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。     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling 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. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

Transient vibrations of laminated composite cylindrical shells exposed to underwater shock waves

The problem of the transient vibration of an elastic laminated composite cylindrical shell with infinite length exposed to an underwater shock wave is solved approximately. The linear acoustic plane wave assumption and Sanders thin shell theory are adopted. The reflected-afterflow virtual-source (RAVS) procedure is used to model the fluid–structure interaction involved during the underwater shock event. For the validity of the present analysis, the response of a laminated cylindrical shell under step plane wave is first analyzed and compared with the numerical solution available in the literature. Detailed numerical results for the transient responses of the shells under an exponentially decaying underwater shock wave are presented, and the influences of fiber angle, shell radius and thickness upon the dimensionless radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity of the shells, are investigated.     

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.     

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.     

Assessment of shell theories for the static analysis of cross-ply laminated circular cylindrical shells

This paper examines the accuracy of classical shell theories (CST) according to Flugge, Sanders, Love and Donnell, with respect to the recently available three-dimensional elasticity solution, for cross-ply laminated circular cylindrical shells under static loads. Further, a study has also been made to examine to what extent incorporation of first order shear deformation (FSDT), in aforementioned shell theories, improves the results. In general, all the basic equations (for both CST and FSDT), of aforementioned shell theories, have been presented in a unified form using tracer coefficients. A Navier type solution has been used to analyse both a simply supported circular cylindrical shell of revolution and an all round simply supported circular cylindrical shell panel. A parametric study has been carried out keeping in view the lamination schemes and geometrical parameters of the shell. From the detailed comparisons of the results it has been shown that (i) Donnell's theory (CST and FSDT) could be in error for certain lamination schemes and geometrical parameters and (ii) improved results for stresses and displacements could be obtained by incorporating shear deformation on more accurate theory like Flugge (CST).     

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.     

Non-linear free and forced vibrations of piezoelectric laminated shells in thermal environments

This article is concerned with the non-linear free vibration and transient response of laminated composite cylindrical and spherical shells with piezoelectric layers in thermal environments. The theoretical formulations are based on the first-order shear deformation theory and the von Kármán-type non-linear kinematics. The analysis is carried out using the quadratic C ⁰ eight-noded isoparametric element. The governing non-linear equations are solved by using the direct iteration method for the eigenvalue problem for free vibration and the Newmark average acceleration method in time integration in conjunction with the modified Newton-Raphson iteration scheme for the transient analysis. The validity of the numerical model is demonstrated by comparing the present results with those available in the literature. The effects of temperature, voltage, curvature, thickness, number of layers and boundary conditions on the non-linear free vibration and transient response of piezoelectric laminated cylindrical and spherical shells are investigated.     

复合材料层合壳体热弹耦合简化模型

为有效分析复合材料层合壳体单向耦合的热弹性问题,基于变分渐近方法(VAM)建立热弹性简化壳体模型.根据Hamilton扩展原理建立层合壳体三维能量方程,并利用壳体固有小参数将三维能量渐近扩展为系列二维近似能量方程.将近似能量转换为工程常用的Reissner-Mindlin形式,并推导三维场重构关系以准确重构沿厚向的三维场分布.通过热/力环境下4层复合材料层合壳体的柱形弯曲算例验证:该理论建模速度快(等效单层板模型,相比三维有限元法可减少2～3阶计算量);具有很好的非线性逼近能力(收敛于精确解).     

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.     

Static and transient response of cylindrical shells

Static and transient analysis of composite cylindrical shells is presented using a recently proposed shear deformation theory. The dynamic response is obtained by employing the numerical time integration scheme due to Newmark. The results obtained by using classical shell theory (CST) and Mindlin-type shear deformation theory (SDT) are compared with those obtained by using the proposed theory. The comparison studies reveal that the linear stress distribution, as assumed in CST and SDT, differs considerably from the predicted nonlinear distribution of the proposed theory.     

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。     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

Tailoring the elastic postbuckling response of thin-walled cylindrical composite shells under axial compression

The buckling of cylindrical shells has long been regarded as an undesirable phenomenon, but increasing interests on the development of active and controllable structures open new opportunities to utilize such unstable behavior. In this paper, approaches for modifying and controlling the elastic response of axially compressed laminated composite cylindrical shells in the far postbuckling regime are presented and evaluated. Three methods are explored (1) varying ply orientation and laminate stacking sequence; (2) introducing patterned material stiffness distributions; and (3) providing internal lateral constraints. Experimental data and numerical results show that the static and kinematic response of unstable mode branch switching during postbuckling response can be modified and potentially tailored.     

Delamination buckling for composite laminated cylindrical shells in Hamilton system

In this article, a semi-analytical three-dimensional model based on the modified Hellinger–Reissner (H–R) variational principle and a nonlinear spring-layer model are presented for the buckling analysis of composite laminated cylindrical shells with a delamination. The method allows the effect of transverse shear deformation in the control equations of the composite laminated structures. In addition, it uses a two-dimensional mesh and can ensure that the number of variables is independent of the layer number. The nonlinear spring-layer model between the exterior and interior sub-laminates ensures the continuity of transverse stresses and displacements in the undelaminated region by specifying infinite values of springs and therefore avoids the possibility of material penetration phenomenon in the delaminated region. As an application of the present method, the influence of the delamination length on the critical buckling loads of delaminated composite laminated stiffened cylindrical shells is investigated.     

Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory

Forced vibration response of laminated composite and sandwich shell is studied by using a 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the forced vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders' approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at each layer interface in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C₀ finite element formulation has been done to overcome the problem of C₁ continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells besides normal curvature shells like cylindrical, spherical shells etc. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.     

Effect of inplane edge constraints on natural frequencies of simply supported doubly curved shallow shells

Reasonably accurate natural frequencies are presented for simply supported shallow shells on rectangular planform subjected to 55 possible combinations of edge constraints. Thin shallow shell theory is used. Accurate natural frequencies of doubly curved shallow shells are presented and can be used for benchmarking by researchers as well as reference data for practicing engineers. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.     

Natural frequencies of laminated orthotropic thin circular cylinders

Vibration characteristics of laminated orthotropic cylindrical shells are investigated. The analysis, based on the Love-Timoshenko theory, can deal with shells composed of an arbitrary number of bonded layers each with a different thickness and different eleastic orthotropic properties. The analytical method, which is derived and applied here for calculating the frequencies of laminated orthotropic cylindrical shells, is an application of the well-known Rayleigh-Ritz procedure. In applying the Rayleigh-Ritz procedure the expression of strain and kinetic energies in general form for laminated orthotropic cylindrical shells have been used. The results obtained compared very well with some available experimental and analytical results.     

Dynamic buckling of stiffened cylindrical shells of revolution under a transient lateral pressure shock wave

A modal method of analysis is used to determine the response of an infinitely long stiffened cylindrical shell of revolution to a transient lateral pressure produced by an underwater explosion and propagating in an acoustic fluid. The shell is initially immersed, hence prestressed by the external hydrostatic pressure. A theory of dynamic buckling is then developed for cylindrical shells subjected to transverse pressure pulses of different durations.     

Transient dynamics of cylinders under wave slamming

Large diameter slender cylindrical shells used as buoyancy chambers and support legs for compliant marine structures experience a variety of impact loadings which could induce significant levels of dynamic response. By examining the response of a typical range of cylindrical shell geometries to a simulation of the impact loading typical of wave slamming, the paper examines the likely levels and practical significance of the transient dynamic response. It shows that the levels of dynamic response are sufficiently severe to have important implications for the triggering of buckling and fatigue collapse characteristics. It is suggested that this phenomenon requires additional more-detailed consideration, including the provision of reliable predictions of transient slam pressure distributions and the levels and forms of hydrodynamic damping, as well as the effects of more practical shell and stiffening geometries, and ambient stress levels.