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.     

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.     

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.     

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.     

A study on the mean crushing strength of hexagonal multi-cell thin-walled structures

This paper presents a study to extend a previously developed theoretical model to predict the crushing behavior of hexagonal multi-cell thin-walled structures, e.g. honeycombs under quasi-static loading. The low speed compressive tests were conducted on three types of aluminum honeycomb panels. Based on the test data and existing theoretical models, a new analytical model was developed to predict its mean crushing strength. Some key parameters in this new model were determined with the finite element (FE) method. Then the predictions based on the new model were compared with the results reported in the published literature. It has been shown that the new model has a similar or better performance compared to its counterparts. Considering its concise expression, the newly developed model can be deemed as a convenient computational tool in engineering practice.     

The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures

Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability.     

Seismic analysis of steel structures considering damage cumulation

The research on the development of a reliable analytical model for seismic analysis of steel structures is presented. The non-linear damage cumulation hysteretic model incorporating the deterioration of stiffness, strength and strain hardening for structural steel is proposed and validated. The complete loading history, energy dissipation and the effect of the maximum plastic strain are taken into account in the model. The constants in the model are determined from regression analysis of experimental results of simple standard tensile and cyclic tests. Finite element formulations for beam and structural solid element considering the damage cumulation are derived. A computer program capable of calculating the hysteretic model of steel members, predicting the damage state and crack initiation, and carrying out non-linear time history seismic analysis of steel structures is developed. Solutions obtained from the model are in good agreement with experimental results. It was demonstrated that the damage cumulation effect is considerable and important in structural seismic analysis.     

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.     

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.     

中国空间结构六十年

综述了自建国以来空间结构在中国的进展情况。简要地描述了薄壳结构、网架结构、网壳结构、索结构和膜结构的发展历程及其特点,反映了中国在空间结构所取得的巨大成就。最后讨论了今后中国空间结构的发展前景并提出需要注意的问题。     

Recent advances on postbuckling analyses of thin-walled structures: Beams, frames and cylindrical shells

The lateral postbuckling response of thin-walled structures such as bars and frames with members having steel rolled shapes as well as circular cylindrical shells under axial compression is thoroughly reconsidered. More specifically via a simple and very efficient technique it is found that beams with rolled shapes (symmetric or non symmetric) under uniform bending and axial compression exhibit a stable lateral-torsional secondary path with limited margins of postbuckling strength. New findings for the static and dynamic stability of frames with crooked steel members-due to the presence of residual stresses-are also reported. It is comprehensively established that the coupling effect due to initial crookedness and loading eccentricity may have a beneficial effect on the load-carrying capacity of the frames. Moreover, simple mechanical models are proposed for simulating the buckling mechanism of axially compressed circular cylindrical shells. Very recently Bodner and Rubin proposed an 1-DOF mechanical model whose buckling parameters correlated to those of the shells by using an empirical formula based on experimentally observed shell buckling loads. In the present analysis a new 2-DOF model for the static and dynamic buckling of axially compressed circular cylindrical shells, which can include mode coupling, is presented.     

网壳结构的屈曲分析研究(二):壳体屈曲和缺损的非线性分析

介绍了柯以特理论,在讨论了壳体临界荷载和敏感度、缺损的类型,并简单地回顾上个世纪60年代以来普遍采用的平衡路线跟踪方法的原理的基础上,提出基于广义稳定的概念、屈曲的定义及其数学描述的屈曲路线跟踪方法.通过分析,讨论了影响网壳结构屈曲类型及分枝荷载的因素,为空间格构结构中常用的网壳结构设计临界荷载值的确定提出了建议.     

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.     

A Koiter's perturbation strategy for the imperfection sensitivity analysis of thin-walled structures with residual stresses

This paper suggests a strategy for the imperfection sensitivity analysis of elastic thin-walled structures with notable residual stresses. The analysis is carried out by means of a Koiter's perturbation approach. The concept of imperfection, traditionally associated with geometric and load factors, is extended in this paper to the residual stresses. The strategy is implemented in a FEM code. A comparison of the obtained results allows a discussion on the accuracy and the influence of the different coefficients connected to the asymptotic analysis of the residual stresses.     

基于ABAQUS的钢管混凝土柱有限元分析

ABAQUS作为一款大型有限元分析软件,其在工程结构研究领域得到了大量的应用。本文基于混凝土损伤塑形模型,采用该软件对两钢管混凝土轴压柱进行有限元模拟,讨论了钢管混凝土柱的三维非线性分析的建模方法和模型参数取值。研究了钢管混凝土柱的破坏特征、应力和应变特点等,并与试验结果对比,验证有限元模拟结果的可靠度。     

Lower bound estimation of load-carrying capacity of thin-walled structures with intermediate stiffeners

The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with the interactive buckling of thin-walled structures with central intermediate stiffeners under axial compression and/or a constant bending moment. The structures are assumed to be simply supported at the ends. The lower bound estimation of load-carrying capacity on the basis of the post-buckling behaviour of thin-walled structures with imperfections is studied when the distortional deformations are taken into account. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed using the transition matrix method. The present paper is a continuation of previous work by the authors (Int. J. Solids Struct. 32 (1995) 1501; 33 (1996) 315; 37 (2000) 3323), where the interactive buckling of thin-walled beam-columns with central intermediate stiffeners in the first- and the second-order approximation were considered. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The results obtained are compared with data reported by other authors.     

具有缺陷和应力限值的预应力钢支撑柱屈曲性能

通过预应力支撑加固的钢柱,一般增加了轴向抗压强度。过去,十分强调获得更高的临界屈曲荷载,然而,后屈曲性能是结构安全性和功能的重要保证。对具有几何缺陷和与可能的材料失效相关的应力极限的支撑柱的屈曲性能进行检验。考虑有几何缺陷支撑柱的屈曲性能,采用Rayleigh-Ritz方法对几何非线性模型公式化,并通过有限元方法进行验证。研究显示：对于承受最高临界荷载的预应力状态,系统对有几何缺陷的柱更为敏感。对某一给定形状结构,实际的最大荷载似乎随着预应力的增加而增加。研究建议：最佳的预应力取值应该大于基于传统方法的线性分析的结果。     

On some aspects of the modified TSAI-WU criterion in thin-walled composite structures

For anisotropic materials, Tsai-Wu [1] proposed the failure criterion that takes into account the difference in strength due to positive and negative stresses. Hashin [2] pointed to some internal incoherencies of the function of material effort with respect to stress parameters. The minimum of the External Function does not coincide with the unstressed state. Therefore, the criterion presented by Tsai-Wu [1] has limited possibilities of application for optimization purposes. A modification of the Tsai-Wu criterion, needed in the case of the multi-criterion optimal design of thin-walled composite structures, has been presented. A proposal of the evaluation of the load carrying capacity of multi-layered composites with respect to their failure mode has been put forward.     

A probabilistic formulation of the damage evolution law

The inhomogeneous character of composites has many consequences regarding their behaviour. Using a two-level approach (micro- and macro-), a scalar is constructed where the damage of a representative volume of material is no longer considered as deterministically known, but results from a probabilistic formulation. A probabilistic elastic—brittle behaviour is assumed at the micro-level and the evolution law of damage results as a sum, through a loose parallel bundle of size N_t (Daniel's model) over all the micro-states. The approach developed appears as an intermediate model between those arising in the fields of Damage Mechanics and Probabilistics Brittle Fracture.

The model has been implemented in a finite element code and some significant results are presented. A concrete specimen is loaded in pure compression and pure tension, with the external boundary conditions remaining deterministic. The interaction between the external loading and the inhomogeneities creates some anisotropy and it is found that the specimen behaves more like a structure than like a theoretical volume of material.