关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.     

Measurement and assessment of geometric imperfections in thin-walled panels

Thin-walled members may be subject to performance limitations arising through local or distortional buckling of slender elements comprising the cross-section of the member, or overall buckling of the member. The effects of structural instability may be aggravated by the presence of geometric imperfections in these elements. An investigation is presented into methods of measuring and assessing geometric imperfections in cold-rolled thin-walled steel panels. These methods can be used to characterise the geometry of prismatic thin-walled members that exhibit performance sensitivity due to geometric imperfections. The measurement procedures investigated include close-range photogrammetry, precise optical levelling, and the use of a co-ordinate measurement machine. The assessment procedure comprises a least-squares spectral decomposition of the measurements to characterise the imperfections existent in the panels under investigation, and estimates of the precision of the derived Fourier coefficients are used to inter-compare the three measurement procedures. The investigation has demonstrated that statistically significant imperfections may exist in thin-walled members at short and medium wavelengths, leading to a reduction in the load carrying capacity. Both optical levelling and the co-ordinate measurement machine technique can yield desirable results, but for high precision work, use of the co-ordinate measurement machine is recommended.     

Investigation of geometric imperfections and joint stiffness of support scaffold systems

This paper describes the findings from various site measurements of geometric imperfections of support scaffold systems, also known as falsework in industry. The measurements consist of out-of-straightness of the standards (uprights), out-of-plumb of the frame and loading eccentricity between the timber bearer and the U-head screw jack. The measurements were taken from different support scaffold construction sites before the pouring of concrete, representing actual initial geometric imperfections and loading eccentricity encountered in practice. The paper also reports the results of support scaffold joint tests. The tests were performed on randomly chosen used components to investigate the joint stiffness for rotations about vertical and horizontal axes. Tests were performed for various joint configurations (two-way, three-way, and four-way connections), bending axes, and loading directions. The statistical analysis of the data is presented in the paper for practical application in modelling and probabilistic assessment of support scaffold systems.     

The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.     

Effect of imperfections on wind-loaded cylindrical shells

The wind-induced buckling of thin-walled steel cylinders, such as silos and tanks, was investigated by wind-tunnel testing for a limited range of the parameters. While wind-buckling of short, stocky shells can be well represented by an equivalent uniform external pressure, long shells show quite a different behaviour, which is strongly influenced by the axial compression forces. This paper presents a study of this behaviour, based on numerical analyses and considering various types of imperfection shape. The effect of geometrical nonlinearity, as well as material plasticity, has also been included. A comparison with test results shows good agreement with the numerical results of imperfect shells, provided that special eigenmode-shaped modes of imperfections are excluded.     

Form of circumferential weld-induced imperfections for tapered-wall cylindrical shell structures

Initial geometric imperfections have a great effect on the buckling strength of thin-walled cylindrical shells under axial compression, and the circumferential weld-induced imperfection is usually the most deleterious imperfection form. Two axisymmetric imperfection forms proposed by Rotter and Teng have widely been employed in the buckling analysis of cylindrical shells. However, the applicability of the two forms for tapered-wall cylinders needs further study, since they are derived from the elastic bending theory for long thin-walled cylinders with a constant wall thickness. This paper presents a modified form of circumferential imperfection for tapered-wall cylinders. Finite element analyses are carried out by employing the trapezoidal strain field approach to model the welding process, and the obtained circumferential depression shapes are used to evaluate the availability of the modified imperfection form. It is shown that the modified imperfection form is reasonable for any wall thickness ratio between two adjacent strakes, and the most suitable shape function, which is very close to the FE results, can be obtained by giving suitable values of the roundness in the modified form.     

Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections

The effect of localized axisymmetric initial imperfections on the critical load of elastic cylindrical shells subjected to axial compression is studied through analytical modeling. Some classical results regarding sensitivity of shell buckling strength with respect to distributed defects having axisymmetric or asymmetric forms are recalled. Special emphasis is placed after that on the more severe case of localized defects satisfying axial symmetry by displaying an analytical solution to the Von Kármán–Donnell shell equations under specific boundary conditions. The obtained results show that the critical load varies very much with the geometrical parameters of the localized defect. These variations are not monotonic in general. They indicate, however, a clear reduction of the shell critical load for some defects recognized as the most hazardous isolated ones. Reduction of the critical load is found to reach a level which is up to two times lower than that predicted by general distributed defects.     

The measurement of imperfections in cylindrical thin-walled members

The structural behaviour of thin-walled circular cylindrical members has been shown to be imperfection sensitive. However, only little information of the exact nature of imperfections in such members is available. In this paper a method of measuring imperfections in circular cylindrical members is described, the method is simple to implement in a laboratory environment while providing accurate measurements. Numerical methods to process the measurements into three-dimensional imperfection maps are also presented along with an algorithm to distinguish between significant imperfection patterns and measurement ‘noise’. Results from a recent research project where this method has been used illustrate the derivations in this paper.     

Probabilistic analysis of secant piles with random geometric imperfections

The failure to achieve minimum design overlap between secant piles compromises the ability of a structure to perform as designed, resulting in water leakage or even ground collapse. To establish a more realistic simulation and provide guidelines for designing a safe and cost-effective secant-pile wall, a three-dimensional model of a secant pile, considering the geometric imperfections of the diameter and direction of the borehole, is introduced. An ultrasonic cross-hole test was performed during the construction of secant piles in a launching shaft in Beijing, China. Based on the test results, the statistical characteristics of the pile diameters and orientation parameters were obtained. By taking the pile diameter D, inclination angle β, and azimuth angle α as random variables, Monte Carlo simulations were performed to discuss the influence of different design parameters on the probability density functions of the overlap of secant piles. The obtained results show that the randomness of the inclination angle and pile diameter can be well described by a normal distribution, whereas the azimuth angle is more consistent with a uniform distribution. The integrity of the secant-pile wall can be overestimated without considering the uncertainty of geometric imperfections. The failure of the secant-pile wall increases substantially with increasing spatial variability in drilling inclination and diameter. A design flowchart for pile spacing under the target safety level is proposed to help engineers design a safe and economical pile wall.     

Vibration damping of cylindrical shells partially coated with a constrained viscoelastic treatment having a standoff layer

The task of providing lightly-damped shells with an enhanced modal damping is encountered in many applications. This paper explores the use of a standoff-layered viscoelastic damping treatment for cylindrical shells requiring a minimal distribution area and low added weight. It is shown that partial distribution of the treatment as damping patches can be more beneficial than using full coverage, provided the patches are located in regions of high modal strain energy, as determined from strain energy intensity distribution maps derived for the purpose. The analysis uses the finite element method, and a suitable curved shell element is formulated for the add-on damping treatment. Numerical studies show that the combination of partial coating and a standoff layer can offer a viable approach for achieving optimal damping in the presence of space and weight constraints.     

On the incorporation of equivalent member imperfections in the in-plane design of steel frames

This work deals with the incorporation of equivalent member imperfections in the global analysis of steel frames and, in particular, is intended to clarify the Eurocode 3 (EC3) provisions involved in such procedure. In fact, these provisions stem from the well-known “European column buckling curves”, which means that they are based on the behaviour of simply supported isolated members under uniform compression (columns). First, one addresses the geometrically non-linear behaviour of isolated columns displaying arbitrary support conditions and different initial geometrical configurations. Then, the results obtained are used to propose a systematic and rational method to evaluate the appropriate “equivalent initial imperfections” that need to be incorporated in the second-order global elastic analysis of a frame or isolated compressed member. This method (i) is fully consistent with the EC3 column buckling curves and (ii) adopts critical buckling mode shape initial imperfections with amplitudes determined by means of closed-form analytical expressions. In order to enable a better grasp of the concepts involved and also to illustrate the capabilities of the proposed methodology, several numerical examples are presented and discussed throughout the paper.     

Free vibrations of fluid-filled cylindrical shells on elastic foundations

The free vibration characteristics of fluid-filled cylindrical shells on elastic foundations are presented by a semi-analytical finite element method. A shell is discretized into cylindrical finite elements where shell governing equations based shape functions in the longitudinal direction are used instead of the usual simple polynomials. Non-uniformities of the foundations in the circumferential and longitudinal directions are handled by the Fourier series and an element mesh strategy, respectively. The fluid domain is described by the potential flow theory. The hydrodynamic pressure acting on shells is derived from the condition for dynamic coupling of the fluid-structure. The effect of fluid in a shell, shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells is investigated. Numerical results based on the present method converge more rapidly than those obtained by the simple polynomial formulation. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.     

Calculation of guyed masts in accordance with EN 1993-3-1 standard taking into account mast shaft geometrical imperfections

Selected problems concerning designing of guyed masts with lattice shaft in accordance with the “EN 1993-3-1: Design of steel structures. Part 3-1: Towers, masts and chimneys-Towers and masts” European standard have been described in this paper. The method of application of the mast shaft geometrical imperfections in calculations has been discussed. Based on the performed comparative analysis of a certain mast, the influence of such imperfections on the ultimate values of internal forces in the mast shaft has been demonstrated.     

3D buckling analysis of a cylindrical metal bin composed of corrugated sheets strengthened by vertical stiffeners

The paper presents 3D results of a quasi-static buckling analysis of a funnel-flow cylindrical metal bin composed of horizontally corrugated sheets strengthened by vertical columns. A linear buckling and a non-linear analysis with geometric and material non-linearity were carried out with a perfect and an imperfect real silo shell by taking into account axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1 and different initial geometric imperfections and load non-uniformities around the circumference. The calculated buckling forces were compared with the permissible one given by Eurocode 3.     

Finite element techniques for the analysis of cooling tower shells with geometric imperfections

Two finite element methods for analysing geometrically imperfect cooling tower shells are presented. In the first the geometry of the imperfection is modelled by the elements; in the second the imperfection is represented by an equivalent load on the shell. Axisymmetric and general shell elements have been considered.Results are given which show that the first approximation to the equivalent load is sufficiently accurate and that it is possible to represent local imperfections by axisymmetric imperfections which require less computation. It is also shown that axisymmetric elements should be used wherever possible, because of their greater efficiency, following the geometry of an axisymmetric imperfection but representing local imperfections by equivalent loads.     

基于可靠度的单层网壳稳定设计方法

基于可靠度的钢结构稳定设计理论,提出了通过抗力分项系数验算网壳结构稳定性的方法。在确定分项系数时,分别考虑了材料、几何初始缺陷和计算模式的不确定性,使用基于响应面函数的蒙特卡罗模拟方法对结构进行二阶弹塑性分析。首先对两个网壳试验模型的试验结果做了数值分析对比,验证了本文有限元模型的有效性。然后选择应用最广的K8作为重点对象,使用基于响应面函数的蒙特卡罗模拟方法对结构进行考虑初始缺陷的二阶弹塑性分析,得出了抗力分项系数。     

初始缺陷对张弦梁结构影响的有限元研究

张弦梁结构的初始缺陷主要包括几何缺陷和残余应力,对结构力学性能产生不利影响,但由于问题的复杂性和较高的分析成本,目前针对性研究还非常少,因而设计人员在进行张弦梁结构设计时通常不考虑初始缺陷的影响,从而可能使得结构存在一定程度的不安全因素.本文用有限元方法分析了初始缺陷对张弦梁结构预应力张拉阶段和工作阶段的力学影响,指出初始缺陷对预应力张拉阶段无明显影响,但几何缺陷对工作阶段的平面外位移有不可忽视的影响,应设法进行控制,并进一步指出通过在张弦梁上弦加侧向支撑的方法可以有效减小工作阶段的平面外位移,增加安全性.     

Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure

A reduced stiffness lower bound method for the buckling of laterally pressure loaded sandwich cylindrical shell is proposed. Also, an attempt is made to assess the validity of the proposed reduced stiffness lower bound with FEM numerical examples. In addition, the proposed method is compared with classical and Plantema's approaches of the buckling of the laterally pressure loaded sandwich cylindrical shell. Comparison of the proposed reduced stiffness lower bound with that obtained from non-linear FEM analysis verifies that it indeed provides a safe lower bound to the buckling of laterally pressure loaded sandwich cylindrical shells. The attractive feature of the proposed reduced stiffness method is that it can be readily used in designing laterally pressure loaded sandwich cylindrical shells without being concerned about geometrical imperfections.