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.     

Vibration, buckling and dynamic stability of cracked cylindrical shells

The presence of cracks in a structure can considerably affect its behaviour. This paper presents a finite element study on the vibration, buckling and dynamic stability behaviour of a cracked cylindrical shell with fixed supports and subject to an in plane compressive/tensile periodic edge load. The effects of crack length and orientation are analysed. Under tension load, the results show that the frequency of the shell initially increases with the load, but then decreases as the load further increases leading to buckling due to tension load. The size and the orientation of the crack and the loading parameter can all have a significant effect on the dynamic stability behaviour of the shell under both compressive and tensile loading. The effects of these parameters are discussed in detail.     

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.     

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.     

Vibration correlation technique for the estimation of real boundary conditions and buckling load of unstiffened plates and cylindrical shells

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.     

Numerical and experimental investigations on buckling of steel cylindrical shells with elliptical cutout subject to axial compression

The effect of cutouts on load-bearing capacity and buckling behavior of cylindrical shells is an essential consideration in their design.In this paper, simulation and analysis of thin steel cylindrical shells of various lengths and diameters with elliptical cutouts have been studied using the finite element method and the effect of cutout position and the length-to-diameter (L/D) and diameter-to-thickness (D/t) ratios on the buckling and post-buckling behavior of cylindrical shells has been investigated. For several specimens, buckling test was performed using an INSTRON 8802 servo hydraulic machine and the results of experimental tests were compared to numerical results. A very good correlation was observed between numerical simulation and experimental results. Finally, based on the experimental and numerical results, formulas are presented for finding the buckling load of these structures.     

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.     

Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression

A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.     

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.     

Buckling of intermediate ring supported cylindrical shells under axial compression

This paper is concerned with the elastic buckling of axially compressed, circular cylindrical shells with intermediate ring supports. The simple Timoshenko thin shell theory and the more sophisticated Flügge thin shell theory have been adopted in the modeling of the cylindrical shells. We used these two representative theories to examine the sensitivity of the buckling solutions to the different degree of approximations made in shell theories. By dividing the shell into segments at the locations of the ring supports, the state-space technique is employed to derive the solutions for each shell segment and the domain decomposition method utilized to impose the equilibrium and compatibility conditions at the interfaces of the shell segments. First-known exact buckling factors are obtained for cylindrical shells of one and multiple intermediate ring supports and various combinations of boundary conditions. Comparison studies are carried out against benchmark solutions and independent numerical results from ANSYS and p-Ritz analyses. The influence of the locations of the ring supports on the buckling behaviour of the shells is examined.     

Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression

Buckling and postbuckling behaviour of perfect and imperfect cylindrical shells of finite length subject to combined loading of external pressure and axial compression are considered. Based on the boundary layer theory which includes the edge effect in the buckling of shells, a theoretical analysis for the buckling and postbuckling of circular cylindrical shells under combined loading is presented using a singular perturbation technique. Some interaction curves for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, and it is shown that both agree well. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of cylindrical shells have also been discussed.     

对轴压力作用下带有椭圆形开孔的圆柱形壳体屈曲的数值和试验研究

在圆柱形壳体的设计中,开孔对于其承载能力及屈曲性能的影响非常大。采用有限元方法对具有不同尺寸开孔的薄壁钢圆柱形壳进行模拟和分析,分析了开孔的位置、长度与直径比值（L／D）和直径与厚度比值（D／t）对圆柱形壳届曲和后屈曲性能的影响。采用INSTRON 8802液压系统对一些构件进行屈曲试验,并将试验结果与数值计算结果进行对比发现,两者具有非常好的一致性。最后,基于试验和数值分析结果,提出计算这类结构屈曲荷载的公式。     

Stability of circular cylindrical steel shells under combined loading

Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.     

Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method

This paper presents the Ritz method for the elastic buckling analysis of shells with ring-stiffeners under general pressure loading. The stiffeners may be of any cross-sectional shape and arbitrarily distributed along the shell length. Using polynomial functions multiplied by boundary equations raised to appropriate powers as the Ritz functions, the method can accommodate any combination of end conditions. As far as it is known, the Ritz method has not been automated in this way for the buckling of ring-stiffened shells. By formulating in a nondimensional form, generic buckling solutions for shells with various end conditions, stiffener distributions and under various pressure distributions, were presented. These new buckling solutions should serve as useful reference sources for checking the validity and accuracy of other numerical methods and software for buckling of cylindrical shells. This paper also shows that the appropriate distribution of ring stiffeners can lead to a significant increase in the buckling capacity over that of a stiffened shell with evenly spaced and identical ring stiffeners.     

Buckling of steel cylindrical shells with an elliptical cutout

Numerical simulation and analysis of steel cylindrical shells with various diameter and length having an elliptical cutout, subjected to axial compression were systematically carried out in this paper. The investigation examined the influence of the cutout size, cutout angle and the shell aspect ratios L/D and D/t on the pre-buckling, buckling, and post-buckling responses of the cylindrical shells. For several specimens, an experimental investigation was also carried out via an INSTRON 8802 servo hydraulic machine and the results obtained from the experiments were compared with numerical results. A very good accordance was observed between the results obtained from the finite element simulation and the experiments. Furthermore, some equations in the form of a buckling load reduction factor were developed.     

Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells – FEM study

The paper is devoted to buckling and post-buckling problems of an elastic seven-layered cylindrical shell under uniformly distributed pressure. The shell is an untypical sandwich structure composed of main corrugated core and two three-layer faces. Numerical FEM model for the shell has been elaborated. The calculations have been performed with the use of the ANSYS code for elastic shells of different dimensions. The linear and non-linear analyses of the shells have been performed with the use of the finite elements method. Critical pressure and equilibrium paths for the family of seven-layered shells subjected to uniformly distributed external pressure are calculated. The influence of corrugation pitch of main core and the length of the shell on the critical pressure has been determined. The results of these investigations are presented on the graphs.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

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。     

外压作用下偏心加劲功能梯度圆柱壳的非线性屈曲和后屈曲分析

通过解析法研究外压作用下功能梯度加劲薄圆柱壳的非线性屈曲和后屈曲性能。通过其在内部的偏心环和纵梁对壳体进行加固,假定壳体和加固件的材料性能在厚度方向为连续梯度。根据VonKarman理论中的刚度法和传统的壳理论推导出基本关系和平衡方程,可更准确地选择三种关于挠曲的近似公式,且使用盖勒金法得出的显式表达式可以推测出临界荷载和后屈曲压力-挠曲曲线。数值结果显示了加固件能有效地增强壳体稳定性。     

Experimental collapse of thin cylindrical shells submitted to internal pressure and pure bending

A thin-walled pressurised cylindrical shell is sensitive to buckling phenomena when it experiences locally a compressive stress. It is often considered that its behaviour under bending is rather similar to pure compression, but very few are the experimental investigations that precise the real behaviour of a thin pressurised cylinder submitted to a bending load. A large amount of experimental results is presented here, obtained on thin shells (550<R/t<1450) of moderate length (L/R≈2). The evolution of the cylinders' behaviour that has been recorded when internal pressure increases is outlined. It is shown that one must distinguish between local buckling and global collapse of the structure. A comparison of our experimental data to design recommendations given by two standards (NASA SP8007 and Eurocode 3) is finally achieved, putting in advance safety margins provided by these codes.