Some Approaches to the Solution of Problems on Thin Shells with Variable Geometrical and Mechanical Parameters

A number of approaches to the solution of stress problems for anisotropic inhomogeneous shells in the classical formulation are discussed. A review is made of approaches to the solution of one- and two-dimensional static problems for thin shells with variable parameters and to the solution of stress–strain problems for anisotropic shells of revolution under axisymmetric and non-axisymmetric loading, shallow convexo-convex shells, noncircular cylindrical shells, plates of various shapes, and shells of complex geometry     

On a class of method for solving problems with random boundary notches and/or cracks

As we know, problems with boundary imperfections (notches or cracks) are the more important one in practical fracture analysis. Frequently, these imperfections would appear in the boundaries of the bodies as a randomly distributed group, and under the loading circumstances would grow up to be unstable cracks which induces catastrophic fracture of the bodies. For right evaluation the fracture behavior of the bodies with such boundary imperfections, it demands mathematical solutions for problems with random boundary notches and/or cracks.     

The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied     

Investigation of high elastoplastic straining of shells of revolution under complex tensile and torque loading

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.     

Elastoplastic state of nonshallow flexible ellipsoidal shells under concentric loading

The elastoplastic stress-strain state of flexible ellipsoidal shells under concentric loading is investigated by the solution of nonlinear boundary-value problems. Numerical results are presented for open shells in the case of a free (unsupported) edge and a shell with a central opening (the periphery of the opening is supported by a thin ring). Solutions of the problems in linear and nonlinear statements are analyzed. Numerical results for ellipsoidal and spherical shells are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 54–60, April, 1999.     

Physically and Geometrically Nonlinear Static Problems for Thin-Walled Multiply Connected Shells

Physically and geometrically nonlinear two-dimensional problems are formulated for multiply connected thin shells (weakened by several curvilinear holes). A technique and algorithm are proposed for their solution with allowance for elastoplastic strains and finite deflections of shells under static loading. Numerical results for a shell with two circular holes are presented and the stress concentration is analyzed     

Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes

Results on stress concentration in thin shells with curvilinear holes subject to plastic deformation and finite deflections are reviewed. The holes (circular, elliptical) are reinforced with thin-walled elements (rings, rods) of different stiffness. A numerical method of solving doubly nonlinear problems of statics for shells of complex geometry is outlined. The stress distribution near curvilinear holes in spherical, cylindrical, and conical shells under statical loading is studied. The numerical results are analyzed     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

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爆炸加载下金属壳体膨胀断裂过程中的关键物理问题

爆炸加载下金属壳体膨胀断裂过程是武器研制领域关注的重要课题,该过程包含着丰富的力学与材料学基础科学问题,吸引着众多学者的长期关注。本文中通过分析爆炸加载下金属壳体膨胀断裂过程,明确了其中蕴含的3个关键物理问题:材料动态拉伸本构、壳体膨胀断裂机理和破片尺寸控制机理,综合分析了这3个关键物理问题的研究现状与趋势。     

Mechanical interpretation of the Berger's hypothesis for the global stability of statically loaded shells

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.     

Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells

The results from studies into the vibrations and dynamic stability of thin elastic shells with initial geometric imperfections are analyzed. The corresponding dynamic problems are solved in both linear and nonlinear formulations. The influence of initial axisymmetric and nonaxisymmetric deflections on natural, forced, parametrically excited, and self-excited vibrations (flutter) is studied. The dynamic buckling of imperfect shells under short-term impulsive loading is examined. Some aspects of experimental investigation into the vibrations of shells with small geometric imperfections (deviations from the design shape) are considered     

Nonlinear deformation and buckling of elastic inhomogeneous shells under thermomechanical loads

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads     

Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.     

Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

The paper outlines an approach to identifying the principal dynamic-instability domain for systems composed of shells of revolution with different shapes under axisymmetric periodic loading. The original problem is reduced to one-dimensional eigenvalue problems with respect to the meridional coordinate. Results of calculations for a specific shell system are presented     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

结构流—固冲击屈曲研究进展

本文回顾和综述结构在流－固冲击载荷作用下的动力屈曲问题的研究工作，重点分析、评述流－固冲击屈曲的特征、实验资料及已取得的成果，并展望了该领域今后的研究     

层状纤维圆柱壳轴向压缩破损实验研究

通过对端部引发缺陷层状纤维复合材料圆柱壳在轴向准静态和冲击压缩下的实验研究,分析其渐进压缩破损模式和破坏模式的形成机理．研究此类结构的缓冲性能．实验研究表明随着纤维铺设角度的改变其破损模式的主导形式与分层扩展强度、环向断裂强度和纤维与基体脱胶裂纹相关．它们的断裂韧度的高低决定结构的能量吸收能力     

Nonstationary oscillations of three-layer cylindrical shells under axisymmetric loading

The nonstationary behavior of three-layer cylindrical shells under an axisymmetric loading is considered with the application of hypotheses to each layer. Independent postulations are proposed for the approximation of displacements and transverse strains across the thickness of each layer. Reissner's variational principle for dynamic processes is used to derive the motion equations. The problem of the dynamic deformation of three-layer cylindrical shells under a nonstationary loading is considered in the case where the ends of the shells are rigidly fixed. The values obtained were compared with those predicted from hypotheses relating to the whole packet of the structure (the Timoshenko-type theory of multilayered shells). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 3–9, August, 1999.     

Electromechanical Vibrations and Dissipative Heating of Viscoelastic Thin-Walled Piezoelements

The results of studying the electromechanical response of thin-walled viscoelastic piezoactive elements under harmonic loading are generalized. The nonlinear electrothermoviscoelastic problem for a harmonically deformed body is formulated in a simplified form with regard for the facts that the mechanical, thermal, and electric fields are coupled, the material is physically nonlinear, and its properties depend on temperature. Classical and refined electromechanical models of single-layer and multilayer shells and plates under general and harmonic loading are reviewed. The models consider that the electromechanical characteristics of the material depend on temperature and physical and geometrical nonlinearities. Methods for solving nonlinear coupled electrothermoviscoelastic problems are discussed. Analytical and numerical solutions are given to specific quasistatic and dynamic electrothermoviscoelastic problems for thin-walled elements such as rods, plates, and shells of various shapes under harmonic electric loading. The effect of dissipation, the temperature dependence of the material properties, and physical and geometrical nonlinearities on the harmonic and parametric vibrations and stability of piezoelectric elements is studied     

Torsional,flexural, and torsional-flexural buckling modes of a cylindrical shell under combined loading

Stability problems for cylindrical shells under various loading modes were considered in numerous papers. A detailed analysis of such problems can be found, e.g., in the monograph [1]. We refer to the solutions presented in this monograph as classical.For long cylindrical shells in axial compression, one of the buckling modes is the purely beam flexural mode similar to the classical buckling mode of a straight rod. It is well known that it can be studied by using the nonlinear or linearized equations of the membrane theory of shells. In [2], it was shown that, on the basis of such equations constructed starting from the noncontradictory version of geometrically nonlinear elasticity relations in the quadratic approximation [3], under the separate action of the axial compression, external pressure, and torsion, there are also previously unknown nonclassical buckling modes, most of which are shear ones.In the present paper, we show that the use of the above equations for cylindrical shells under compression and external pressure with simultaneous pure torsion or bending permits revealing the earlier unknown torsional, beam flexural, and beam torsional-flexural buckling modes, which are nonclassical, just as those found in [2]. The second of these buckling modes is realized when axially compressing forces are formed in the shell with simultaneous torsion, and the third of them is realized under compression combined with pure bending.It was found that, earlier than the classical buckling modes, the torsional buckling modes can be realized for relatively short shells with small shear rigidity in the tangent plane, while the second and third buckling modes can be realized for relatively long shells.