复合材料层合板壳非线性力学的研究进展

复合材料层合板壳是由多种组分材料组合而成.与单一材料的板壳结构相比,它无明确的材料主方向,各层间材料间断和不连续,具有明显的几何非线性和材料非线性等新的特点.其失效模式也远比单一材料的情况复杂,具有如基体开裂、脱胶、分层、分层裂纹偏转、多分层以及分层传播等多种模式.各国学者基于不同的考虑,提出了多种方法研究复合材料层合板壳的失效.首先,在简要介绍了层合板壳线性力学基本理论的基础上,重点回顾了层合板壳结构非线性力学几种基本理论发展的过程,主要阐述了经典大挠度非线性理论、一阶剪切变形理论、高阶剪切变形理论、锯齿理论、广义分层理论的理论体系及基本公式,并对几种理论之间的联系和差异进行了总结;其次,介绍了当前层合结构非线性领域的研究进展,综述了典型复合材料板壳结构的失效机理及优化设计、复合材料板壳结构在复杂环境下的破坏机理、复合材料板壳结构的物理非线性、含脱层纤维增强复合材料板壳结构的破坏机理等各研究热点的最新研究成果;最后,对该领域未来的研究方向进行了展望.     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

Stability and initial postbuckling behavior of anisotropic cylindrical shells under external pressure

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 __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 86–103, March 2007.     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

爆炸冲击下复合材料层合扁球壳的动力屈曲

研究计及横向剪切的复合材料层合扁球壳在爆炸冲击载荷作用下的非线性轴对称动力屈曲问题。通过在复合材料层合扁球壳非线性稳定性的基本方程中增加横向转动惯量项并引入R.H.Cole理论的爆炸冲击力,得到爆炸冲击下复合材料层合扁球壳的动力控制方程,应用Galerkin方法得到用顶点挠度表达的爆炸冲击动力响应方程,并采用Runge-Kutta方法进行数值求解,采用Budiansky-Roth准则确定冲击屈曲的临界载荷,讨论了壳体几何尺寸对复合材料层合扁球壳冲击屈曲的影响;数值算例表明,此方法是可行的。     

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.     

Stress Concentration Near Openings in Composite Shells

The results of studying the stress–strain distribution in composite shells with curvilinear openings are reported. Nonclassical generalizing formulations and methods for solution of linear and nonlinear problems are stated. Numerical results obtained for thin and nonthin shells are analyzed with regard for features of the deformation of composites     

Iterative method for large deflection nonlinear problem of laminated composite shallow shells and plates

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Nonlinear shell-type to beam-type fea simplifications for composite frp poles

This paper presents a semi-analytical finite element analysis of pole-type structures with circular hollow cross-section. Based on the principle of stationary potential energy and Novozhilov’s derivation of nonlinear strains, the formulations for the geometric nonlinear analysis of general shells are derived. The nonlinear shell-type analysis is then manipulated and simplified gradually into a beam-type analysis with special emphasis given on the relationships of shell-type to beam-type and nonlinear to linear analyses. Based on the theory of general shells and the finite element method, the approach presented herein is employed to analyze the ovalization of the cross-section, large displacements, the P-Δ effect as well as the overall buckling of pole-type structures. Illustrative examples are presented to demonstrate the applicability and the efficiency of the present technique to the large deformation of fiber-reinforced polymer composite poles accompanied with comparisons employing commercial finite element codes.     

Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions

The geometrically nonlinear forced vibration response of non-continuous elastic-supported laminated composite thin cylindrical shells is investigated in this paper. Two kinds of non-continuous elastic supports are simulated by using artificial springs, which are point and arc constraints, respectively. By using a set of Chebyshev polynomials as the admissible displacement function, the nonlinear differential equation of motion of the shell subjected to periodic radial point loading is obtained through the Lagrange equations, in which the geometric nonlinearity is considered by using Donnell’s nonlinear shell theory. Then, these equations are solved by using the numerical method to obtain nonlinear amplitude–frequency response curves. The numerical results illustrate the effects of spring stiffness and constraint range on the nonlinear forced vibration of points-supported and arcs-supported laminated composite cylindrical shells. The results reveal that the geometric nonlinearity of the shell can be changed by adjusting the values of support stiffness and distribution areas of support, and the values of circumferential and radial stiffness have a more significant influence on amplitude–frequency response than the axial and torsional stiffness.

     

Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections

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.     

Nonlinear vibrations of cylindrical shells with initial imperfections in a supersonic flow

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 __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 63–73, September 2007.     

具脱层的正交铺设圆柱壳的初始后屈曲分析

基于非线性弹性理论,建立了含脱层正交铺设圆柱壳的后屈曲控制方程,应用Koiter初始后屈曲理论和小参数摄动法,导出了系统的一阶和二阶摄动控制方程,以及相应的边界条件、位移连续条件和力平衡条件,然后逐阶求解．算例中,讨论了不同脱层深度和长度对脱层复合材料圆柱壳屈曲和初始后屈曲特性的影响,并与已有文献进行了比较．     

Contact interaction between prestressed laminated shells of revolution and a flat foundation

A nonclassical model of shells that accounts for transverse shears and reduction is used to develop a method for solving the contact problem for inhomogeneous anisotropic shells of revolution subject to a field of mechanical and thermal loads. The prestresses are described by parametric terms in the linearized geometrically nonlinear equations of the second-order theory of flexible shells. The influence of the prestressed state of shells interacting with a flat surface on the contact area and the distribution of contact pressure is analyzed. Some computational features of the technique are discussed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 67–77, October 2006.     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

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Statement of the problem of intraocular pressure measurement modeling by a pneumotonometric method

The process of intraocular pressure measurement by an optical analyzer is numerically modeled. The cornea and sclera are treated as axially symmetric deformable shells of revolution rigidly fixed along the edges; the space between the shells is filled with an incompressible liquid. The stress-strain state of the cornea and sclera is described by using a nonlinear theory of shells. The optical system is calculated on the basis of concepts of geometrical optics. Two types of boundary conditions are compared; for each of them, the relation between the pressure in the air jet and the area of the surface from which the reflected light is recorded by the photodetector is analyzed.     

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff–Love theory.     

Dynamic Problems in the Theory of Sandwich Shells of Revolution with a Discrete Core under Nonstationary Loads

The equations of motion of sandwich shells of revolution with a discrete core are analyzed within the framework of the geometrically nonlinear theory of shells and plates. An efficient numerical algorithm is constructed to investigate nonstationary wave processes in elastic structures that are discrete-inhomogeneous across the thickness. Numerical examples are given     

集中载荷作用下具有光滑中心波纹膜片的非线性分析

波纹膜片是一种薄壳弹性体，由于它的参数很多，又相互制约，所以使得它的设计很复杂。在大多数位移式仪器仪表中，要求波纹膜片产生至少和膜片厚度是同样数量级的弹性位移。这就要求使用薄壳的几何非线性理论进行分析。大多数学者研究波纹膜片的弯曲问题，是采用扁壳理论讨论具有浅波纹的膜片。而工程实际中，经常遇到深波纹膜片，这就要求从一般壳体大挠度方程进行求解。本文采用轴对称旋转壳体的简化Re-issner方程。研究了在中心集中载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用积分方程方法，可以获得膜片的特征关系（载荷-中心挠度关系）和应力分布。文末给出实例计算的数值结果。     

Stability of Cylindrical Shells with Local Imperfections

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