Experimental Study and Fragility Analysis of Effective-Length Factors in Column Buckling

The design of columns relies heavily on the basis of Leonhard Euler’s Theory of Elastic Buckling.However,to increase the accuracy in determining the maximum critical load a column can withstand before buckling,a constant was introduced.This dimensionless coefficient is K,also known as the effective-length factor.This constant is often found in building design codes and varies in value depending on the type of column support that is applied.This paper presents experimental and analytical studies on the determination of the effective-length factor in the buckling stability of columns with partially-fixed support conditions.To this end,the accurate K value of the columns tested by the Instron Testing Machine(ITM)at California State University,Northridge’s(CSUN’s)Mechanics Laboratory is determined.The ITM is used in studying the buckling of columns where the supports are neither pinned nor fixed,and the material cross-section rather rests upon the machine while loading is applied axially.Several column specimens were tested and the experimental data were analyzed in order to estimation of the accurate effective-length factor.The calculations from the tested results as well as the conducted probabilistic analysis shed light on how a fragility curve may aid in predicting the effective-length value of future tests.

TORSIONAL BUCKLING OF SPHERICAL SHELLS UNDER CIRCUMFERENTIAL SHEAR LOADS

By the aid of differential geometry analysis on the initial buckling of shell element, a set of new and exact buckling bifurcation equations of the spherical shells is derived. Making use of Galerkin variational method, the general stability of the hinged spherical shells with the circumferential shear loads is studied. Constructing the buckling mode close to the bifurcation point deformations, the critical eigenvalues, critical load intensities and critical stresses of torsional buckling ranging from the shallow shells to the hemispherical shell are obtained for the first time.

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting method scheme for approximating them. We present the perturbation and the numerical approximations of the first and second buckling loads and the corresponding shapes.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

Buckling analysis of super-long rock-socketed filling piles in soft soil area by element free Galerkin method

In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditional first type, and a newly invented numerical analysis method, i.e. the element-free Galerkin method (EFGM), was introduced to consider the non-concordant deformation and nonlinearity of the pile-soil interface. Then, based on the nonlinear elastic-ideal plastic pile-soil interface model, a nonlinear iterative algorithm was given to analyze the pile-soil interaction, and a program for buckling analysis of piles by the EFGM (PBAP-EFGM) and arc length method was worked out as well. The application results in an engineering example show that, the shape of pile top load-settlement curve obtained by the program agrees well with the measured one, of which the difference may be caused mainly by those uncertain factors such as possible initial defects of pile shaft and the eccentric loading during the test process. However, the calculated critical load is very close with the measured ultimate load of the test pile, and the corresponding relative error is only 5.6%, far better than the calculated values by linear and nonlinear incremental buckling analysis (with a greater relative error of 37.0% and 15.4% respectively), which also verifies the rationality and feasibility of the present method.

Structural Integrity Assessment of Offshore Jackets Considering Proper Modeling of Buckling in Tubular Members-a Case Study of Resalat Jacket

In the present research,results of buckling analysis of 384 finite element models,verified using three different test results obtained from three separate experimental investigations,were used to study the effects of five parameters such as D/t,L/D,imperfection,mesh size and mesh size ratio.Moreover,proposed equations by offshore structural standards concerning global and local buckling capacity of tubular members including former API RP 2A WSD and recent API RP 2A LRFD,ISO 19902,and NORSOK N-004 have been compared to FE and experimental results.One of the most crucial parts in the estimation of the capacity curve of offshore jacket structures is the correct modeling of compressive members to properly investigate the interaction of global and local buckling which leads to the correct estimation of performance levels and ductility.Achievement of the proper compressive behavior of tubular members validated by experimental data is the main purpose of this paper.Modeling of compressive braces of offshore jacket platforms by 3D shell or solid elements can consider buckling modes and deformations due to local buckling.ABAQUS FE software is selected for FE modeling.The scope of action of each of elastic buckling,plastic buckling,and compressive yielding for various L/r ratios is described.Furthermore,the most affected part of each parameter on the buckling capacity curve is specified.The pushover results of the Resalat Jacket with proper versus improper modeling of compressive members have been compared as a case study.According to the results,applying improper mesh size for compressive members can under-predict the ductility by 33%and under-estimate the lateral loading capacity by up to 8%.Regarding elastic stiffness and post-buckling strength,the mesh size ratio is introduced as the most effective parameter.Besides,imperfection is significantly the most important parameter in terms of critical buckling load.

Structure buckling and non-probabilistic reliability analysis of supercavitating vehicles

To perform structure buckling and reliability analysis on supercavitating vehicles with high velocity in the submarine,supercavitating vehicles were simplified as variable cross section beam firstly.Then structural buckling analysis of supercavitating vehicles with or without engine thrust was conducted,and the structural buckling safety margin equation of supercavitating vehicles was established.The indefinite information was described by interval set and the structure reliability analysis was performed by using non-probabilistic reliability method.Considering interval variables as random variables which satisfy uniform distribution,the Monte-Carlo method was used to calculate the non-probabilistic failure degree.Numerical examples of supercavitating vehicles were presented.Under different ratios of base diameter to cavitator diameter,the change tendency of non-probabilistic failure degree of structural buckling of supercavitating vehicles with or without engine thrust was studied along with the variety of speed.

WEIGHTED SOLUTION OF SMALL-DEFLECTION BUCKLING EQUATION OF THIN SHELL

Based on small-deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions, Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision.

THE DYNAMIC BUCKLING OF AN ORTHOTROPIC CYLINDRICAL THIN SHELL UNDER TORSION VARYING AS A POWER FUNCTION OF TIME

The subject of this investigation is to study the buckling of orthotropic cylindrical thin shells under torsion, which is a power function of time. The dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a time dependent differential equation with variable coefficient by using Galerkin's method. Finally, the critical dynamic and static loading, the corresponding wave numbers, the dynamic factors, critical time and critical impulse are found analytically by applying the Ritz type variational method. Using those results, the effects of the variations of the power of time in the torsion load expression, of the loading parameter, the ratio of the Young's moduli and the ratio of the radius to thickness on the critical parameters are studied numerically. It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading.

静水外压下纤维缠绕复合材料圆柱厚壳的稳定性研究

针对静水外压下纤维缠绕复合材料圆柱厚壳的临界屈曲载荷理论预报,本文基于Sander非线性壳体理论,结合圆柱壳变形几何方程以及纤维缠绕层的本构关系,推导出静水外压下纤维缠绕复合材料圆柱厚壳的屈曲控制方程;通过求解控制方程提出一种适用于静水外压下复合材料圆柱厚壳临界屈曲压力预报的解析方法;基于有限元模型对不同缠绕形式和缠绕角下的壳体临界屈曲压力进行对比计算,验证解析方法的准确性;基于解析方法,研究复合材料圆柱厚壳关键几何参数及材料设计对临界屈曲压力的影响。

特高压GIS断路器用管型绝缘拉杆动态受力真型试验与材料压缩特性分析

作为特高压GIS断路器中连接触头与操作机构的关键部件,绝缘拉杆在操作过程中需要承受外载荷作用。为掌握绝缘拉杆动态受力特性、材料力学性能,文中通过在特高压GIS断路器中布置力传感器测得其主绝缘拉杆操作过程中动态受力情况,根据测试结果进行了拉杆材料管型试样的压缩试验,并利用仿真分析了不同长径比拉杆的压缩屈曲特性。试验结果表明,操作过程中主绝缘拉杆受交变冲击载荷作用,操作机构对绝缘拉杆所施加压力峰值与拉力峰值相差不大,且二者均达到110 k N以上,绝缘拉杆材料的压缩特性应得到关注。压缩试验结果表明长度和内、外径将会直接影响管型绝缘拉杆材料压缩性能,大长径比绝缘拉杆更容易在压缩载荷下出现塑性变形和屈曲失稳现象,所能承受的最大压缩载荷更小。基于材料压缩试验,文中通过仿真计算建立了管型绝缘拉杆临界屈曲载荷与长度之间的近似关系式,并提出通过管型试样压缩试验得到原尺寸拉杆临界屈曲载荷的方法。文中研究成果可为特高压GIS绝缘拉杆材料试验、设计制造提供参考。

单轴对称截面轴压构件弯扭失稳换算长细比的一般计算式

单轴对称截面轴压构件弯扭失稳的换算长细比是计算其极限荷载的重要参数。基于单轴对称截面轴压构件弯扭失稳的平衡微分方程,采用Galerkin法推导了4种边界约束条件弯扭失稳临界荷载的一元二次方程,并进一步得到了基于荷载比、双长细比的弯扭失稳换算长细比理论式。基于理论式,分别对比了我国现行标准GB 50017—2017中双角钢组合T形截面轴压构件扭转失稳、弯扭失稳的换算长细比,揭示了其中存在的问题;提出了新的双角钢组合T形截面轴压构件扭转失稳、弯扭失稳换算长细比的计算式,并与理论式的计算结果进行对比。结果表明,对于不同边界约束条件的轴压构件,其弯扭失稳临界荷载或换算长细比的形式不尽相同;相较于GB 50017—2017中的公式,所建议的双角钢组合T形截面轴压构件扭转失稳、弯扭失稳的换算长细比具有更高的精度,且适用于4种边界约束条件和115个等边双角钢组合T形截面、71个长肢相并的不等边双角钢组合T形截面和71个短肢相并的不等边双角钢组合T形截面。

THEORY OF PERTURBATION FINITE ELEMENT ANALYSIS FOR SOLUTION OF NONLINEAR BUCKLING CRITICAL LOADS OF STRUCTURES

The author presents a theory, including the complete analysis and incomplete analysis,of perturbational finite element analysis for the solution of nonlinear buckling critical loadsof structures.

某中低速磁悬浮转向机构拉杆的失稳分析

通过有限元分析对某中低速磁悬浮转向机构的拉杆进行了失稳分析,通过理论计算,屈曲分析以及大变形计算方法对拉杆分别进行了临界载荷的计算。在屈曲分析中对比了不同初始载荷对计算结果的影响,在大变形分析中对比了不同的扰动力大小对临界载荷计算的影响。研究结果表明:欧拉公式、屈曲分析以及大变形方法计算所得的临界载荷基本一致;当施加的初始载荷不同时,特征值屈曲分析的临界载荷基本一致;大变形分析中,在不同的扰动作用下,扰动越小,计算所得的临界载荷越接近理论值。

功能梯度压电半导体拉-弯梁的屈曲分析

基于三维压电半导体理论和一阶剪切变形理论,考虑材料拉伸、弯曲和剪切耦合变形,建立了功能梯度压电半导体拉-弯梁在轴向压力作用下的屈曲模型。借助有限元分析软件COMSOL对压电半导体拉-弯梁进行稳定性分析,得到了功能梯度压电半导体简支梁的前三阶屈曲临界载荷及各机电场的分布规律。通过数值算例,讨论了梁长高比、初始电子浓度和功能梯度参数等对压电半导体拉-弯梁屈曲临界载荷的影响。

基于改进Reddy型三阶剪切变形理论的弹性地基上FG-CNTRC板屈曲无网格分析

针对含碳纳米管转向的Pasternak地基上功能梯度碳纳米管增强复合材料FG-CNTRC(functionally graded carbon nanotube-reinforced composite)板的屈曲问题,提出了一种基于改进Reddy型三阶剪切变形理论TSDT(third-order shear deformation theory)和移动最小二乘近似MLS(moving-least square)的无网格分析模型。该模型避免了无网格法第二类边界条件的施加困难问题,且能够满足中厚/厚板的自由表面条件,无需额外引入剪切修正因子。基于最小势能原理推导了弹性地基上FG-CNTRC板的无网格屈曲控制方程,采用完全转换法处理本质边界条件。通过基准算例验证了本文方法的收敛性及有效性,讨论了碳纳米管的转向角、体积分数、分布形式、地基系数、宽厚比和边界条件等对FG-CNTRC板临界屈曲荷载的影响。

基于满足多边界条件基函数的微分求积法及其应用

提出了一种由基函数来处理梁边界条件的改进微分求积法(MDQM).在构造挠度函数时,通过多次积分来满足梁的所有边界条件,进而利用此函数计算微分求积法中的加权系数矩阵,解决了通过多项式测试函数计算该系数矩阵时难以在同一个点运用多个边界条件的问题.为了研究该方法在梁的各类分析中的应用,首先构造了2类梁在各种边界条件下对应的挠度基函数,再根据Euler-Bernoulli梁振动理论和稳定性理论,基于微分求积法将计算梁的固有频率问题和临界荷载问题转化为求解矩阵特征值的问题,并将结果与精确解进行比较.此外,还根据理想弹塑性梁的平面弯曲理论,利用该方法计算了梁在各种边界条件下的弹塑性位移,并将结果与其他方法对比.结果表明,所提方法对于梁的稳定性分析、固有频率分析及弹塑性分析都具有较高的计算效率和精度.

超高层混凝土结构稳定性计算方法对比研究

刚重比是影响重力P-Δ效应的主要参数,是反映结构整体稳定性的主要因素。高规的刚重比公式适用于竖向荷载沿高度均匀分布的结构,对于非均布荷载或体型复杂的超高层建筑,用高规的刚重比公式计算偏保守、存在缺陷。在论述刚重比与临界屈曲荷载因子之间的关系基础上,提出了直接采用有限元屈曲分析法。对比了不同规范对结构稳定的设计思路和判别方法,研究了影响刚重比的主要因素,并对深圳某超高层建筑的4种力学模型验算了结构稳定性。结果表明:直接采用有限元屈曲分析法得到的超高层建筑结构临界屈曲荷载因子作为判别结构稳定的依据满足安全要求。

带金属挤压套管铰接连接FRP轴心压杆整体屈曲性能研究

本文针对拼装式桁架结构中两端设有金属挤压套管连接的FRP受压杆件,通过轴向压缩试验和有限元分析方法研究了此类组合杆件两端铰接时的整体屈曲性能,并通过参数化分析揭示了金属连接段对不同长度FRP杆件屈曲临界承载力的影响规律。基于试验和有限元结果,对目前工程中常用的五种FRP杆件整体屈曲临界承载力计算公式进行了比较验证,明确了适用于此类组合杆件整体屈曲临界承载力的计算方法。结果表明:相比于未设置端部金属加强段的杆件,FRP圆管在金属外套管端部发生剪切断裂,而非杆件中部断裂,即金属外套管局部构造对杆件整体破坏模式有较大影响。另外,端部设有金属段的杆件整体临界屈曲荷载得到了一定提升;随着长细比的增加,端部金属区段对FRP杆件整体屈曲临界荷载影响的增幅逐渐减小。建议采用Engesser或Haringx修正公式作为两端设有挤压型金属套管铰接连接的FRP压杆的设计计算公式。