Dynamic buckling of elastic-plastic complete spherical shells under step loading

The dynamic axisymmetrical behaviour of a perfect complete spherical shell made from a bilinear or work hardening material and subjected to a uniform external step pressure loading is investigated. A perturbation method of analysis leads to a Mathieu equation which gives the dynamic buckling pressure and associated mode for a complete spherical shell. The influence of the plastic parameter and damping on the dynamic buckling pressure and mode number are also discussed.     

充液及内空圆柱壳在爆炸荷载下动力屈曲特性研究

采用实验与数值模拟相结合方法,对充液及内空圆柱壳在爆炸载荷下动力屈曲响应特性进行对比研究。将壁厚δ=2.0 mm、外径Φ=100 mm钢圆柱壳（内空及充水）置于75gTNT药柱、200gTNT药柱产生的爆炸场中进行冲击实验,获得不同工况下圆柱壳变形破坏模式。利用动力有限元程序LS-DYNA及Lagrangian-Eulerian流固耦合方法进行数值计算,分析壳壁屈曲变形过程及壳壁关键点速度、水介质内压力等动态参数。计算结果与实验结果一致性较好。研究表明,由于内充水介质的近似不可压缩性,承受冲击荷载时内压增大,因而参与对外界爆炸冲击载荷抗力作用,圆柱壳抗爆能力显著提高。     

Dynamic buckling of functionally graded cylindrical thin shells under non-periodic impulsive loading

Summary.  This paper is concerned with the study of the amplitude of the steady-state vibration in a right finite cylinder made of a mixture consisting of three components: an elastic solid, a viscous fluid and a gas. An exponential decay estimate of Saint-Venant type in terms of the distance from one end of the cylinder is obtained from a first-order differential inequality for a cross-sectional area measure associated with the amplitude of the steady-state vibration. The decay constant depends on the excitation frequency, the constitutive coefficients and the first positive eigenvalue for the fixed membrane problem for the cross-sectional geometry. The paper also indicates how to extend the results to a semi-infinite cylinder. Received October 24, 2002 Published online: April 17, 2003     

Twin-characteristic-parameters analysis for elastic dynamic buckling of thin cylindrical shells under axial step loading

The relations of the critical stress and transverse inertia effect to the loading duration are investigated for the dynamic buckling of thin cylindrical shells under axial step loading. The critical stress and the inertial exponent are treated as the two characteristic parameters. The criterion of energy conservation is used to derive the supplementary restraint condition for buckling deformations at compression wave front. By use of the Galerkin method, an algebraic eigenvalue problem for the two characteristic parameters is derived from the governing equations and boundary conditions. The solution of the eigenvalue problem, which satisfies the supplementary restraint condition, gives the values of the critical stress and the inertial exponent for the dynamic buckling. The relation of critical stress to loading duration, predicted by the theoretical analysis, is in reasonable agreement with the experimental results.     

Simultaneous buckling design of stiffened shells with multiple cutouts

Buckling is usually initiated from a local region near the cutout for cylindrical stiffened shells under axial compression, and then the evolution of buckling waves is governed by the combined effects of local and global stiffness, which limit the load-carrying capacity. Therefore, a simultaneous buckling pattern is crucial for improving the structural efficiency. In this study, a multi-step optimization strategy for the integrated design of near and far fields away from cutouts is proposed, and the convergence criterion of buckling optimization is improved as a deformation-based index. The numerical implementation of the asymptotic homogenization method is utilized to construct an efficient finite element model for post-buckling analysis. A 5?m diameter stiffened shell in a launch vehicle demonstrates that the proposed framework can provide a simultaneous buckling design with high structural efficiency in an efficient manner. Both the buckling deformations and stress of the optimum design are more uniform compared to other optimum designs.     

Dynamic pulse buckling of composite shells subjected to external blast

Dynamic pulse buckling of woven E-Glass/Vinyl Ester and laminated E-Glass/Epoxy cylindrical shells subjected to uniform overpressure and asymmetric pressure pulse (side-on explosion) were examined. The solutions for the radial shell deformations were represented by Mathieu differential equations. The dynamic instability of the shells was determined from a Mathieu stability diagram. It was found that the stability of the shells depended on lay-up, aspect ratio as well as impulse distribution. The stable vibration response of the shells with side-on explosion compared well with finite element solutions using a Dynamic, Implicit analysis in ABAQUS Standard. First-ply failure of the woven E-Glass/Vinyl Ester shell with side-on explosion was predicted using a modified Hashin–Rotem failure criterion. It was shown that the thinner woven E-Glass/Vinyl Ester shells were more likely to fail by dynamic instability, whereas the thicker woven E-Glass/Vinyl Ester shells were more likely to fail by first-ply failure.     

功能梯度材料薄球壳热屈曲问题

研究了由金属和陶瓷组成的功能梯度材料薄球壳热屈曲问题。用张量方法推导得到轴对称球壳稳定性方程。将热本构方程应用到球壳稳定性方程中,得到以位移表示的球壳热屈曲方程组。分别考虑均布外压和温度作用,采用伽辽金法计算分析简支球壳的热屈曲问题,给出薄球壳厚度、物性参数变化、内外表面温差变化引起的临界温度变化趋势和临界压力变化趋势。     

An experimental investigation into the buckling and post-buckling of CFRP shells under combined axial and torsion loading

The results of an experimental study of the buckling and post-buckling behaviour of four unstiffened thin-walled CFRP cylindrical shells are presented. The test equipment allows axial and torsion loading, applied separately and in combination, using a position control mode, and includes a laser scanning system for the measurement in situ of the geometric imperfection as well as of the progressive change in deformations. The results identify the effect of laminate orientation, show that the buckling loads are essentially independent of load sequence and demonstrate that the shells are able to sustain load in the post-buckling field without any damage. The measured data are fundamental for the development and validation of analytical and numerical models and contribute to the definition of applicable strength design criteria of composite cylindrical shells in the post-buckling field, with the final aim of a larger structure weight saving.     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥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三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

Delamination buckling of cylindrical shells under axial compression

A model is developed for the study of delamination buckling of axially loaded cylindrical shells. Delamination is assumed to exist before load application, it spans the entire circumference, and it lies on the contact surface of neighboring laminae. The mathematical model employs Donnell-type kinematic relations and linearly elastic material behavior. Furthermore, each lamina is assumed isotropic, and the emphasis is on studying the effect of delamination size and position on the critical load. Two sets of boundary conditions are used with the model: simply supported and clamped. The study reveals several important conclusions. Among them, one may list the following: (a) the critical load is primarily controlled by the position of the delamination from the reference surface, provided that the delamination is not very close to the boundaries; and (b) for long delaminations (relative to the cylinder length), the critical load is not appreciably affected by the boundary conditions.     

Reduced-stiffness method in the theory of buckling of stiffened shells

The reduced-stiffness method is used to establish the lower bounds of buckling loads for stringer- or ring-stiffened cylindrical shells. The numerical results obtained by using this method are compared with the experimental data. We also consider the problem of applicability of the reduced-stiffness method in design practice as well as the prospects for its development and generalization. The present work is a continuation of the review [1]. Translated from Problemy Prochnosti, No. 2, pp. 90–104, March–April, 2000.     

Nonlinear dynamic buckling of orthotropic cylindrical shells subjected to rapidly applied loads

Dynamic buckling of an orthotropic cylindrical shell which is subjected to rapidly applied compression is considered. A nonlinear differential equation of Donnell–Karman type is derived with the initial imperfection taken into account. An energy method is used to obtain the equation of motion which is then solved numerically by means of a Runge-Kutta method. These numerical results show that the critical load is increased over the corresponding static case. An analytical solution is also obtained for the problem of hydrostatic pressure.     

Localized plastic buckling deformation in axially compressed cylindrical shells

Summary A linear partial differential equation is derived to describe growth of an axisymmetric perturbation in the plastic buckling of axially compressed cylindrical shells. Simple J ₂ flow theory is used along with rigid-plastic material behavior. An asymptotic solution is then constructed for large values of a parameter which characterizes localization of an initial imperfection. The perturbation remains localized. The solution is compared with experimental results.     

Nonlinear behavior and buckling of cylindrical shells subjected to localized external pressure

Buckling loads and postbuckling behavior of cylindrical shells subjected to localized external pressure are considered. The modified extended Kantorovich method with path-tracing technique is applied to determine the buckling loads of the cylindrical shells. It is found that the load is dependent nonmonotonically on geometrical parameters of the area subjected to external pressure. Respective postbuckling shapes show correlation with the shapes corresponding to secondary bifurcation paths for the cases of a cylindrical shell under uniform external pressure and a cylindrical shell under uniform axial load.     

Vibrations and buckling of composite orthotropic cylindrical shells with nonuniform axial loads

The vibrational response of orthotropic composite cylindrical shells, subjected to circumferentially nonuniform axial loads, is investigated based on Flügge-type field equations. The use of a complex finite Fourier transform provides a simple method for handling any arbitrary nonuniform load but introduces modal coupling between the transformed equations. For simply supported boundaries (conditions SS3) the determination of the critical buckling load reduces to finding the eigenvalues of a finite matrix. Two different nonuniform loads are considered, having forms proportional to (1+2cos θ) and (θ*−θ), where is the Heaviside function, θ is the circumferential coordinate and aθ* is the width of an axial strip of the shell of radius a. Computed results indicate the sensitivity of the critical buckling loads and free vibrational frequency to the type of nonuniform load and the material lay-ups of the cylinders.