Analysis of the Influence of a Geometrical Parameter on the Deformation of a Rigidly Fixed, Flexible, Noncircular Cylindrical Shell

The exact analytical solution of the deformation problem for a flexible long noncircular cylindrical shell is used to analyze how a geometrical parameter characterizing the wall thickness and curvature of the shell affects its behavior when its longitudinal edges are rigidly clamped. Plots of the deflection–load relationship are presented for various values of the geometric parameter     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

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Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators

A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Kármán–Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.     

STRESS ANALYSIS OF THICK RING SHELL SUBMITTED TO THE ACTION OF INTERNAL PRESSURE

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Bifurcation analysis of fan casing under rotating air flow excitation

A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s principle, the dynamic equations axe established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.     

四边简支功能梯度圆锥壳的非线性振动分析

研究了四边简支条件下功能梯度圆锥壳的非线性自由振动。首先,通过Voigt模型和幂律分布模型描述了功能梯度材料的物理属性。然后,考虑von-Karman几何非线性建立了功能梯度圆锥壳的能量表达式,利用Hamilton原理推出圆锥壳的运动方程。在此基础上,采用Galerkin法,只考虑横向振动,功能梯度圆锥壳运动方程可简化为单自由度非线性振动微分方程。最后,通过改进的L-P法和Runge-Kutta法求解非线性振动方程,讨论功能梯度圆锥壳的非线性振动响应,分析几何参数和陶瓷体积分数指数对圆锥壳非线性频率响应的影响。结果表明,几何参数对非线性频率和响应的影响相较于陶瓷体积分数指数更明显;圆锥壳的几何参数和陶瓷体积分数指数通过改变非线性频率影响振动响应;功能梯度圆锥壳呈弹簧渐硬非线性振动特性。     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

Calculation of a composite cylindrical shell of piecewise constant thickness with consideration of transverse shears

The optimal geometric and physical parameters of a stepped cylindrical shell are determined. These parameters are optimal in the sense that they ensure the maximum carrying capacity of the shell for its given overall size and weight. The shell is made of a composite material. The refined theory of anisotropic shells is used with consideration of transverse shear effects on the stress-strain state.     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

A perturbation method for nonlinear vibrations of imperfect structures: Application to cylindrical shell vibrations

A perturbation method is used to analyse the nonlinear vibration behaviour of imperfect general structures under static preloading. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The effects on the linearized and nonlinear vibrations caused by geometric imperfections, a static fundamental state, and a nontrivial static state are included in the perturbation procedure.The theory is applied in the nonlinear vibration analysis of anisotropic cylindrical shells. In the analysis the specified boundary conditions at the shell edges can be satisfied accurately. The characteristics of the analysis capability are shown through examples of the vibration behaviour of specific shells. Results for single mode and coupled mode nonlinear vibrations of shells are presented. Parametric studies have been performed for a composite shell.     

Effect of multiple localized geometric imperfections on stability of thin axisymmetric cylindrical shells under axial compression

Stability of imperfect elastic cylindrical shells which are subjected to uniform axial compression is analyzed by using the finite element method. Multiple interacting localized axisymmetric initial geometric imperfections, having either triangular or wavelet shapes, were considered. The effect of a single localized geometric imperfection was analyzed in order to assess the most adverse configuration in terms of shell aspect ratios. Then two or three geometric imperfections of a given shape and which were uniformly distributed along the shell length were introduced to quantify their global effect on the shell buckling strength. It was shown that with two or three interacting geometric imperfections further reduction of the buckling load is obtained. In the ranges of parameters that were investigated, the imperfection wavelength was found to be the major factor influencing shell stability; it is followed by the imperfection amplitude, then by the interval distance separating the localized imperfections. In a wide range of parameters this last factor was recognized to have almost no effect on buckling stresses.     

Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory

The present paper is focused on the experimental and theoretical analysis of circular cylindrical shells under base excitation. The shell axis is vertical, it is clamped at the base and connected to a rigid body on the top; the base provides a vertical seismic-like excitation. The goal is to investigate the shell response when a resonant harmonic forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude of excitation. A violent resonant phenomenon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and provide an explanation of the complex dynamics observed experimentally; the model takes into account geometric shell nonlinearities, electrodynamic shaker equations and the shell shaker interaction.     

基于激光测距仪的薄壳结构初始缺陷测量系统

薄壳结构的屈曲通常对初始缺陷十分敏感,因此对几何初始缺陷的精确测量是高质量的壳体屈曲试验的必要环节。本研究旨在开发一套基于激光测距仪的初始缺陷测量系统,以实现对壳体结构的快速、精确、非接触的测量。本文详细介绍该系统的设计思想及实现方法,包括激光测距仪的选择、转动与直线运动的实现、数据采集与计算机自动控制技术等。利用该系统对两个柱支承钢筒仓模型进行了仔细的初始缺陷三维测量,验证了系统的适用性和可靠性。文中还提出了利用二重傅立叶分解技术分析实测缺陷的方法。本文成果与方法为薄壳结构屈曲试验奠定了基础。     

初始几何缺陷对网壳截面优化结果影响研究

单层网壳结构是缺陷敏感结构,初始几何缺陷不同对"网壳截面优化结果"有显著影响,该文研究了网壳杆件截面取值与缺陷分布、结构极限承载力之间的关系.结果表明:经截面优化设计的网壳结构最不利应力最早并且一直出现在初始几何缺陷较大处;优化寻优结果与初始几何缺陷分布有直接关系,增大缺陷较大处杆件截面能显著提高结构承载力;由于缺陷随机分布,经截面优化设计的网壳结构须校核其在不同缺陷下的稳定承载力以确保结构安全.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

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变厚度载流旋转壳体的热磁弹性分析

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题，基于薄壳的几何方程、物理方程、运动方程、电动力学方程，建立其热磁弹性基本方程．应用线性化方法，得到了关于热磁弹性问题的线性迭代方程，转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体，给出Lorentz力表达式，导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律，并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

有限厚度、大压入的球压试验材料力学响应

针对磁场环境中受机械载荷作用变厚度载流旋转壳体热磁弹性问题,基于薄壳的几何方程、物理方程、运动方程、电动力学方程,建立其热磁弹性基本方程．应用线性化方法,得到了关于热磁弹性问题的线性迭代方程,转化为包括8个基本未知量的标准型方程组．关于载流旋转壳体,给出Lorentz力表达式,导出了温度场及温度场积分特征值．分析了变厚度锥形旋转壳体应力、温度及变形随外加电磁参量的变化规律,并通过数值模拟对理论分析进行了验证．研究结果可为载流旋转壳体热磁弹性问题研究提供理论参考．     

考虑形位公差的薄壁筒壳折减因子预测方法研究

缺陷敏感性是薄壁筒壳结构设计所面临的主要问题之一,通常利用折减因子来量化筒壳结构的缺陷敏感性程度。然而现有缺陷敏感性分析方法大多以预测筒壳折减因子下限为目的,未考虑不同形位公差水平对筒壳折减因子的影响。针对此问题,本文提出了一种考虑形位公差的薄壁筒壳折减因子预测方法。该方法基于多点最不利扰动载荷法进行最不利缺陷搜索,获得筒壳不同形位公差下的折减因子下限值,从而确定考虑形位公差的薄壁筒壳折减因子参考值,并利用不完全折减刚度法对计算过程进行加速。算例结果表明本文提出的筒壳折减因子预测方法可在保证安全可靠的前提下,有效提高折减因子预测精度,消除筒壳结构设计过程中不必要的安全裕度,对结构减重有积极意义。未来可基于本方法展开我国新一代航天结构薄壁筒壳折减因子设计规范的研究工作,进一步提高我国航天筒壳结构设计的精细化和轻量化水平。     

The asymptotic solving equations of thick ring shell and its solution under moment Mo

In this paper, from the fundamental equations of three dimensional elastic mechanics, we have found a sequence of asymptotic solving equations of thick ring shell (or body) applied arbitrary loads by the perturbation method based upon a geometric small parameter a=r_o/R_o, which may be divided into two independent equation groups which are similar to the equation groups for plane strain and torsional problems. Using these equations, we have also found first order and second order approximate solutions of thick ring shell applied moment M_o.