Stability of thin-walled high-pressure vessels subjected to uniform corrosion

The stressed state in real metal constructions changes in the process of operation even under permanent external loading. It takes place due to changes in the cross-sections of the loaded elements, resulting from the surface corrosion. This paper proposes a method for determining the critical time of stability loss in thin-walled high-pressure vessels subjected to uniform corrosion from the inside. The method is based upon the model of a thin elastic cylindrical shell. It is shown that this critical time can be established if the solution of the respective problem of the static stability loss for the vessel, not subjected to corrosion, and the law of corrosion rate change are known. Several special cases of the law of corrosion rate are examined.     

Stability of thin-walled high-pressure cylindrical pipes with non-circular cross-section and variable wall thickness subjected to non-homogeneous corrosion

This paper proposes a method for determining the critical time of stability loss of thin-walled cylindrical pipes with non-circular cross-section and variable wall thickness along the directrix subjected to non-homogeneous corrosion from the inside. The method is based upon the model of a thin elastic cylindrical shell with a non-circular cross-section and variable wall thickness along the directrix. It is shown that the critical time can be established if the solution of the respective problem of the static stability loss for the non-circular cylindrical shell with variable wall thickness along the directrix, not subjected to corrosion, and the law of corrosion rate change are known. Numerical results are connected with the pipe of the elliptical cross-section.     

Buckling strength of the cylindrical shell and tank subjected to axially compressive loads

This paper aims to develop practical design equations and charts estimating the buckling strength of the cylindrical shell and tank subjected to axially compressive loads. Both geometrically perfect and imperfect shells and tanks are studied. Numerical analysis is used to evaluate buckling strength. The modeling method, appropriate element type and necessary number of elements to use in numerical analysis are recommended. According to the results of the parametric study of the perfect shell, the buckling strength decreases significantly as the diameter-to-thickness ratio increases, while it decreases slightly as the height-to-diameter ratio increases. These results are different from those in the case of columns. The buckling strength of the perfect tank placed on an extremely soft foundation and a stiff foundation increases by up to 1.6% and 5.6%, respectively, compared with that of the perfect shell. The buckling strength of the shell and tank decreases significantly as the amplitude of initial geometric imperfection increases. Convenient and sufficiently accurate design equations and charts used for estimating buckling strength are provided.     

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.     

Buckling of cylindrical shells with longitudinal joints under external pressure

In this article, the bucking of cylindrical shells with longitudinal joint has been investigated through the experimental and numerical analysis. It was clarified that the buckling behavior of cylindrical shells with longitudinal joints under lateral external pressure is not only related to its dimension, but also longitudinal joint and an imperfection. The buckling of cylindrical shells with rigid joint buckles only once and in multi-lobe buckling, whereas one with flexible joints buckles twice and firstly in single-lobe buckling in the vicinity of the joint, secondly in multi-lobe buckling in remaining un-deformed area. And the more flexible the longitudinal joint, the lower the critical pressure, with respect to the same dimension of jointed cylindrical shells and imperfection condition. Moreover the numerical analysis approaches were also presented and verified, by which the imperfection can greatly enlarge the effect of joint on buckling has been demonstrated.     

Effects of openings of the buckling of cylindrical shells subjected to axial compression

Experimental and numerical methods are used to study the stability problem of cylindrical shells with cut-outs. The paper presents parametric research of the shape (square, rectangular, circular), the dimensions (axial and circumferential sizes, diameter) of the hole. The effect of the location and the number of the holes are also studied. The analysis indicates that the critical load is sensitive to the opening angle or circumferential size of the hole. The function (critical load-opening angle) is linear for large openings and independent of the geometrical imperfections of the shell. However for small openings, it is necessary to take into account the coupling between the initial geometrical imperfections and the openings. The linear approach does not fit because of the importance of the evolution of the displacements near the openings. These results will be used for the development of European rules.     

Elastic-plastic collapse of non-uniform cylindrical shells subjected to uniform external pressure

The objective of this paper is to derive analytical solutions for the elastic buckling and plastic collapse pressures of a cylindrical shell with reduced thickness over part of its circumference. The section of reduced thickness is used to represent a corroded region in a pipe. The proposed solutions are extensions of Timoshenko's solutions for the elastic-plastic collapse of a linear elastic, perfectly plastic cylindrical shell subjected to uniform external pressure. A modified interaction formula for the fully plastic membrane forces and bending moments in the non-uniform cylinder has been proposed for plastic collapse. A parametric study shows that the elastic buckling pressure decreases smoothly with corrosion angle when the corrosion depth is less than 0.5t. When the corrosion depth is greater than 0.5t, the elastic buckling strength first decreases very rapidly with corrosion angle. Furthermore, the elastic buckling pressure decreases uniformly with corrosion depth when the corrosion angles are greater than 30°, while the elastic buckling strength decreases more rapidly at higher corrosion depths when corrosion angles are less than 30°. Another parametric study on a steel pipe shows that the initial and fully plastic yield pressures both decrease monotonically with corrosion depth for a given corrosion angle and imperfection.     

Inelastic stability of tightly fitted cylindrical liners subjected to external uniform pressure

The critical external pressure at which a thin cylindrical liner may buckle elastically has gained many researchers' attention. In contrast, the inelastic buckling pressure of thick cylindrical liners has never been examined thoroughly. A previous attempt was reported by Jacobsen who had limited the critical external pressure to the value that coincided with the onset of yielding of the most heavily stressed part of the cylindrical liner.The liner thickness-to-diameter and yield stress-to-Young's modulus ratios, both control the ultimate capacity of any liner. This paper presents a parametric study using the Finite Element Method (FEM), evaluates Jacobsen solution and provides charts that help in estimating the ultimate pressure capacity of such cylindrical liners.     

Buckling of thin-walled orthotropic cylindrical shells under uniform external pressure.: Application to corrugated tin cans

The general instability of thin-walled orthotropic circular cylindrical shells under external pressure is investigated. The buckling pressure can be predicted with the use of simple analytical formulae derived from an asymptotic analysis of the corresponding eigenvalue problems. The results predicted by these formulae are compared with finite element solutions and the four types of experimental models investigated by Ross (Thin Walled Structures 1996;26(3):179–93). The comparison proved to be accurate enough for practical purpose except for experimental model 1.     

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.     

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.     

Reliability of maintained ship hull girders subjected to corrosion and fatigue

A formulation is presented to account for the effect of corrosion and fatigue on the reliability of ship hulls. A time variant formulation is presented in which the effect of these degradation phenomena on the hull section modulus is quantified. The effect of maintenance actions is accounted for by considering that the repaired elements are restored to a state as new. Different repair policies can be studied and the approach can be used as a tool to plan the maintenance actions based on reliability results.     

Critical assessment of Eurocode approach to stability of metal cylindrical silos with corrugated walls and vertical stiffeners

The paper deals with stability of steel cylindrical silos composed of corrugated walls and vertical open-sectional stringers. Comprehensive three-dimensional finite element analyses were carried out with perfect slender, semi-slender and squat silos by means of a linear buckling approach. Corrugated walls were simulated as an equivalent orthotropic shell and vertical open-sectional stringers as beam elements. The FE results were compared with the Eurocode approach. In addition, comprehensive FE computations for axially compressed cylindrical shells composed of an orthotropic shell and stringers were carried out. An improvement of standard formulae was proposed.     

Probabilistic loss assessment of light-frame wood construction subjected to combined seismic and snow loads

In some areas, e.g., mountainous areas in the western United States, both seismic and snow loads are significant. Limited research has been conducted to investigate the seismic risk of light-frame wood construction in those areas considering the combined loads, particularly the snow accumulation. An object-oriented framework of the risk assessment for light-frame wood construction subjected to combined seismic and snow hazards is proposed in this paper. A typical one-story light-frame wood residential building is selected to demonstrate the proposed framework. Economic losses of the building due to the combined hazards are evaluated using the proposed framework. It is found that in areas with significant snow accumulation, the snow load has significant effects on the seismic risk assessment for light-frame wood construction.     

轴力与双向弯矩作用下方钢管焊接球节点的承载力与实用计算方法研究

国家游泳中心“水立方”结构中采用了连接方钢管、且承受轴力与弯矩共同作用的焊接空心球节点。文献[1]系统研究了方钢管焊接球节点在轴力与单向弯矩作用下的承载能力并建立了实用计算方法。本文进一步对轴力与双向弯矩作用下的这类节点进行深入研究。对轴力与双向等弯矩共同作用的节点,通过有限元分析、试验研究以及简化理论解三条途径,系统研究其受力性能,并提出节点承载力的实用计算方法。而对双向任意弯矩作用的情况,提出了对单向弯矩及双向等弯矩两种情况进行线性插值的简化计算方法。     

双锥型压弯(扭)圆钢管的试验研究

双锥型变截面类构件在压弯(扭)复合荷载作用下,受力情况复杂,目前规范尚未给出一套完整的强度、稳定计算公式。本文通过双锥型圆钢管的压弯(扭)载荷试验,对该类型构件在复合荷载作用下的承载能力、破坏模态、位移-荷载曲线及应变-荷载曲线进行了分析比较。试验分析表明:试件的破坏模态表现为结构的局部屈曲,提供一个较小的坡度,便能使塑性区发生内移,以获得更大的延性;双锥型构件比等截面构件具备更好的受力性能,其承载能力的提高与锥体坡度直接相关,对于塑性铰位于交界面处的构件,其承载能力的提高可达40%左右。