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1.
The paper gives exact solutions to the stability and vibration problems for nonclosed circular cylindrical shells hinged along
the longitudinal edges and reinforced with a regularly arranged discrete longitudinal ribs. These problems are also solved
approximately in the cases of regularly and quasiregularly arranged ribs
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 20–27, January 2008. 相似文献
2.
提出了一种分析交各向异性圆柱壳和阶梯圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Fluegge薄壳理论,通过定义广义位移变量和对应的广义力变量,建立了圆柱壳混合变量能量泛函;然后通过引入条形单元,定义混合状态变量和采用传递函数方法对超级壳单元求解,得到具有多种边界条件圆柱壳屈曲问题的半解析解;最后通过位移连续和力平衡条件,可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。 相似文献
3.
陈国栋 《应用数学和力学(英文版)》1988,9(4):401-416
According to the classical shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the
axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic
solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a2/R0h. In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are
given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions. 相似文献
4.
A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based
on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional
problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these
problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of
the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using
the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007. 相似文献
5.
Recep Faruk Yükseler 《International Journal of Non》2003,38(4):597-602
The parameters affecting the differences between the solutions to problems related with incompressible rubber—like shells of revolution, undergoing axisymmetric finite strains and rotations, corresponding to two different definitions of the reference surface of deformed rubber-like shells of revolution are obtained through an asymptotic analysis. 相似文献
6.
The exact solutions of the equations of motion derived under refined theories of shells and ribs based on the Timoshenko model
are used to plot dispersion curves for harmonic waves propagating along a cylindrical shell reinforced with discrete longitudinal
ribs
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 37–41, May 2006. 相似文献
7.
The class of stress problems for orthotropic shells of revolution loaded along narrow ring zones or by forces concentrated in the meridional direction is analyzed on the basis of a refined model. It is established that the solutions of these two problems for essentially anisotropic shells do not fully agree 相似文献
8.
H. Altenbach O. Morachkovsky K. Naumenko A. Sychov 《Archive of Applied Mechanics (Ingenieur Archiv)》1997,67(5):339-352
Summary A phenomenological constitutive model for characterization of creep and damage processes in metals is applied to the simulation
of mechanical behaviour of thin-walled shells and plates. Basic equations of the shell theory are formulated with geometrical
nonlinearities at finite time-dependent deflections of shells and plates in moderate bending. Numerical solutions of initial/boundary-value
problems have been obtained for rectangular thin plates (two-dimensional case) and axisymmetrically loaded shells of revolution
(one-dimensional case). Based on the numerical examples for the two problems, the influence of geometrical nonlinearities
on the creep deformation and damage evolution in shells and plates is discussed.
Accepted for publication 30 October 1996 相似文献
9.
Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells 总被引:1,自引:0,他引:1
IntroductionEquationsforcircularringshellsaredifficulttosolve.Theresearchofthisproblemstartedatthebeginningofthiscentury.Inthelate1970sandearly1980s,W.Z.Chien(1979,1980,1981)[1~3]rebuiltthecomplexequationsofaxis_symmetricallyloadedringshellspresented… 相似文献
10.
Shen Hui-chuan 《应用数学和力学(英文版)》1987,8(4):367-376
This work is the continuation of the discussion of Refs. [1-5]. In this paper:[A] The Love-Kirchhoff equations of vibration problem with small deflection for orthorhombic misotropic thin shells or orthorhombic anisotropic thin plates on Winkler’s base are classified as several of the same solutions of Schrodmger equation, and we can obtain the general solutions for the two above-mentioned problems by the method in Refs. [1] and [3-5].[B] The. von Karman-Vlasov equations of large deflection problem for shallow shells with orthorhombic anisotropy (their special cases are the von Harmon equations of large deflection problem for thin plates with orthorhombic anisotropy) are classified as the solutions of AKNS equation or Dirac equation, and we can obtain the exact solutions for the two abovementioned problems by the inverse scattering method in Refs. [4-5].The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or rib-reinforced plates and shells as special cases is included in this paper. 相似文献
11.
Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are
obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect
to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing
conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of
elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008. 相似文献
12.
《International Journal of Non》1987,22(1):73-77
In the present paper the mechanical interpretation of the Berger's hypothesis is considered. Using the geometrical method of Pogorelov and the asymptotic representation of the solutions of the non-linear partial differential equations, the values of the first and second invariants of the strain tensor are evaluated. This method confirms the hypothesis of Berger for the class of non-linear problems of shells under static loading. The result obtained is valid for isotropic and anisotropic shells. 相似文献
13.
Chen Guo-dong 《应用数学和力学(英文版)》1988,9(6):597-602
In this paper, the uniformly valid asymptotic solutions for the complex equation of the axial symmetrical problems of a/,r2>0 toroidal shells with constant thickness in bending theory are given. 相似文献
14.
A procedure is proposed for solving two-dimensional boundary-value problems on the stress-strain state of open and closed
noncircular cylindrical shells of variable thickness under surface loads. The solution is based on the use of the spline-collocation
method along the directrix and the method of discrete othogonalization along the generatrix. Examples of solutions for ellipsoidal
shells of variable thickness are given.
Translated from Prikladnaya Mekhanika, Vol. 34, No. 12, pp. 26–33, December, 1998. 相似文献
15.
A. B. Kiselev 《Moscow University Mechanics Bulletin》2012,67(5-6):116-121
One-dimensional nonstationary problems of adiabatic expansion for thick-wall spherical and cylindrical viscoplastic shells are solved exactly under the assumption that, at the initial instant of time, the distributions of radial velocities satisfy the condition of incompressibility of the shell material. The resulting solutions can easily be modified for the case of compression of such shells. 相似文献
16.
Chen Guo-dong 《应用数学和力学(英文版)》1987,8(9):861-873
In this paper the uniformly valid asymptotic solutions of axisymmetrical problems for the cylindrical shells with varying wall thickness are given. 相似文献
17.
Peng Xiaolin 《Acta Mechanica Sinica》1987,3(1):52-61
The boundary integral equations for elasto-plastic problems of shallow shells are established by using the fundamental solutions
of shallow shells derived previously. The strains and stress-resultants in the plastic region are used as unknown variables.
The simultaneous nonlinear equations of these variables and unknown boundary values are established and solved by direct iteration
method. 相似文献
18.
陈国栋 《应用数学和力学(英文版)》1986,7(10):1005-1016
In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given. 相似文献
19.
For thin shells of revolution the existence of torsional-vibration modes, uncoupled from bending and extensional modes, has been established[1]. Here a linear second-order differential equation for the uncoupled torsional stress mode is obtained and its solution for impact loading of shells is sought. The mode-superposition method which utilizes the natural modes of vibration predicted by elementary theory, is, in general, not satisfactory for sharp impact loading as many modes are often required for convergence. Hence we employ two novel techniques for solving the impact problems. Firstly a formal asymptotic procedure, based on extensions to geometrical optics, is employed to generate asymptotic wavefront expansions. Rigorous justifications for this formal technique are provided in an appendix. Secondly a transform technique whereby solutions are sought in terms of Bessel functions is discussed and applied to particular impact loading problems. The Bessel function solutions found here can be used to determine the natural frequencies of the shells. Shells both finite and infinite in extent are discussed and reflections at a stress-free end are examined. 相似文献
20.
《European Journal of Mechanics - A/Solids》2008,27(1):79-105
Three-dimensional (3D) solutions for the static analysis of doubly curved functionally graded (FG) magneto-electro-elastic shells are presented by an asymptotic approach. In the present formulation, the twenty-nine basic equations are firstly reduced to ten differential equations in terms of ten primary variables of elastic, electric and magnetic fields. After performing through the mathematical manipulation of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recurrent sets of two-dimensional (2D) governing equations for various order problems. These 2D governing equations are merely those derived in the classical shell theory (CST) based on the extended Love–Kirchhoffs' assumptions. Hence, the CST-type governing equations are derived as a first-order approximation to the 3D magneto-electro-elasticity. The leading-order solutions and higher-order corrections can be determined by treating the CST-type governing equations in a systematic and consistent way. The 3D solutions for the static analysis of doubly curved multilayered and FG magneto-electro-elastic shells are presented to demonstrate the performance of the present asymptotic formulation. The coupling magneto-electro-elastic effect on the structural behavior of the shells is studied. 相似文献