Nonlinear strain components of general shells with initial geometric imperfections

On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation is not confined to a special shell, therefore they possess general properties. These formulations provide the theoretical basis of the strain analysis for geometric nonlinear problems of shells with initial geometric imperfections     

薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法

针对薄壁圆筒壳结构轴压屈曲载荷的缺陷敏感性以及真实几何缺陷的不确定性,提出一种基于实测缺陷数据和极大熵原理的初始缺陷建模与屈曲载荷预测方法。首先,将初始几何缺陷视为二维随机场,并利用实测缺陷数据和Karhunen-Loève展开法将初始缺陷的随机场建模转化为随机向量的建模;其次,利用极大熵方法确定随机向量的概率分布;最后,基于所构建的初始缺陷随机模型,利用MCMC抽样方法和确定性屈曲分析方法,进行随机屈曲分析并给出基于可靠度的屈曲载荷折减因子。数值算例表明,与直接假设随机场相关结构的方法相比,本文方法的结果是对薄壁圆筒壳屈曲载荷的一个更无偏估计。     

Buckling analysis of cylindrical shells with random geometric imperfections

In this paper the effect of random geometric imperfections on the limit loads of isotropic, thin-walled, cylindrical shells under deterministic axial compression is presented. Therefore, a concept for the numerical prediction of the large scatter in the limit load observed in experiments using direct Monte Carlo simulation technique in context with the Finite Element method is introduced. Geometric imperfections are modeled as a two dimensional, Gaussian stochastic process with prescribed second moment characteristics based on a data bank of measured imperfections. (The initial imperfection data bank at the Delft University of Technology, Part 1. Technical Report LR-290, Department of Aerospace Engineering, Delft University of Technology). In order to generate realizations of geometric imperfections, the estimated covariance kernel is decomposed into an orthogonal series in terms of eigenfunctions with corresponding uncorrelated Gaussian random variables, known as the Karhunen-Loéve expansion. For the determination of the limit load a geometrically non-linear static analysis is carried out using the general purpose code STAGS (STructural Analysis of General Shells, user manual, LMSC P032594, version 3.0, Lockheed Martin Missiles and Space Co., Inc., Palo Alto, CA, USA). As a result of the direct Monte Carlo simulation, second moment characteristics of the limit load are presented. The numerically predicted statistics of the limit load coincide reasonably well with the actual observations, particularly in view of the limited data available, which is reflected in the statistical estimators.     

Natural vibrations of a cylindrical shell reinforced with rectangular plates

This paper outlines a technique of determining the natural frequencies and modes of an elastic structure consisting of a cylindrical shell and noncrossing rectangular plates inserted into it. The influence of the position, number, and thickness of the plates on the natural frequencies and modes is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 89–96, March 2006.     

轴压随机几何缺陷圆柱壳可靠性分析

轴压随机几何缺陷圆柱壳屈曲的失效函数具有较强的非线性，对于该结构已应用的可靠性分析方法不能同时满足计算精度和计算效率的要求。本文发展一个修正的ＭｏｎｔｅＣａｒｌｏ法，由两个步骤执行：应用一阶可靠性方法计算Ｈａｓｏｆｅｒ－Ｌｉｎｄ可靠性指标β；将简单ＭｏｎｔｅＣａｒｌｏ法的采样区域限制在基本随机变量构成的ｎ维β－球外部，采样点由一个χ２分布的随机半径Ｒ≥β和（－１，１）均匀分布的随机方向组成，该修正的ＭｏｎｔｅＣａｒｌｏ法用于轴压随机几何缺陷圆柱壳屈曲强度可靠性分析表明，在相同精度的情况下修正的ＭｏｎｔｅＣａｒｌｏ法的样本容量比简单ＭｏｎｔｅＣａｒｌｏ法要低３个数量级，一阶可靠性方法的计算误差随着与分支屈曲模态一致的初始几何缺陷项数的增加越来越显著     

考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法

利用随机场对圆柱薄壳结构的初始几何缺陷进行建模,并据此建立了一种用于含初始几何缺陷轴压圆柱薄壳屈曲分析的随机分析方法。首先,指出已有将圆柱薄壳初始几何缺陷表征为二维高斯随机场的方法会导致与实际不相符的初始几何缺陷,如圆柱周长显著增大或缩小的几何缺陷。其次,提出一种考虑周长不变约束的随机场建模方法,以剔除与实际不相符的随机几何缺陷。最后,基于所建立的初始几何缺陷随机场模型,利用非干涉多项式混沌展开法进行圆柱薄壳的随机屈曲分析,给出临界屈曲载荷的概率分布。数值试验结果表明,基于随机场理论的初始几何缺陷建模方法可有效刻画几何缺陷对结构承载能力的影响,而提出的约束随机场建模方法又能有效减小结果的分散性。     

Nonlinear vibrations of cantilevered circular cylindrical shells in contact with quiescent fluid

Large-amplitude vibrations of liquid-filled cantilevered (clamped–free) circular cylindrical tanks are studied theoretically for the first time. The influence of liquid height and initial geometric imperfections is investigated in detail. The tank motions are described by a nonlinear model based on Flügge׳s shell theory, and the liquid motions are modelled by means of linearized potential flow theory. Equations of motion are obtained using the extended Hamilton׳s principle and are discretized by expanding the solution with trigonometric functions in the circumferential direction and the cantilevered beam eigenfunctions in the axial direction. The geometric boundary conditions are satisfied exactly, while the natural ones are satisfied in an energy minimization sense. The system is integrated numerically by employing the appropriate modal composition of the solution to guarantee convergence. Results are presented in the form of frequency–response curves in the neighbourhood of the lowest natural frequency. It is found that the response may be of softening or hardening type, depending on the liquid height and the imperfection parameters.     

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.     

Studying the forced vibrations of fluid-filled cylindrical shells with regard to the nonlinear interaction of different flexural modes

The paper is concerned with the forced nonlinear multimode vibrations of thin cylindrical shells fully filled with a perfect incompressible fluid. The frequency response characteristics of shells undergoing steady-state vibration as simple (standing wave) and compound (traveling wave) deformation modes are plotted and examined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 97–106, August 2006.     

Experimental analysis of the natural vibrations and stability of cylindrical shells reinforced with rectangular plates

The paper presents experimental results on the effect of reinforcing cylindrical shells with rectangular plates on the axial compressive critical loads and the natural frequencies and modes of two sets of shells __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 100–103, May 2008.     

Nonlinear forced vibrations of a cylindrical shell with two internal resonances

Forced vibrations of cylindrical shells described by a system of three ordinary differential equations are studied. There are two internal resonances. Standing and traveling waves in the shells are described by a system of six modulation equations derived using the multiple-scales method. These waves are analyzed for stability __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 51–58, February 2006.     

On effect of initial imperfections on parametric vibrations of cylindrical shells with geometrical non-linearity

The effect of initial imperfections on the parametric vibrations of cylindrical shells is analyzed. The shell has moderate amplitudes of vibrations; therefore, geometrically nonlinear theory is used. The shell vibrations are described by the Donnel equations. The interaction of three pairs of conjugate modes is considered in the analysis. Therefore, the shell vibrations are described by six-degrees-of-freedoms nonlinear dynamical system. The multiple scales method and the continuation technique are used to analyze the system dynamics. The role of initial imperfections in nonlinear dynamics of shell is discussed using frequency responses.     

Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

The paper proposes a method to calculate the natural frequencies of ribbed cylindrical shells with local axisymmetric deflections. The influence of initial imperfections of two types on the minimum frequencies of vibration is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 63–72, September 2008.     

Superior aeroelastic behaviors of axially functional graded cylindrical shells in supersonic airflow

It is well known that mode localization occurs in the panel flutter structural systems. Therefore, it is reasonable to expect the aeroelastic stability of the structure to be enhanced by changing the geometrical sizes and material properties of the structure along the airflow direction. In this investigation, an axially functionally graded (AFG) cylindrical shell is designed and its super aeroelastic behaviors in supersonic airflow are studied. The enhanced aeroelastic stability and the excellent capability in the passive flutter suppression are achieved by the present AFG design. For the thickness of the cylindrical shell, three types of functions are analyzed. Numerical results show that all these three functions can increase the flutter bound of the cylindrical shell to some extent. It is also noted that in some situations, local mode coalescence happens. In this study, an effective method is proposed to eliminate the local mode coalescence by adding the lumped mass. For the material properties, two groups of functions are considered. It is found that under suitable parameters of the functions, even if the effective stiffness of the whole structural system decreases, the flutter bound of the structure can still be increased due to the AFG design. In addition, the flutter stability of the AFG cylindrical shell is much better than that of the traditional transversely functionally graded shell. The present study is significant in the aeroelastic design of aerospace vehicles.     

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to bt, cubic polynomials and to satLyfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical.shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.     

Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

The paper addresses the dynamic interaction of an orthotropic cylindrical shell with the fluid flowing inside. Its velocity has a constant component and low-amplitude pulsations. A method to calculate the characteristics of the parametric vibrations of the shell when the velocity of the fluid is close to critical is proposed. The amplitude–frequency characteristics of the shell–fluid system at fundamental parametric resonance are determined     

Stability of cylindrical shells made of a damageable physically nonlinear material

The bifurcation-instability problem for cylindrical shells made of physically nonlinear materials progressively damaged with increasing load is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 56–66, October 2006.     

Forced nonlinear oscillations of cylindrical shells interacting with fluid flow

The dynamic interaction of thin cylindrical shells with the fluid flow inside them under external periodic loads is studied. A technique is proposed to calculate the parameters of forced nonlinear oscillations of shells with a fluid moving with nearly critical velocities. The amplitude-frequency characteristics of the fluid-shell system under steady-state oscillation are plotted __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 91–99, April 2006.