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.     

An experimental study on externally pressurized stiffened and thickened cylindrical shells

It has long been identified that stiffening of steel shells is one of the most effective ways of enhancing the capacity of these structures. Stiffeners largely in the form of welded elements have been employed to strengthen shell structures in which the stiffeners generally cover the whole length of the structure. In this research the effect of partial and full length stiffening of shells was studied in which the stiffeners were attached without welding to avoid the adverse effect of the residual stresses. Furthermore, local thickening of the shells by the same stiffening strips was investigated and the results were evaluated against the plain specimen. The effect of strengthening provided by local thickening was slightly less but comparable to that provided by the stiffeners.     

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。     

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.     

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。     

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.     

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.     

Active/passive control of sound radiation and power flow in fluid-loaded shells

The vibration and noise radiation from fluid-loaded cylindrical shells are controlled by using multiple stiffeners and passive constrained layer damping treatment. Dynamic and fluid finite elements are developed to study the fundamental phenomena governing the coupling between the stiffened shell, with and without damping, and the fluid domain surrounding it. The models are used to predict the response of the shell and to evaluate the effect of stiffening rings and damping treatment on both the structural vibration and noise radiation in the fluid domain. The geometry of the shell and fluid domain allows the formulation of a harmonic-based model, which uncouples the fluid–structural response of modes corresponding to different numbers of circumferential nodes.In this study, it is shown that stiffening of the shell reduces the amplitude of the vibration and noise radiation, particularly for high-order lobar modes. The attenuation of the shell response and sound radiation can be increased significantly through the application of passive constrained layer damping treatments on the inner surface of the stiffening rings.     

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.     

Effect of inplane edge constraints on natural frequencies of simply supported doubly curved shallow shells

Reasonably accurate natural frequencies are presented for simply supported shallow shells on rectangular planform subjected to 55 possible combinations of edge constraints. Thin shallow shell theory is used. Accurate natural frequencies of doubly curved shallow shells are presented and can be used for benchmarking by researchers as well as reference data for practicing engineers. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.     

A comparative study of concrete properties using coconut shell and palm kernel shell as coarse aggregates

The high cost of conventional building materials is a major factor affecting housing delivery in Nigeria. This has necessitated research into alternative materials of construction. This paper presents the results of an investigation carried out on the comparative cost analysis and strength characteristics of concrete produced using crushed, granular coconut and palm kernel shells as substitutes for conventional coarse aggregate in gradation of 0%, 25%, 50%, 75% and 100%. Two mix ratios (1:1:2 and 1:2:4) were used. A total of 320 cubes of size 100×100×100 mm were cast, tested and their physical and mechanical properties determined. The results of the tests showed that the compressive strength of the concrete decreased as the percentage of the shells increased in the two mix ratios. However, concrete obtained from coconut shells exhibited a higher compressive strength than palm kernel shell concrete in the two mix proportions. The results also indicated cost reduction of 30% and 42% for concrete produced from coconut shells and palm kernel shells, respectively. Considering the strength/economy ratio, it was concluded that coconut shells were more suitable than palm kernel shells when used as substitute for conventional aggregates in concrete production.     

Deformation and buckling of axially compressed cylindrical shells with local loads in numerical simulation and experiments

By means of geometrically non-linear modeling of the test process for high-quality specimens of thin-walled cylinders using a shell finite element implemented in ANSYS, it has been proved that this numerical approach is applicable for design of real axially compressed circular cylindrical shells under external local quasi-static loads.     

Collapse analysis of real RC spatial structures using known failure schemes of ferro‐cement shell models

Large‐span reinforced concrete (RC) shells collapses that occurred in the last decade caused many death toll as well as significant losses to national economies. The most famous cases were the collapse of the aqua park cover in Moscow on February 2004 and the 2E terminal roof destruction at Charles de Gaulle Airport near Paris on May 2004. Following the publications of the appropriate commissions that have studied the reasons of these events, the influence of concrete creep and changes in the shell geometry on buckling of RC thin‐walled shells was not properly considered in the design. This study is focused on buckling of such shells, taking into account geometrical and physical nonlinear behaviour of compressed concrete. Other important reasons of concrete shells collapse are also analysed. The study is based on available experimental and theoretical investigations of ferro‐cement shells' models previously performed by the first author. The results of these investigations, obtained for small‐scale ferro‐cement models of thin‐walled shallow RC shells, are discussed. Behaviour of the tested models is compared with that of the above‐mentioned real shells and similar structures, which also collapsed. The critical buckling loads for the shells are obtained. It is shown that these loads are lower than the actual ones; thus, the shells buckling was unavoidable. To prevent brittle shell failure, they should be designed using other dominant failure modes that appear before the buckling. Possible failure schemes of real RC shells can be predicted using dominant failure modes obtained by laboratory testing of scaled models. Copyright © 2012 John Wiley & Sons, Ltd.     

球面壳体表面风压分布特性风洞试验研究

球面壳体是工程中一种常用的屋面结构形式。本文通过刚性模型风洞试验,对不同场地类别下球面壳体表面风压分布进行了同步测量。根据测到的同步风压分布数据,对壳体表面风压场特性进行了分析,包括平均风压系数及脉动风压系数分布、脉动风压的自功率谱及互功率谱分布、风压场的本征正交分解特性、雷诺数对壳体表面风压分布的影响等。结果表明,球面壳体模型表面风压分布受雷诺数的影响明显,且模型的曲面特性使得由风场本征正交分解得到的前几阶特征模态对整个风压分布的贡献增大。该研究为这类结构在抗风分析中风荷载的确定及数值模拟提供试验依据。     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

Exact vibration frequencies of segmented axisymmetric shells

Axisymmetric shells are commonly used in all fields of engineering and their dynamic characteristics are of great importance in their overall performance. Segmented shells are shells that are built of several pieces that form together an axisymmetric shell with a joint axis. These can be cylindrical, conical or plate segments, which are connected to form a complete shell. In this research, the exact dynamic stiffness matrix for each segment is derived and used in the assembly of the complete structure dynamic stiffness matrix. Then the natural frequencies of vibrations are found as the frequencies that cause this matrix to become singular. Examples are given for the frequencies and modes of segmented shells made of conical, cylindrical, and plate segments.     

Strength of damaged ring and orthogonally stiffened shells—Part II: T-ring and orthogonally stiffened shells

This paper is the second 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 twenty stringers, and the other with forty.This Part II deals with the tests on the T-ring and orthogonally stiffened shells. It is concluded from the test results that the T-ring stiffeners were much more effective than the corresponding plain-rings with regard to limiting the deformations which would result from minor impacts and practical conditions of loading. It is generally recommended that plain rings should not be used in shells which form parts of structural components potentially liable to damage from a minor collision, etc. It is also recommended that further work be done, including analysis and testing, to determine the optimum design of T-ring stiffeners to limit the effects of damage in an effective manner.     

Parametric stress distribution in shell-of-revolution sludge digesters of parabolic ogival form

Egg-shaped sludge digesters have become popular in relatively recent times owing to their superior functional performance and lower maintenance costs in comparison with conventional cylindrical digesters. These innovative structures are usually constructed as thin shells of revolution in concrete, designed to withstand principally the hydrostatic pressure loading from the contained liquid. As regards the precise shape of the egg shell, a number of mathematical shell surfaces may be envisaged, and the stress distribution will very much depend on the chosen form. In this paper, it is desired to explore the possible adoption of the parabolic ogival shell as a sludge digester. The stress distribution in such a shell is expressed in terms of a single governing parameter ξ, greatly facilitating the investigation. For various values of ξ covering the most practical range for egg-shaped digester shells, recommendations are made regarding the positioning of supports. Taking into account maximisation of tank capacity, minimisation of peak stress resultants in the shell, and ease of prestressing, the best range of ξ for parabolic ogival digester shells is identified. The overall conclusion is that from a structural and functional point of view, the parabolic ogival profile is suitable for adoption in the design of egg-shaped concrete sludge-digester shells.     

网状扁壳与带肋扁壳组合结构的拟三层壳分析法

本文对网状扁壳与带肋扁壳共同工作的组合结构(可简称组合网状扁壳),采用连续化的拟三层壳的计算模型,按弹性小挠度薄壳理论进行分析计算,推导建立了混合法的基本方程式。由于这种构造上的拟三层壳在一般情况下不存在中面,因而壳体的薄膜内力、弯矩与薄膜应变,弯曲应变是耦合的,存在一个耦合矩阵,使得基本方程式比单层光面的符氏扁壳方程要复杂得多。对于周边简支的组合网状扁壳可求得基本方程式的解析解。文中对三向、四向组合网状扁壳进行了详细讨论,并指出了在特定条件下,可退化为一个当量的各向同性单层扁壳。对于一般网状扁壳的拟壳分析法及带肋扁壳的拟壳分析法分别属于本文的两种特殊情况。文中附有计算例题。     

A parametric finite element study of cracked plates and shells

The overall behavior of plates and shells as affected by the presence of a through crack in the elastic range has been studied. Due attention has been paid to finite element modeling aspects of the problem. Forty different cracked plate and shell FE models have been generated and analyzed by a special computer program developed for the purpose of this study. The significance of various parameters such as the order of mesh refining at the crack tip, the effect of boundary conditions, Poisson's ratio, crack length and shell curvature are studied. FE model consisting of isoparametric 4-noded shell elements moderately refined at the crack tip predicted the overall stress and displacement field with acceptable precision.