复合圆柱形壳在径向冲击荷载和轴压荷载作用下的瞬时动力响应

基于首次逼近理论,利用第一阶剪切变形理论对圆柱形壳的自由和强迫振动进行分析。边界条件（BCs）考虑为悬臂状态。分析复合壳体在横向冲击和轴向压力作用下的动力响应（轴压荷载小于临界屈曲荷载）,同时对复合柱形壳进行了建模分析。利用卷积积分对给定荷载状况下的壳体进行分析。揭示纤维方向、轴向荷载及一些几何参数对壳体时间响应的影响。结果表明：动力响应主要由结构的自振周期所控制。     

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.     

Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element

A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons demonstrate the applicability and the high performance of the element in stability analysis of thin and moderately thick cross-ply laminated composite shells of revolution under compressive loads.     

Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell

This paper presents a finite element formulation of Koiter's initial post-buckling theory using a multi-mode approach. Initial post-buckling theory provides direct information about the imperfection sensitivity of a structure under compressive loading, and is also the basis of a nonlinear reduced order model. The objective of the present work is to illustrate the capability of the implementation for buckling analysis of shell structures including modal interaction. A coupled mode initial post-buckling analysis for a composite cylindrical shell under axial compression, including the effect of a nonlinear pre-buckling state, has been carried out using a small number of representative modes. For small imperfection amplitudes the limit-point buckling loads obtained with the reduced order model compare reasonably well with full model nonlinear analysis, illustrating that a fast prediction of the coupled mode response of imperfect shells is possible using the approach proposed.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

Elasto-plastic instability of single-layer reticulated shells under dynamic actions

This paper addresses the issue on dynamic collapse mechanism of single-layer reticulated shells subjected to harmonic load, sudden load and seismic load. The method for failure mechanism has reviewed the relationship between the response of the reticulated shell and the peak acceleration of dynamic action. Besides, the steel damage accumulation is considered in the method by compiling a user subroutine based on the computing program ABAQUS. An example is introduced to describe dynamic instability collapse resulting from geometric nonlinearity of the shell and the other example is presented to describe strength failure resulting from excessive development of plastic deformation, for it is discovered that the structure is not only to be prone to instability collapse in dynamic action. According to the responses of the single-layer reticulated shell under dynamic loads, this study discusses the relationship between the failure model and the corresponding dynamic load parameters. Then, the method for distinguishing failure modes is proposed based on the fuzzy synthetic evaluation theory and the structural responses of sufficient samples at the failure state. The technique feasible to be used to distinguish different failure modes of single-layer reticulated shells under different dynamic loads is validated.     

Dynamic pulse buckling of single curvature composite shells under external blast

Dynamic pulse buckling of a single curvature composite shell under external pressure was examined using Lagrange's equation of motion and the Budiansky–Roth criterion. The predicted transient shell response compared very well with results from ABAQUS Implicit, and the predicted buckling loads also agreed with experiments on steel arches. Load duration determined whether the buckling was impulsive, dynamic or quasi-dynamic. Thicker composite shells were more likely to fail by first-ply failure rather than buckling. It was shown that the composite lay-up could be adjusted to increase the buckling resistance of the shell.     

Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads

The dynamic behavior of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads is studied. The material properties are assumed to have continuous variations in the shell thickness direction. The equations of motion are derived based on the first-order shear deformation theory (FSDT) using Hamilton׳s principle. The finite element method (FEM) together with Newmark׳s time integration scheme is employed to discretize the equations of motion in the spatial and temporal domain, respectively. The formulation and method of solution are validated by studying their convergence behavior and carrying out the comparison studies in the limit cases with existing solutions in the literature. Then, the influences of material graded index, radius-to-length ratio, semi-vertex angle, thickness, boundary conditions and moving load velocity on the dynamic behavior of the FG truncated conical shells are studied. In addition, the difference between the responses of the FG shells under symmetric and asymmetric loadings is compared.     

The effect of elastic foundations on the nonlinear buckling behavior of axially compressed heterogeneous orthotropic truncated conical shells

The buckling problem of a heterogeneous orthotropic truncated conical shell subjected to an axial load and surrounded by elastic media is analyzed based on the finite deformation theory. Using von-Karman nonlinearity, the governing equations of elastic buckling of heterogeneous orthotropic truncated conical shells surrounded by elastic media are derived. The governing equations are solved using superposition and Galerkin methods and obtained expressions for upper and lower critical axial loads. The influences of elastic foundations, heterogeneity, orthotropy and geometric characteristics on the upper and lower critical loads of conical shells with and without elastic foundations are studied in detail.     

Dynamic buckling of fiber composite shells under impulsive axial compression

The paper deals with dynamic buckling due to impulsive loading of thin-walled carbon fiber reinforced plastics (CFRP) shell structures under axial compression. The approach adopted is based on the equations of motion, which are numerically solved using a finite element code (ABAQUS/Explicit) and using numerical models validated by experimental static buckling tests. To study the influence of the load duration, the time history of impulsive loading is varied and the corresponding dynamic buckling loads are related to the quasi-static buckling loads. To analyse the sensitivity to geometric imperfections, the initial geometric imperfections, measured experimentally on the internal surface of real shells, are introduced in the numerical models. It is shown numerically that the initial geometric imperfections as well as the duration of the loading period have a great influence on the dynamic buckling of the shells. For short time duration, the dynamic buckling loads are larger than the static ones. By increasing the load duration, the dynamic buckling loads decrease quickly and get significantly smaller than the static loads. Since the common practice is to assume that dynamic bucking loads are higher than the static ones, which means that static design is safe, careful design is recommended. Indeed, taking the static buckling load as the design point for dynamic problems might be misleading.     

Buckling and postbuckling of cylindrical shells with one end pinned and the other end free

Using finite element analysis, this paper examines the linear bifurcation buckling loads, and nonlinear collapse loads, of cylindrical shells with one end pinned and the other end free, under a variety of axial and pressure load combinations. The pinned end is formulated so as to provide no axial restraint. For the bifurcation analysis, loads are related back to the classical solutions for cylinder buckling loads, to explain the very low values found for this set of boundary conditions.The nonlinear analysis includes both imperfections and material plasticity. In this analysis, it is found that cylindrical shells with pinned-free boundary conditions are notably imperfection insensitive, and for a range of geometries are able to reach collapse loads significantly greater than their bifurcation load. For other geometries, collapse loads very close to the bifurcation load are found. This unusual imperfection insensitivity for a cylindrical shell is explained in terms of the large flexibility engendered by the pinned-free boundary conditions and the oval buckling mode.     

Dynamic instability of three-layered cylindrical shells containing an FGM interlayer

In this study, the dynamic instability of three-layered cylindrical shells containing a functionally graded (FG) interlayer subjected to static and time dependent periodic axial compressive loads are investigated. The governing relations, modified Donnell type dynamic stability and deformation compatibility equations are derived. The governing equations are reduced Mathieu–Hill equation by using Galerkin׳s method and the expressions for boundaries of unstable regions of three-layered cylindrical shell with an FG interlayer are found. Finally, the effects of variations of volume fractions of FG interlayer and shell characteristics on the magnitudes of boundaries of unstable regions are studied numerically.     

Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such as the peak load, fold lengths, axial compression and energy absorption are studied. An examination is also made of the influence of filtering on the accuracy of data obtained usually in dynamic tests.     

网状扁壳与带肋扁壳组合结构的拟三层壳分析法

本文对网状扁壳与带肋扁壳共同工作的组合结构(可简称组合网状扁壳),采用连续化的拟三层壳的计算模型,按弹性小挠度薄壳理论进行分析计算,推导建立了混合法的基本方程式。由于这种构造上的拟三层壳在一般情况下不存在中面,因而壳体的薄膜内力、弯矩与薄膜应变,弯曲应变是耦合的,存在一个耦合矩阵,使得基本方程式比单层光面的符氏扁壳方程要复杂得多。对于周边简支的组合网状扁壳可求得基本方程式的解析解。文中对三向、四向组合网状扁壳进行了详细讨论,并指出了在特定条件下,可退化为一个当量的各向同性单层扁壳。对于一般网状扁壳的拟壳分析法及带肋扁壳的拟壳分析法分别属于本文的两种特殊情况。文中附有计算例题。     

薄壁槽形截面压杆弹性整体屈曲数值计算研究

为研究薄壁槽钢整体屈曲下的数值算法的适用性,以4种不同杆端约束下的薄壁槽形截面压杆为研究对象,根据广义梁理论确定其发生弹性整体屈曲的有效长度及临界荷载,与开口薄壁理想压杆的线性及非线性解析解进行对比,得到一致的临界荷载。利用ABAQUS有限元分析软件建立壳体有限元模型,采用杆端截面形心集中加载,依据约束情况确定杆端约束,以及根据有效长度施加不同初始缺陷的计算模型,开展特征值算法和隐式弧长法数值计算分析。计算结果表明:当开口薄壁压杆的有效长度足够大时,临界荷载的特征值数值解与理论解一致,弧长法计算得到的非线性解误差相对较大。当有效长度不够大时,弧长法计算得到的极限荷载与理论解基本一致,且弧长法可有效追踪后屈曲路径。     

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.     

Multiobjective optimization of orthogonally stiffened cylindrical shells for minimum weight and maximum axial buckling load

In the present research, the weight and axial buckling optimization of orthogonally stiffened cylindrical shells is carried out by the Genetic Algorithm. Constraints include two nondimensional functions of weight and buckling load in such a way that the stiffened shell has no increase in the weight and no decrease in the buckling load with respect to the initial unstiffened shell. In analytical solution, the Rayleigh–Ritz energy procedure is applied and the stiffeners are treated as discrete members. The optimization is implemented for shells with simply supported end conditions stiffened by four shapes of stiffeners including rectangular-, cee-, I-, and hat-shaped ones. The results show that the I-section and rectangular-section stiffeners are, respectively, the most and the least efficient in designing stiffened cylindrical shells for minimum weight and maximum critical axial buckling load.     

Simple solution for buckling of orthotropic circular cylindrical shells

Most papers dealing with the analysis of the buckling behaviour of orthotropic circular cylindrical shells provide solutions which are complex in nature and difficult to use. In this paper the theory has been developed to the point that relatively simple solutions of a general nature have been formulated. Based on Flugge's linear theory for isotropic cylindrical shells, a general buckling solution under combined axial compression and external pressure was derived. For moderate-length orthotropic cylindrical shells loaded by either external pressure or axial compression, buckling loads are formulated in a simple form.     

薄壁空心球节点承载能力的非线性数值分析

现行网架规程中的焊接空心球承载力设计公式是以试验为基础的经验公式 ,对以稳定性控制的球壳 ,难以求得较为精确的屈曲临界点。应用对称旋转薄壳屈曲的非线性有限元理论 ,对空心球节点进行大位移弹塑性屈曲分析 ,得出了可供设计参考的空心球承载力数据表 ,并回归出适用于大直径空心球计算的近似公式 ,以确定空心球节点的失效状态及临界荷载。     

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the local buckling modes of the cylindrical shell depends mainly on the crack orientation. For cylindrical shells with relatively long axial crack, buckling loads associated with local buckling modes of the cylindrical shell reduce drastically on increasing the shell internal pressure. In contrast, the internal pressure has the stabilizing effect against the local buckling for circumferentially cracked cylindrical shells. A critical crack length for each crack orientation and loading condition is defined as the shortest crack causing the local buckling to precede the global buckling of the cylindrical shell. Some insight into the effect of internal pressure on this critical crack length is provided.