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。     

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.     

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 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.     

A semi-analytical model for local post-buckling analysis of stringer- and frame-stiffened cylindrical panels

A fast semi-analytical model for the post-buckling analysis of stiffened cylindrical panels is presented. The panel is comprised of a skin (shell) and stiffeners in both longitudinal (stringers) and circumferential direction (frames). Local buckling modes are considered where the skin may buckle within a bay and may induce rotation of the stiffeners. Stringers and frames are considered as structural elements and are thus not ‘smeared’ onto the skin. Large out-of-plane deflections and thus non-linear strain–displacement relations of skin and stiffeners are taken into account. The displacements of skin and stiffeners are approximated by trigonometric functions (Fourier series). First, a linear buckling eigenvalue analysis is carried out and some combination of buckling eigenmodes is chosen as imperfection. Then the load history is started and the Fourier coefficients are determined by minimizing the stiffened panel's energy at each load level. A curve-tracing algorithm, the Riks method, is used to solve the equations. The present model can be used to assess the post-buckling behavior of stiffened panels, for example, aircraft fuselage sections.     

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.     

Strength of damage ring and orthogonally stiffened shells—part I: Plain ring stiffened shells

This paper is the first of two parts describing the procedure of, and results from, a series of tests on ring and orthogonally stiffened thin-walled shells. The primary purpose of the work was to investigate the collapse behaviour of the shells subjected to simulated damage and then tested under a combination of external pressure and axial compressive loading.

The test specimens consisted of two five-bay cylinders stiffened with plain ring stiffeners; two three-bay cylinders stiffened with T-ring stiffeners and two three-bay orthogonally stiffened cylinders, one with 20 stringers, and the other with 40.

This Part I deals with the tests on the plain ring stiffened cylinders.

A major conclusion that can be drawn from the results of these few tests is that although the design of the plain rings was adequate to prevent general buckling of the undamaged shells, they were ineffective in limiting the area of initial damage when the shell was subjected to pressure loading.     

Experimental Investigation of Damaged Stiffened Cylindrical Shells

Thin walled cylindrical shells, stiffened with rings and longitudinal stiffeners, are components in marine and aeronautical structures. The shells may become damaged in use and require some form of repair to restore some of the strength which may have been lost due to the damage. This paper presents the results of an experimental investigation into the effects of damage, and the efficacy of one method of repair, on an orthogonally stiffened shell. The shells were tested with combinations of external pressure and axial compressive loading. It is shown that local damage reduces the strength of the shell and that the addition of the chosen form of strengthening does not restore the intact strength. However, the efficacy of the repair is greater for a combination of pressure and axial loading.     

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 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.     

Torsional buckling behaviour of stiffened cylinders under combined loading

In this study cylindrical boundary conditions for finite element analysis are formulated that allow torsional displacement and buckling of a sector of a cylinder of half axial height, and of a circumferential arc angle that will divide into 360°. Finite element tests are carried out on un-stiffened elastic cylinders to verify the method of analysis against classical elastic torsional buckling theory.Elastic–plastic limit point finite element tests are carried out on ring and stringer stiffened and stringer stiffened cylinders to investigate the effects of stiffeners on post-buckling behaviour in torsion.A stringer stiffened cylinder is subjected to many combinations of axial force and surface pressure in the elastic range of response and then tested to failure in torsion to investigate the effects of axial and surface pressure loads on the resistance to plastic collapse in torsion.     

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.     

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.     

Experiments on the deflection and buckling behavior of ring-stiffened cylindrical shells under wind pressure

Buckling behavior of thin circular cylindrical shells stiffened by one or two rings has been studied in a wind tunnel. Both the prebuckling deflection and the buckling load were measured with a variety of a specimens in a smooth flow, and the effects of the stiffeners on them were examined. For comparison purposes, the buckling load of each specimen under hydrostatic pressure was also measured.The results indicate that the prebuckling deflection and ovalling oscillation can be significantly suppressed by relatively light stiffeners. As the flexural rigidity, E_sI_s, of the ring increases, the axial buckling mode changes from a symmetric one accompanied by ring deflection to another one with the rings acting as nodes, at a critical value of E_sI_s. This critical value was found to be nearly equal to that for the hydrostatic pressure. On the other hand, contrary to the hydrostatic pressure case, the buckling load gradually increases with an increase in E_sI_s, even for values of E_sI_s greater than the critical value.     

Numerical and experimental investigations on the compression behaviour of stiffened plates

The main objective of this paper is to present the results of the finite element method for non-linear analysis of stiffened plates subjected to axial compression load considering post-buckling behaviour up to collapse. For this purpose two series of well executed experimental data on longitudinally stiffened steel plates with and without transversal stiffeners subjected to uniform axial in-plane load carried out to study the buckling and post-buckling up to final failure have been chosen. The first series are those of Ghavami where the influences of stiffener cross-section of the type rectangular (R), L and T, their spacing and the presence of rigid transversal stiffeners have been studied. The second series of Tanaka & Endo, where the behaviour of stiffened plates having three and two flat bars for longitudinal and transversal stiffeners respectively were analysed. For the purpose a well-established commercially available Finite Element program ANSYS has been chosen. The selected element was SHELL43, which can trace the full-range, elastic-plastic behaviour of the stiffened plates. It is seen that the simulated results of FEM are in good consistency with the test results.     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

钢-混凝土组合薄壳屋盖的研究进展--施工阶段钢底壳的模型试验研究

钢-混凝土组合薄壳屋盖(Comshell屋盖体系)由兼作永久模板并替代钢筋的薄壁加劲钢底壳和现浇混凝土两部份组成。薄壁钢底壳由模块化单元件通过螺栓连接而成,单元件呈无盖扁盒状,由底板及周边板组成。其周边板在钢壳上构成两个方向的薄壁加劲板。这一新体系保留了混凝土薄壳屋盖的所有优点。又不需要使用临时模板．并大幅减少临时支撑。本文对这种新型结构体系及其各种可能的破坏模式进行了简单介绍,并给出了针对该结构体系施工阶段稳定性所进行模型试验的主要结果。     

Worst Multiple Perturbation Load Approach of stiffened shells with and without cutouts for improved knockdown factors

An optimization framework of determining the worst realistic imperfection was proposed by the present authors to study the reduction of the load-carrying capacity of unstiffened cylindrical shells. However, with regard to stiffened shells, especially when cutouts are included, the dimple combination pattern should be judged in a more rational manner. In this study, node coordinates are utilized to describe the position of each dimple-shape imperfection for Worst Multiple Perturbation Load Approach (WMPLA), which is an improvement of the MPLA using an optimization algorithm to find the application positions that will reduce the buckling load. Further, a novel method to determine the density of possible positions of dimple-shape imperfections is proposed based on eigenmode shape for stiffened shells without cutout. In addition, the effects of cutouts on the proposed method are investigated in detail. The effectiveness of the proposed method is demonstrated by comparison of several conventional methods to obtain improved knockdown factors (KDFs).     

Nonlinear mechanical,thermal and thermo-mechanical postbuckling of imperfect eccentrically stiffened thin FGM cylindrical panels on elastic foundations

This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FGM cylindrical panels on elastic foundations subjected to mechanical loads, thermal loads and the combination of these loads. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. Governing equations are derived basing on the classical shell theory incorporating von Karman–Donnell type nonlinearity, initial geometrical imperfection, the Lekhnitsky smeared stiffeners technique and Pasternak type elastic foundations. Explicit relations of load–deflection curves for FGM cylindrical panels are determined by applying stress function and Galerkin method. The effects of material and geometrical properties, imperfection, elastic foundations and stiffeners on the buckling and postbuckling of the FGM panels are discussed in detail. The obtained results are validated by comparing with those in the literature..     

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.