Stability analysis of generally laminated conical shells with variable thickness under axial compression

Abstract

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to investigate all combinations of classical boundary conditions. The results are verified in comparison with Galerkin method and the available results in the literature. Effects of thickness function coefficient, semi-vertex angle, lamination sequence, length to diameter ratio, and initial thickness of the cone on the buckling load are investigated. It is observed that these parameters have considerable effects on the critical buckling load of a conical shell.     

Frequency analysis of rotating truncated circular orthotropic conical shells with different boundary conditions

In this paper, a study is made of the influences of orthotropic properties and boundary conditions on the free vibrations of a rotating, truncated, circular orthotropic conical shell. The study includes the effects of the Coriolis and centrifugal accelerations and the initial hoop tension. It is based on the Love first-approximation theory and Galerkin procedure. Results are obtained for the frequency characteristics of different orthotropic parameters, rotating velocities, cone angles and boundary conditions. Influences of orthotropic properties and boundary conditions on the relationships between frequency parameter and rotation velocity are discussed for different cone angles. To validate the present analysis, comparisons are made with those available in the open literature and very good agreements are obtained.     

Vibration control of laminated truncated conical shell via magnetostrictive layers

Abstract

In this study feedback control is applied to control the free vibration response of an isotropic truncated conical shell embedded with magnetostrictive layers. Classical shell theory is applied to derive the shell vibration equations. The results are derived based on the Galerkin method and the results are compared with published results and the results of finite element software in order to determine the accuracy of using method. The influence of several parameters such as the thickness of magnetostrictive layers, control gain, length and radius of the large edge of the shell on the vibration suppression of fundamental frequency is determined.     

Buckling analysis and design of anisogrid composite lattice conical shells

Composite lattice anisogrid shells have now become a popular choice in many aerospace applications. Their use in various structural components, such as rocket interstages, payload adapters for spacecraft launchers, fuselage components for aerial vehicles, and parts of the deployable space antennas requires the development of more advanced finite-element models and analysis techniques capable of predicting buckling behaviour of these structures under variety of loadings. A specialised finite-element model generation procedure (design modeller) is developed and applied to the buckling analysis of the composite anisogrid conical shells treated as three-dimensional frames composed of the curvilinear ribs made of unidirectional composite material. Featuring a dedicated control procedure for positioning the beam elements, the design modeller enables a close approximation of the original twisted geometry of the curvilinear ribs. The parametric finite-element buckling analyses of the anisogrid conical shells subjected to axial compression, transverse bending, pure bending, and torsion showed the robustness and potential of the modelling approach. It was demonstrated that the buckling resistance can be significantly enhanced by either increasing the stiffness of a few hoop ribs located in the close proximity to the section with the larger diameter, or by introducing the additional hoop ribs in the same part of the conical shell. The effectiveness of the design analyses is demonstrated using particular examples. It has been shown that the resultant optimised designs can produce up to 22% mass savings in comparison with the non-optimised lattice shells.     

Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load

Dynamic buckling of functionally graded materials truncated conical shells subjected to normal impact loads is discussed in this paper. In the analysis, the material properties of functionally graded materials shells are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Geometrically nonlinear large deformation and the initial imperfections are taken into account. Galerkin procedure and Runge–Kutta integration scheme are used to solve nonlinear governing equations numerically. From the characteristics of dynamic response obtain critical loads of the shell according to B-R criterion. From the research results it can be found that gradient properties of the materials have significant effects on the critical buckling loads of FGM shells.     

Buckling analysis of moderately thick FG carbon nanotube reinforced composite conical shells under axial compression by DQM

A semi-analytical method is presented to study the buckling of moderately thick carbon nanotube reinforced composite conical shells under axial compression. Material properties are assumed to be graded across the shell thickness. In order to derive the equilibrium equations of the shell, first-order shear deformation theory is used. Then, the partial differential equations are transformed to algebraic type by using the differential quadrature method. To validate the results obtained in this study, comparisons are made with the outcomes of previous studies. Finally, the effects of the geometry of the shell, circumferential mode number, volume fraction of the carbon nanotube, and boundary conditions are studied.     

温度-机械混合载荷作用下先进复合材料格栅加筋截顶圆锥壳体的屈曲分析

基于均匀化原理,推导了考虑沿格栅加筋圆锥壳体随母线变化的等效刚度阵和等效热膨胀系数,并采用前屈曲薄膜理论给出了在温度和均布外压载荷作用下格栅加筋圆锥截顶壳体稳定性分析的总势能表达式。基于最小势能原理得到了该壳体总体失稳的临界载荷值解析表达式,对典型复合材料格栅加筋截顶圆锥壳体的稳定性计算结果与有限元法所得结果相比较,验证了本文中方法的适用性。基于文中提出的方法,通过对不同温度条件下具有不同顶锥角复合材料格栅加筋截顶圆锥壳体热-力屈曲分析结果的讨论,指出温度对复合材料格栅加筋截顶圆锥壳体稳定性的影响程度将随其顶锥角增加而增大。     

Vibration analysis of orthotropic cantilever cylindrical shells with axial thickness variation

A semi-analytical finite element method is used to determine the free vibration characteristics of thin orthotropic cantilever circular cylindrical shells. Love's first approximation shell theory is used for the formulation. The effect of the variation of thickness along the axial direction on natural frequencies, especially on the lowest frequency, has been studied with a constraint on the total mass of the shell for a particular length to middle surface radius ratio. Studies have been conducted for different degrees of orthotropy and various values of length to radius ratio.     

Analytical investigation on the free vibration behavior of rotating FGM truncated conical shells reinforced by orthogonal eccentric stiffeners

This article presents an analytical investigation on the free vibration behavior of rotating functionally graded truncated conical shells reinforced by stringers and rings with the change of spacing between stringers. Using the Donnell shell theory, smeared stiffeners technique, and taking into account the influences of centrifugal force and Coriolis acceleration, the governing equations are derived. These variable coefficient partial differential equations are studied by the Galerkin method. The sixth-order polynomial equation of natural frequency is obtained. Numerical results show effects of stiffener and input parameters on the frequency of shell.     

The generalized differential quadrature method for frequency analysis of a rotating conical shell with initial pressure

Using the generalized differential quadrature (GDQ) method which is an improved version of the differential quadrature (DQ) method, this paper examines the influence of initial pressure load on the free vibration of a rotating thin truncated circular isotropic conical shell with different boundary conditions. The present governing equations of motion include the influence of initial stress field and the effects of initial hoop tension and also the centrifugal and coriolis accelerations due to rotation. The influence of initial pressure on the frequency characteristics is discussed in detail for various conditions. To validate the present analysis, frequency comparisons are made with those available in published works, and very good agreements are obtained. Copyright © 2000 John Wiley & Sons, Ltd.     

截锥壳颤振分析的微分求积法

引入微分求积法(Differential Quadrature Method,简称DQM)对截锥壳气动弹性方程离散,采用一阶活塞理论气动力,运用特征值分析方法求解系统的颤振临界动压。研究了半顶角、径厚比、长径比等几何参数对颤振临界动压的影响。结果表明,DQM求解截锥壳气动弹性方程具有良好的精度和计算效率,结构产生1阶~2阶耦合型颤振的最低临界动压对应的周向波数较大,并因几何参数而异;颤振临界动压参数随半顶角的增大而减小,随着径厚比的增大而增大,随长径比的增大而减小。     

Vibration of axisymmetric composite piezoelectric shells coupled with internal fluid

This paper presents the theoretical and finite element formulations of piezoelectric composite shells of revolution filled with compressible fluid. The originality of this work lies (i) in the development of a variational formulation for the fully coupled fluid/piezoelectric structure system, and (ii) in the finite element implementation of an inexpensive and accurate axisymmetric adaptive laminated conical shell element. Various modal results are presented in order to validate and illustrate the efficiency of the proposed fluid–structure finite element formulation. Copyright © 2007 John Wiley & Sons, Ltd.     

基于变环肋间距的碳纤维/环氧树脂复合材料格栅加筋截顶圆锥壳体稳定性

研究均布外压作用下具有非均匀特征的碳纤维/环氧树脂复合材料格栅加筋（AGS）圆锥壳体构型优化。首先,充分考虑复合材料格栅圆锥壳体中格栅非均匀分布造成结构小端材料利用不充分问题,提出变环肋铺设间距的优化分布方式,使格栅在截顶圆锥壳体结构上小端疏大端密。之后,基于考虑格栅非均匀分布及变环肋间距铺设特征的等效刚度模型,并采用最小势能原理得到环肋铺设优化后的AGS圆锥壳体临界载荷值解析式。针对典型锥壳的有限元验证表明解析算法的误差在1%左右,证实了本文提出的分析方法的可靠性和有效性。最后,通过对环肋间距优化圆锥壳体的参数分析,发现优化环肋分布方式可以使AGS锥壳结构的外压稳定性大幅上升。本文研究内容为碳纤维/环氧树脂复合材料AGS圆锥壳体的优化设计提供了一种具有较高承载力的构型,并为此类结构的计算提供了解析算法。     

厚度不连续悬臂梁板的自由振动分析

将厚度不连续梁板视为层合板, 分别应用Hamilton 正则方程半解析法建立每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性, 联立各层的方程得到整个结构的特征方程, 其主要的优越性表现为: 控制方程不限制不连续梁板的厚度, 并能适合处理厚度不对称且不连续的层合板。本文中的方法可修改或扩展用来分析加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳等问题。      

Transient dynamic and free vibration analysis of functionally graded truncated conical shells with non-uniform thickness subjected to mechanical shock loading

This paper is focused on the transient dynamic and free vibration analysis of functionally graded (FG) axisymmetric truncated conical shells with non-uniform thickness. Two numerically efficient and accurate solution methods are presented to study the transient dynamic responses of FG shells subjected to either internal or external mechanical shock loading. Employing the displacement-based layerwise theory in conjunction with the Hamilton’s principle, the transversely discretized equations of motion are obtained. The differential quadrature method (DQM) is used to discretize the resulting equations in the axial direction. To solve the developed time-dependent equations, either DQM (named LWDQ) or Newmark’s time integration scheme (named LWDQN) is employed. The material properties are graded continuously in the thickness direction according to a volume fraction power-law distribution. The developed results are successfully compared with those obtained by ANSYS and also with the available results in the literature. The comparisons demonstrate the accuracy and effectiveness of the aforementioned methods on achievement of fast convergence rate with relatively low computational cost. Finally, the effects of different geometric and material parameters on the dynamic behavior of the FG shells are investigated. Due to high accuracy of the method, the results can be used as benchmarks for future research.     

Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations

This paper deals with free vibration analysis of radially functionally graded circular and annular sectorial thin plates of variable thickness, resting on the Pasternak elastic foundation. Differential quadrature method (DQM) is used to yield natural frequencies of the circular/annular sectorial plates under simply-supported and clamped boundary conditions on the basis of the classical plate theory (CPT). The inhomogeneity of the plate is characterized by taking exponential variation of Young’s modulus and mass density of the material along the radial direction whereas Poisson’s ratio is assumed to remain constant. The validity of the present solution is first examined by studying the convergence of the frequency parameters. Then, a comparison of results with those available in literature confirms the excellent accuracy of the present approach. Afterwards, the frequency parameters of the circular/annular sectorial thin plates with uniform, linear, and quadratic variations in thickness are computed for different boundary conditions and various values of the material inhomogeneity constants, sector angles, and inner to outer radius ratios.     

Vibration analysis of solid ellipsoids and hollow ellipsoidal shells of revolution with variable thickness from a three-dimensional theory

Summary A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of complete ellipsoidal shells of revolution with variable thickness and solid ellipsoids. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u _r , u _θ, and u _z in the radial, circumferential, and axial directions, respectively, are taken to be periodic in θ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the ellipsoidal shells of revolution and solid ellipsoids are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactness is demonstrated for the first five frequencies of the ellipsoidal shells of revolution. Numerical results are presented for a variety of ellipsoidal shells with variable thickness. Frequencies for five solid ellipsoids of different axis ratios are also given. Spherical shells and solid spheres are special cases which are included. Comparisons are also made between the frequencies from the present 3D Ritz method, a 2D Ritz method, and a 3D finite element method. The multiple degeneracies (two or more modes having the same frequency) of spherical bodies are examined by analyzing some almost-spherical ellipsoids.     

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Based on the first-order shear deformation theory, the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The two-constituent FG shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using differential quadrature method. Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four different end boundary conditions, and for some special cases, acquired results were compared with those available in the literature. Furthermore, effects of geometrical parameters, material graded power index, and boundary conditions on the natural frequencies of the FG truncated conical shell are carried out.     

A refined buckling theory for the analysis of sandwich shells with transversely soft filler

A state of the art of the problem of buckling in sandwich structures is discussed and the shortcomings of some existing theories shown. A specified classification of the forms of stability is given and, in accordance with it, a refined theory for the study of the mixed forms of stability is formulated. Different models of the fillers are classified according to their stress–strain state. For the transversely soft model of the filler a set of geometrically nonlinear refined relations is derived. These relations are used to describe the subcritical instantaneous equilibrium of the sandwich plates in the case of both large and small changes in the shear stresses.