weakened by a curvilinear (circular) hole is analyzed considering finite
deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The
distributions of stresses (strains, displacements) along the hole boundary and in the zone of their concentration are studied.
The results obtained are compared with solutions that account for physical (plastic strains) or geometrical (finite deflections)
nonlinearity alone and with a numerical linear elastic solution. The stress-strain state around a circular hole is analyzed
for different geometries in the case where both nonlinearities are taken into account
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 115–123, December, 2006. 相似文献
4.
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2011,47(6):679-684
The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions
of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress–strain
state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results
are presented as plots and tables 相似文献
5.
I. S. Chernyshenko E. A. Storozhuk I. B. Rudenko 《International Applied Mechanics》2008,44(12):1397-1404
The elastoplastic state of a thin spherical shell weakened by an elliptic hole is analyzed. Finite deflections are considered.
The hole is reinforced with a thin ring. The shell is made of an isotropic homogeneous material. The load is internal pressure.
A relevant problem is formulated and solved numerically with allowance for physical and geometrical nonlinearities. The distribution
of stresses, strains, and displacements along the elliptic boundary and in the zone of their concentration is studied. The
stress–strain state of the shell near the hole is analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 93–101, December 2008. 相似文献
6.
I. S. Chernyshenko E. A. Storozhuk I. B. Rudenko 《International Applied Mechanics》2007,43(10):1142-1148
The stress-strain state of thin flexible spherical shells weakened by an eccentric circular hole is analyzed. The shells are
made of an isotropic homogeneous material and subjected to internal pressure. A problem formulation is given, and a method
of numerical solution with allowance for geometrical nonlinearity is outlined. The distribution of displacements, strains,
and stresses along the hole boundary and in the region of their concentration is examined. The data obtained are compared
with numerical solutions of the linear problem. The stress-strain state around the eccentric circular hole is analyzed with
allowance for geometrical nonlinearity
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 92–98, October 2007. 相似文献
7.
Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes
The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are
on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure
of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when
the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value
problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account)
and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly
elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities
accounted for
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005. 相似文献
8.
9.
The stress-strain state of an anisotropic plate containing an elliptic hole and thin, absolutely rigid, curvilinear inclusions
is studied. General integral representations of the solution of the problem are constructed that satisfy automatically the
boundary conditions on the elliptic-hole contour and at infinity. The unknown density functions appearing in the potential
representations of the solution are determined from the boundary conditions at the rigid inclusion contours. The problem is
reduced to a system of singular integral equations which is solved by a numerical method. The effects of the material anisotropy,
the degree of ellipticity of the elliptic hole, and the geometry of the rigid inclusions on the stress concentration in the
plate are studied. The numerical results obtained are compared with existing analytical solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 173–180, July–August, 2007. 相似文献
10.
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2008,44(7):802-809
The elastoplastic state of cylindrical shells with a circular hole is studied considering finite deflections. The material
of the shells is isotropic and homogeneous; the load is axial tension. The distribution of stresses, strains, and displacements
along the hole boundary and in the zone of their concentration is studied by solving a doubly nonlinear problem. The data
obtained are compared with the solutions of the physically and geometrically nonlinear problems and a numerical solution of
the linear elastic problem
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 101–109, July 2008. 相似文献
11.
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2007,43(4):418-424
The elastoplastic state of thin conical shells with a curvilinear (circular) hole is analyzed assuming finite deflections.
The distribution of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are
studied. The stress-strain state around a circular hole in shells subject to internal pressure of prescribed intensity is
analyzed taking into account two nonlinear factors
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 73–79, April 2007. 相似文献
12.
V. A. Maksimuuk V. S. Tarasyuk I. S. Chernyshenko 《International Applied Mechanics》1999,35(6):614-620
A study is made of geometrically and physically nonlinear inverse problems concerning the axisymmetric deformation of cylindrical
shells into conical shells. Results obtained from the numerical solution of the problems are used to determine the laws of
distribution of the surface loads, stresses, strains, and displacements in relation to the initial parameters and nonlinearities
of the shells.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya
Mekhanika, Vol. 35, No. 6, pp. 86–91, June, 1999. 相似文献
13.
D. A. Pozharskii 《Mechanics of Solids》2017,52(3):315-322
Numerical and analytical solutions of the 3D contact problem of elasticity on the penetration of a rigid punch into an orthotropic half-space are obtained disregarding the friction forces.A numericalmethod ofHammerstein-type nonlinear boundary integral equations was used in the case of unknown contact region, which permits determining the contact region and the pressure in this region. The exact solution of the contact problem for a punch shaped as an elliptic paraboloid was used to debug the program of the numerical method. The structure of the exact solution of the problem of indentation of an elliptic punch with polynomial base was determined. The computations were performed for various materials in the case of the penetration of an elliptic or conical punch. 相似文献
14.
We solve the problem of determining the stress-strain state of an anisotropic plate with an elliptic hole and a system of thin rectilinear elastic inclusions. We assume that there is a perfect mechanical contact between the inclusions and the plate. We deal with a more precise junction model with the flexural rigidity of inclusions taken into account. (The tangential and normal stresses, as well as the derivatives of the displacements, experience a jump across the line of contact.) The solution of the problem is constructed in the form of complex potentials automatically satisfying the boundary conditions on the contour of the elliptic hole and at infinity. The problem is reduced to a system of singular integral equations, which is solved numerically. We study the influence of the rigidity and geometry parameters of the elastic inclusions on the stress distribution and value on the contour of the hole in the plate. We also compare the numerical results obtained here with the known data. 相似文献
15.
Conclusions We determined the relationship between the nature of the stress distribution on the hole surface in a flexible plate as a function of thickness. We observed a great difference between the stress densities in flattened, thin and moderate-thickness conical shells and the stress concentrations near holes in thin cylindrical shells and thin, almost cylindrical, conical shells. The stress distribution near the hole in flattened conical shells of moderate thickness is similar to the stress distribution near the holes in flexible, thick plates. During loading of conical shells by an axial force, the lowest stress concentration factor near the holes is obtained when the axis of the hole is parallel to the shell axis. As the thickness of the shell is increased, the stress concentration factor near the holes increases.Kiev University. Ukrainian Institute of Water Management Engineers, Rovno. Translated from Prikladnaya Mekhanika, Vol. 24, No. 9, pp. 65–70, September, 1988. 相似文献
16.
《International Journal of Solids and Structures》2005,42(3-4):1129-1150
Free vibrations of layered conical shell frusta of differently varying thickness are studied using the spline function approximation technique. The equations of motion for layered conical shells, in the longitudinal, circumferential and transverse displacement components, are derived using extension of Love’s first approximation theory. Assuming the displacement components in a separable form, a system of coupled equations on three displacement functions are obtained. Since no closed form solutions are generally possible, a numerical solution procedure is adopted in which the displacement functions are approximated by cubic and quintic splines. A generalized eigenvalue problem is obtained which is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibrations of two-layered conical shells, made up of several types of layer materials and supported differently at the ends are considered. Linear, sinusoidal and exponential variations in thickness of layers are assumed. Parametric studies are made on the variation of frequency parameter with respect to the relative layer thickness, cone angle, length ratio, type of thickness variation and thickness variation parameter. The effect of neglecting the coupling between bending and stretching is also analysed. 相似文献
17.
É. I. Grigolyuk Ya. I. Burak Ya. S. Podstrigach 《Journal of Applied Mechanics and Technical Physics》1968,9(4):389-396
One of the possible ways of stating and solving the selection problem for optimum temperature fields for localized axisymmetric heating of shells is investigated. The minimum of shell elastic energy is taken as the optimization criterion. An infinite cylindrical shell was considered in a similar formulation in [1], The corresponding variational problem is formulated for the functional of elastic energy with additional limitations imposed on the function of twist angle at specified shell sections. The variational problem is reduced to an isoperimetric by the use of singular functionals of the -function kind. The related Euler equation is obtained, and this together with the problem resolvent equation constitute a complete set of equations for determining the extremum temperature field with related stress-strain state of the shell. Cylindrical, conical, and spherical shells are considered separately. A numerical analysis is made for the simplest conditions of localized heating of cylindrical and conical shells.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 4, pp. 47–54, July–August, 1968. 相似文献
18.
The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem. 相似文献
19.
The elastoplastic state of thin cylindrical shells with two equal circular holes is analyzed with allowance made for finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distribution of stresses along the hole boundary and in the stress concentration zone (when holes are closely spaced) is analyzed by solving doubly nonlinear boundary-value problems. The results obtained are compared with the solutions that allow either for physical nonlinearity (plastic strains) or geometrical nonlinearity (finite deflections) and with the numerical solution of the linearly elastic problem. The stresses near the holes are analyzed for different distances between the holes and nonlinear factors.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 107–112, October 2004. 相似文献
20.
Results obtained on the basis of linearized functionals in the theory of nonlinearly elastic composite shells are analyzed and generalized. The Kirchhoff-Love and Timoshenko hypotheses are used. Possible membrane or shear locking is taken into account. New approaches are proposed to improve the convergence of numerical solution for new classes of nonlinear problems for thin and nonthin shells with a curvilinear (circular, elliptical) hole. The stress-strain state of shells is analyzed using different versions of shell theory. The influence of the nonlinear properties and orthotropy of composite materials on the stress distribution in structural members is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 45–84, November 2004.This revised version was published online in April 2005 with a corrected cover date. 相似文献