Imperfection sensitivity of internally-pressurized torispherical shells

The imperfection sensitivity of torispherical shells subjected to internal pressure was investigated numerically, using the finite element displacement method. Imperfection patterns affine to the first buckling mode at the bifurcation points of the perfect structure were considered. Load-normal displacement curves were obtained for the pre- and postbuckling regions of the perfect computation model and also for imperfect computation models with different imperfection amplitudes. The dependence of the critical pressure and the postbuckling minimum on the imperfection amplitudes was presented graphically. Torispherical shells subjected to internal pressure failed to demonstrate any significant imperfection sensitivity for the imperfection patterns analysed.     

夹层板轴向受压时屈曲后性能的有限元分析

以Narayan Pokharel,Mahen Mahendran试验[1]模型为研究依据,用有限元法对受单向轴向压力作用的夹层板进行了屈曲以及屈曲后性能分析。根据Winter公式计算出了板件的有效宽度,并与有限元计算结果以及试验结果进行比较,发现当夹层板宽厚比较大时,Winter公式过高地估计了板件的有效宽度,结果是偏于不安全的。最后,提出了有效宽度的建议公式。     

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.     

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.     

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

A postbuckling analysis is presented for a circular cylindrical shell of finite length which is subjected to combined loading of external liquid pressure and axial compression. The formulations are based on a boundary layer theory which includes effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometrical imperfection of shells. The analysis uses a singular perturbation technique to determine interactive buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect cylindrical shells. Typical results are presented in dimensionless graphical form.     

Influence of autoclaving process parameters on the buckling and postbuckling behaviour of thin-walled channel section beams

The postbuckling behaviour and load carrying capacity of thin-walled composite channel sections subjected to uniform compression are presented. An analysis of the influence of parameters of the composite manufacturing process on strength properties and load carrying capacity of the thin-walled structure made of this composite has been conducted. The microstructure characteristics of composites is presented and discussed. The postbuckling behaviour and load carrying capacity of thin-walled channel section columns subjected to compression have been determined with the finite element method. The ANSYS software has been employed.     

Buckling and postbuckling investigations of imperfect curved stringer-stiffened composite shells. Part B: Computational investigations

Computational investigations of the buckling and postbuckling behaviour of a stringer-stiffened composite wing torsion box employing the finite element method are presented. Perfect and imperfect configurations — considering geometrical imperfections as well as initial stresses - are discussed. Two different loadcases are investigated: pure axial loading and axial loading with a superimposed constant torsion moment. The buckling behaviour is determined by tracing the load-deflection curves using Riks' path following method. Additional investigations, such as accompanying eigenvalue analyses and first-ply failure calculations, are performed for the first loadcase. Special attention is put on the modelling of the stiffened regions, where eccentrically placed layers have to be taken into account due to the bonding of the stiffeners to the inner surface of the box. The results show interesting phenomena, such as additional buckling points in the postbuckling region, which, however, can hardly be detected by simply considering the load-axial displacement path.     

Inelastic buckling behavior of stocky plates under interactive shear and in-plane bending

Inelastic buckling and postbuckling behavior of stocky plates under combined shear and in-plane bending stresses are investigated and compared to slender plates. Aluminum and steel plates having various slenderness ratios are modeled and analyzed by means of (i) numerical nonlinear finite element method and (ii) theoretical p-Ritz energy method; and both results are compared to the classic interaction equation. It is observed that whereas in slender plates, elastic buckling occurs prior to the material's proportional limit load, stocky plates buckle in an inelastic way within the post-yield stage. In contrast to slender plates with considerable postbuckling reserves, the buckling of stocky plates is immediately followed by softening. In addition, it is shown that the classic interaction equation overestimates buckling loads; and therefore, a modified equation that can safely be applied to both stocky and slender plates is proposed.     

Asymmetric interactive buckling of thin-walled columns with initial imperfections

In this paper the effect of the interaction between two or more simultaneous buckling modes on the postbuckling behaviour of uniformly compressed thin-walled members (TWM) is analysed by means of the general theory of elastic stability. The analysis is restricted to third-order terms of the energy expansion and therefore can be fruitfully applied to the investigation of structures with asymmetric postbuckling behaviour only. Initial imperfection effect is taken into account. A simplified procedure is suggested for solving the nonlinear equations relative to the evaluation of the bifurcated paths. By using the finite strip method an extensive parametric analysis is performed. It is found that when the flexural-torsional (FT) buckling interacts with a local symmetric and antisymmetric mode, sensitivity to initial inperfections is remarkable and is comparable to the one arising from the interaction between the Euler (E) and any local buckling.     

Stability analysis of stiffened plates by finite strips

The stability analysis of stiffened plates by means of the finite strip method is presented. The studies are based on the thin shallow theory, giving nonlinear strain displacement relations, but linear curvature displacement relations. The nonlinear equilibrium equations are obtained by the principle of incremental virtual work, using finite strip discretization. The higher order strip with one internal nodal line is applied. It is shown that considerable improvements can be obtained using this kind of strip. It is especially true for the postbuckling analysis. Numerical examples of the strength of stiffened plates in compression are carried out, covering a range of plate and stiffener slenderness.     

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.     

弹性支承单层柱面网壳稳定性

本运用非线性有限元全过程分析方法，结合新建的成都双流机场候机楼屋面大跨度单层柱面网壳，对弹性支承的大跨度单层柱面网壳结构的稳定性进行了分析，对比了不同支承条件、不同矢跨比和不同杆件截面对弹性支承的单层柱面网壳稳定性的影响，得出了有实际应用价值的结论。     

Thermal postbuckling of laminated composite skew plates with temperature-dependent properties

Thermal postbuckling and consequently, the role of temperature dependence of material properties on the thermal postbuckling behavior of laminated composite skew plates have not been addressed in literature. Hence, this problem is investigated here. The plate governing equations are based on the first-order shear deformation theory (FSDT) and the geometrical nonlinearity is modeled using Green’s strain tensor in conjunction with the von Karman assumptions. Since the problem is geometrically and physically nonlinear, the differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the critical temperature (bifurcation point) and consequently the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated skew plates. After validating the formulation and the method of solution, the effects of temperature dependence of the material properties on the postbuckling characteristic of laminated skew plates with different skew angle, boundary conditions, length-to-thickness ratio, number of layers and ply layout are investigated.     

Semi-analytical postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending

A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh–Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises’ yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer program based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.     

Imperfection sensitivity of plate girder webs subjected to patch loading

This paper is aimed at studying the influence of initial geometric imperfections on the postbuckling behavior of longitudinally stiffened plate girder webs subjected to patch loading. A sensitivity analysis is conducted herein using two approaches (deterministic and probabilistic) in order to investigate the effect of varying imperfection shape and amplitude on both, the postbuckling response and ultimate strength of plate girders under patch loading. This sensitivity analysis is performed by means of nonlinear finite element analysis. At first, the initial shape imperfections are modeled using the buckling mode shapes resulting from an eigenvalue buckling analysis. Thereafter, the amplitude of the buckling shapes for the various modes is varied, and then introduced in the nonlinear analysis. The results show the influence of these modes and amplitudes on the resistance to patch loading.     

Wind buckling of tanks with conical roof considering shielding by another tank

Oil storage tanks are usually arranged in groups in tank farms, and this configuration may affect their buckling and postbuckling strength under wind loads. The assessment of wind action on tank structures is performed in this work by means of wind tunnel experiments to evaluate the pattern of pressure distribution for a tank which is shielded by another tank under various configurations and separation between them. The experimental results show significant changes in pressures due to shielding effects. In a second stage the structural response under the pressures previously evaluated is performed by finite element analysis using both linear bifurcation and geometrically nonlinear analysis. Results of two-tank interaction are compared with those of an isolated tank. Based on the results, it is concluded that the changes in wind pressures due to group effects induce changes in buckling loads and in the associated deflected patterns.     

Inelastic postbuckling response of steel trusses under thermal loadings

The paper presents a finite element procedure for the inelastic postbuckling analysis of steel trusses under thermal loadings. First, the force-displacement relation in total form is derived. Then an element is formulated to simulate the inelastic nonlinear behavior of truss members under thermal loadings. The actions due to restraint against elongation and material softening are referred to as thermal loads and reduced member loads, respectively. To account for the material softening at elevated temperatures, the EC3 reduction factors are adopted. The trusses are assumed to be either under constant temperature but increasing loads, or under constant loads but rising temperature. The generalized displacement control (GDC) method is modified to solve for the postbuckling paths of the trusses. The results indicate that the critical load (or temperature) of a truss decreases drastically as the preheating (or preload) increases, and that a truss shows a breaking strength much smaller than the elastic critical load, if the effect of yielding is taken into account. From the design point, the overall capacity of an elastic truss can be well represented by the critical load-temperature curve.     

Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion

Buckling and postbuckling behaviors of imperfect cylindrical shell subjected to torsion are investigated. The governing equations are based on the Karman–Donnell-type nonlinear differential equations. A boundary layer theory of shell buckling is applied to obtain the analytic solutions that meet the boundary conditions strictly. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the current theory gives quite good estimates of the postbuckling paths of cylindrical shells. The effects of the geometric parameters on the buckling and postbuckling behaviors of the cylindrical shells are analyzed. It is confirmed that the postbuckling equilibrium paths of cylindrical shells subjected to torsion are unstable and the relatively shorter shells have higher postbuckling equilibrium paths. Finally, the effects of the initial imperfections on the buckling and postbuckling behaviors of the cylindrical shells are clarified. The illustrated results of the imperfect shells with different initial transverse deflections show that extremely small imperfections do indeed reduce the buckling loads and make the postbuckling equilibrium paths be lower. The buckling and postbuckling of cylindrical shells under torsion exhibit obvious imperfect sensitivity. Furthermore, the effects become greater following with the larger imperfections.     

Dynamic analysis methodology for progressive failure of truss structures considering inelastic postbuckling cyclic member behavior

Over the years, several catastrophic collapses of truss structures have been reported. Sudden failure or reduction in member capacity of a single member in a truss structure gives rise to dynamic force redistribution in the remaining members and may lead to progressive collapse of the entire structure. During failure, truss members can undergo inelastic cyclic behavior (including postbuckling in compression and yielding in tension) that may not have existed in the intact structure. This paper presents a methodology to incorporate the inelastic cyclic member force-deformation behavior in the dynamic analysis of truss structures and at the same time incorporates the possible dynamic effects arising from the sudden change in load carrying capacity of a member due to failure or buckling/postbuckling. The method tracks and generates the force-deformation characteristics of every member of the truss at each incremental time step. The continuous change in the load-carrying capacity and the stiffness of members during the nonlinear force-deformation history has been incorporated in the analysis scheme using the Pseudo-force approach. The solution methodology for obtaining the dynamic response of the structure is based on the finite element technique and considers elasto-plastic material and large deformation geometric nonlinearities. The methodology is applied to a two-dimensional three-member toggle redundant truss subjected to external static, quasi-static, and dynamic (sinusoidal and ramp) loads. Results delineating the effects of the inelastic cyclic axial force-deformation relation of each member and the time variation of joint displacements and member forces are presented for each loading condition. The results show that there exist cases where modeling a compression member with its actual postbuckling behavior, which although has some reserve load carrying capacity, are more critical than the case where the same member is considered to suddenly lose its full load carrying capacity at its buckling load.     

温度荷载作用下钢桁架的弹塑性后屈曲反应分析

针对温度荷载作用下钢桁架的弹塑性后屈曲分析提出一个有限元计算方法。首先,推导出整体的力-位移关系。然后构建一个有限元模型,用于模拟温度荷载作用下桁架构件的弹塑性非线性性能。由于抵抗伸长和材料软化而产生的作用力,分别作为温度荷载和渐减的结构荷载考虑。为考虑到温度升高时材料的软化性能,采用了EC3中提议的折减系数。桁架假定状态为经受温度恒定下荷载逐渐加大,或者是恒定荷载下温度逐渐升高。将修正后的广义位移控制法用于解决桁架的后屈曲反应。结果显示:桁架的临界荷载(或温度)会随着预加热(或预加载)的增加而明显降低,而且如果考虑到屈服的影响,桁架的断裂强度会比弹性临界荷载小很多。从设计观点来看,临界荷载-温度曲线可以很好地表现弹性桁架的整体性能。