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1.
Based on the Timoshenko hypotheses, the equations of the nonlinear theory of plates are derived without restriction on the displacements. Then these equations are systematized in the case where the expressions for transverse-shear strains, curvatures, and torsion contain third-order terms. As an example, the equations are used to solve the problem on the initial postcritical behavior of plates. It is demonstrated that cylindrical bending is the case where the theory should necessarily be corrected as proposed 相似文献
2.
A method of solving problems of nonlinear deformation of anisotropic spherical shells with consideration of critical points
and postcritical behavior is outlined. The method employs the method of incremental loading in which the load increment is
specified with an unknown coefficient determined as an unknown function equivalent to the other ones. The algorithm is based
on the numerical discrete-orthogonalization method, which allows analyzing the deformation path for a number of shells with
different anisotropy parameters 相似文献
3.
A solution is obtained to describe the stability and initial postbuckling behavior of cylindrical shells made of composites
with one plane of symmetry. The solution is based on the Donnell-Mushtari-Vlasov nonlinear theory of anisotropic shells and
Koiter’s theory of buckling and postbuckling behavior. Calculated results are presented for boron plastic shells with reinforcement
of different types under external pressure. It is shown that the conventional model of a composite as an orthotropic material
is erroneous for many types of reinforcement
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 86–103, March 2007. 相似文献
4.
V. G. Bazhenov E. G. Gonik A. I. Kibets D. V. Shoshin 《Journal of Applied Mechanics and Technical Physics》2014,55(1):8-15
The problem of elastoplastic deformation, buckling, and postcritical behavior of spherical shells is solved using a finite element method and a cross-type explicit scheme of time integration. Stability problems for hemispherical shells under external pressure and compression between rigid plates are considered. The influence of holes and boundary conditions on shell deformation is investigated. It is shown that the calculation results are in good agreement with experimental data. 相似文献
5.
A general nonlinear theory for the dynamics of elastic anisotropic circular cylindrical shells undergoing small strains and moderate-rotation vibrations is presented. The theory fully accounts for extensionality and geometric nonlinearities by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvatures and strain-displacement expressions that contain the von Karman strains as a special case. Moreover, the linear part of the theory contains, as special cases, most of the classical linear theories when appropriate stress resultants and couples are defined. Parabolic distributions of the transverse shear strains are accounted for by using a third-order theory and hence shear correction factors are not required. Five third-order nonlinear partial differential equations describing the extension, bending, and shear vibrations of shells are obtained using the principle of virtual work and an asymptotic analysis. These equations show that laminated shells display linear elastic and nonlinear geometric couplings among all motions. 相似文献
6.
NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅰ)──GENERAL THEORY 总被引:1,自引:1,他引:0
In this paper, a nonlinear theory is given for multilayer sandwich shells undergoing small strains and moderate rotations.
Then a simplified theory for the shells undergoing moderate or moderate/small rotations are obtained. 相似文献
7.
A. A. Artem’eva V. G. Bazhenov D. V. Zhegalov D. A. Kazakov E. V. Nagornykh 《Journal of Applied Mechanics and Technical Physics》2015,56(6):951-958
A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported. 相似文献
8.
G. D. Gavrilenko 《International Applied Mechanics》2002,38(12):1496-1500
We propose a nonlinear approach to the stability analysis of imperfect cylindrical shells under axial compression. The approach takes into account the initial deflections (imperfections) of the shell shape from cylindrical. A series of typical initial deflections is analyzed: local and longitudinal bulges (dents) and unilateral annular corrugations. A nonlinear stability problem is solved. The results are represented as plots of the nondimensional stress versus the nondimensional amplitude of initial deflections. It is shown that the capabilities of the nonlinear theory for estimating the critical stresses for thin shells have not been exhausted yet and that it could be used in future to explain some phenomena experimentally observed in shells 相似文献
9.
In this article the initial postbuckling behavior of ring stiffened cylindrical shells under hydrostatic pressure is analyzed
by Koiter's theory. The nonlinear bending equations consistent with boundary conditions have been used in prebuckling state.
The eigenvalue problem is solved by Galerkin's method. The obtained buckling loads are compared with the results which are
based on classical stability theory. As calculating examples, three typical outside-stiffened cylinders with different ring
stiffener parameters are chosen. The results show that the strength of stiffener not only influences buckling load obviously,
but also changes the imperfection-sensitivity of cylindrical shells. 相似文献
10.
A solution is obtained that describes the postbuckling behavior of cylindrical shells in the case of axisymmetric buckling.
The basis for this solution is Koiter’s asymptotic method and the nonlinear equations of the third-order Timoshenko theory
of shells. It is shown that the bifurcation point in this case is a symmetrically unstable one. The effect of the initial
axisymmetric deflections on the buckling loads is weaker when buckling is axisymmetric. The results obtained by Koiter’s special
theory evidence this
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 108–118, April 2006. 相似文献
11.
Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments 总被引:1,自引:0,他引:1
沈惠申 《应用数学和力学(英文版)》2001,22(3):270-281
IntroductionInrecentyears,fiber_reinforcedcompositelaminatedshellstructuresarewidelyusedintheaerospace ,marineindustry ,automobileindustryandotherengineeringapplications.Duringtheoperationallife ,thevarianceoftemperatureandmoisturereducestheelasticmoduli… 相似文献
12.
Bolotin V. V. Grishko A. A. Kounadis A. N. Gantes Ch. Roberts J. B. 《Nonlinear dynamics》1998,15(1):63-81
The behavior of a nonlinear, non-Hamiltonian system in the postcritical (flutter) domain is studied with special attention to the influence of initial conditions on the properties of attractors situated at a certain point of the control parameter space. As a prototype system, an elastic panel is considered that is subjected to a combination of supersonic gas flow and quasistatic loading in the middle surface. A two natural modes approximation, resulting in a four-dimensional phase space and several control parameters is considered in detail. For two fixed points in the control parameter space, several plane sections of the four-dimensional space of initial conditions are presented and the asymptotic behavior of the final stationary responses are identified. Amongst the latter there are stable periodic orbits, both symmetric and asymmetric with respect to the origin, as well as chaotic attractors. The mosaic structure of the attraction basins is observed. In particular, it is shown that even for neighboring initial conditions can result in distinctly different nonstationary responses asymptotically approach quite different types of attractors. A number of closely neighboring periodic attractors are observed, separated by Hopf bifurcations. Periodic attractors also are observed under special initial conditions in the domains where chaotic behavior is usually expected. 相似文献
13.
双曲率壳是飞机、汽车以及船舶上常见的薄壁结构,其中性面可看作是一条动曲线沿着另一条曲线扫掠所形成的曲面.双曲率壳的非线性理论不断更新推动着双曲率壳力学行为的研究.随着工程实际应用的不断改进,如功能梯度材料(FGM),加筋壳,弹性地基模型等的引入,双曲率壳在强度、变形和稳定性等方面的研究得到了进一步促进.本文首先回顾了双曲率壳结构非线性力学基本理论发展过程,主要阐述了经典的二维板壳理论,如Donnell 薄壳理论,一阶剪切变形壳理论,高阶剪切变形壳理论,和三维板壳理论的理论体系及基本公式,并对几种理论之间的联系和应用进行了总结和讨论,简述了近几十年来国内外学者在双曲率壳非线性弯曲、稳定性和振动等方面的最新研究成果,最后对双曲率壳体研究目前的局限性和未来的研究方向进行了探讨. 相似文献
14.
In this paper, based on the nonlinear thin shell theory, a geometrically nonlinear formulation using the total Lagrangian approach for rotational shells, as well as rotational shells on the Winkler-type elastic foundation, is presented. The displacements of the middle surface are approached by a B-spline function. All nonlinear terms of membrane strains are reserved. Two cases in which the arc length as well as ordinate is used as the coordinate parameter along meridional direction are discussed at the same time.The project supported by National natural Science Foundation of China. 相似文献
15.
Abstract. A nonlinear two degree-of-freedom model, describing a flexible elastic suspended cable undergoing galloping oscillations, is analyzed. By using a perturbative approach, the critical conditions occuring for different values of the aerodynamic coefficients are described. Two different type of critical conditions, corresponding to simple or double Hopf bifurcations are found. The nonlinear postcritical behavior of single taut strings in 1:1 primary internal resonance is studied through the multiple scale perturbation method. In the double Hopf bifurcation case the influence of the detuning between the critical eigenvalues on the postcritical behavior is illustrated. It is found that quasi-periodic motions, which are likely to occur in the linear field when the two critical frequencies are incommensurable, are really unstable in the nonlinear range. Therefore, the postcritical behavior of the string consists of stable periodic motions for any detuning values.Sommario. Viene analizzato un modello non lineare a due gradi di libertrappresentativo di un cavo elastico flessibile sospeso alle estremite soggetto ad oscillazioni galoppanti. Utilizzando un approccio perturbativo, vengono descritte le condizioni critiche per differenti valori dei coefficienti aerodinamici. Sono presenti due diversi tipi di condizioni critiche, corrispondenti a biforcazioni di Hopf semplici e doppie. Attraverso il metodo perturbativo delle scale multiple viene studiato il comportamento post-critico non lineare di singole stringhe tese in risonanza interna primaria 1:1. Nel caso di biforcazione doppia di Hopf viene illustrata l'influenza del detuning tra gli autovalori critici sul comportamento post-critico. Si trova che i moti quasi-periodici, presenti in campo lineare quando le due frequenze critiche sono incommensurabili, sono in realtinstabili in campo non lineare. Quindi, il comportamento post-critico della stringa risulta composto da moti periodici stabili per un qualsiasi valore del detuning. 相似文献
16.
The paper studies the dynamics of nonlinear elastic cylindrical shells using the theory of shallow shells. The aerodynamic
pressure on the shell in a supersonic flow is found using piston theory. The effect of the flow and initial deflections on
the vibrations of the shell is analyzed in the flutter range. The normal modes of both perfect shells in a flow and shells
with initial imperfections are studied. In the latter case, the trajectories of normal modes in the configuration space are
nearly rectilinear, only one mode determined by the initial imperfections being stable
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 63–73, September 2007. 相似文献
17.
A technique to determine the axisymmetric elastoplastic state of thin shells with allowance for the third invariant of the
stress deviator is developed. The technique is based on the theory of thin shells that takes into account transverse shear
and torsional strains. Plastic equations that relate the components of the stress tensor in Eulerian coordinates with the
linear components of the finite-strain tensor are used as constitutive equations. The nonlinear scalar functions in the constitutive
equations are found from base tests on tubular specimens under proportional loading for different stress modes. The boundary-value
problem is solved by numerically integrating a system of ordinary differential equations 相似文献
18.
《International Journal of Solids and Structures》1999,36(4):597-617
The effect of local geometric imperfections on the buckling and postbuckling of composite laminated cylindrical shells subjected to combined axial compression and uniform temperature loading was investigated. The two cases of compressive postbuckling of initially heated shells and of thermal postbuckling of initially compressed shells are considered. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometric imperfection of the shell. The analysis uses a singular perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of cross-ply laminated cylindrical shells with or without initial local imperfections, from which results for isotropic cylindrical shells follow as a limiting case. Typical results are presented in dimensionless graphical form for different parameters and loading conditions. 相似文献
19.
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
20.
A technique is proposed to solve elastoplastic deformation problems for branched shells of revolution under the action of asymmetric forces and a temperature field. The kinematic equations are derived within the framework of the linear Kirchhoff–Love theory of shells and the thermoelastic relations within the framework of the theory of small elastoplastic strains. The problem is given a variational formulation based on the virtual-displacement principle and the Fourier-series expansion of the unknown functions and loads with respect to the circumferential coordinate. The additional-load method is used to solve a nonlinear problem and the finite-elements method is used to carry out a numerical analysis. As an example, an asymmetric stress–strain analysis is performed for a cylindrical shell reinforced by a ring plate. 相似文献