Buckling of cracked thin-plates under tension or compression

Plates are easily susceptible to buckling under compression, in particular when plate's thickness becomes sufficiently small with respect to others plate's sizes; such a mode of failure is often prevalent with respect to strength failure. The buckling phenomena under tension loading can also occur, especially in plates containing defects such as cracks or holes; when the buckling load is reached, complex wrinkling deflection patterns in compressed regions develops around such imperfections.In the present paper, the buckling analysis of variously cracked rectangular elastic thin-plates under tension and compression is considered. A short explanation of the buckling phenomena in plates is recalled and several numerical analyses, carried out by using the Finite Element Method (FEM), are performed in order to determine the critical load multiplier, both in compression and in tension, by varying some plates' parameters. In particular, the critical load multiplier is determined for different relative crack length, crack orientation and Poisson's coefficient of the plate's material which is made to range between 0.1 and 0.49.Moreover a simple approximate theoretical model to explain and predict the buckling phenomena in cracked plates under tension is proposed and some comparisons are made with FE numerical results in order to assess its reliability in predicting buckling load multipliers.Finally, the obtained results are graphically summarised (in dimensionless form) in several graphs and some interesting conclusions are drawn.     

Buckling of imperfect functionally graded plates under in-plane compressive loading

Buckling behavior of rectangular functionally graded plates with geometrical imperfections is studied in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive loading. Simultaneous solving of the stability and compatibility equations in conjunction with the equilibrium equations leads to the buckling relation of the plate. The critical buckling load of a sample plate is obtained and compared for different geometrical ratios. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.     

Buckling analysis of cracked plates using hierarchical trigonometric functions

The present paper deals with the estimation of buckling loads of plates with cracking damages. The hierarchical trigonometric functions are used to define the displacement function of the cracked plate. Selective choosing of the trigonometric functions satisfies the various boundary conditions of a plate bounded by support members in a continuous plated structure. Moreover, the analysis of the cracked plate can be carried out with a minimum number of equations accurately. In the present paper, the buckling loads of plates with various types of cracks, such as edge crack and central crack, are estimated under uniaxial compressive load, biaxial compressive load and in-plane shear load. The results are found to correlate well with those obtained using a finite element method.     

全受压和局部边缘受压下有裂纹薄板屈曲的试验和数值研究

受压下薄钢板经常发生屈曲失效,尤其当薄钢板存在一些如开口和裂纹等缺陷时。这种失效模式先于强度失效。给出了轴压下有裂纹板的屈曲荷载的试验结果和数值结果。为此,采用1200A铝合金制作成矩形板,且板的中心有斜裂缝。在试验和数值研究中,分析了裂缝的长度和方向、板的厚度和长宽比的影响。对两种不同的支撑形式和荷载条件(如:局部边缘荷载和支撑)的影响进行研究。最后,将试验结果与数值结果进行对比。     

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.     

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.     

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.     

Buckling of plates with a hole under tension

An FEM analysis is made on the elastic buckling of plates, each of which has a hole and is subjected to tensile loading.In a general way, no attention is paid to the buckling of plates if they are subjected to a tensile load. However, when a plate has a hole, compressive stresses appear near the hole under a tensile load, and the stress may cause local buckling of the plate.In this paper, stress distributions and buckling behaviours of such plates under tension are studied. Aspect ratios, shapes of holes and so on, are adopted as parameters.Through the analysis, variations of buckling coefficients and buckling modes against aspect ratios are obtained. The effects of the hole shapes on the buckling strength are also discussed.     

On the buckling of cylindrical shells with through cracks under axial load

Presence of cracks or similar imperfections can considerably reduce the buckling load of a shell structure. In this paper, the buckling of cylindrical shells with through cracks has been studied. A general finite element model has been proposed, verified and applied to some novel cracked shell buckling problems for which documented results are not available. A special purpose program has been developed for generating finite elements models of cylindrical shells with cracks of varying length and orientation. The buckling behavior of cracked cylinders in tension and compression has been studied. The results of the analysis are presented in parametric form when it seems to be appropriate. Sensitivity of the buckling load to the crack length and orientation has also been investigated.     

Tension buckling of plate having a hole

Generally, it is believed that buckling of plates never arises under tensile load. However, when a plate has a hole, compression stresses appear locally near the hole under a tensile load, and the compression stress may cause local buckling—so-called tension buckling—of the plate. In this paper, some results of numerical analysis on the tension buckling are presented, and basic behaviour on the tension buckling is discussed.     

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the local buckling modes of the cylindrical shell depends mainly on the crack orientation. For cylindrical shells with relatively long axial crack, buckling loads associated with local buckling modes of the cylindrical shell reduce drastically on increasing the shell internal pressure. In contrast, the internal pressure has the stabilizing effect against the local buckling for circumferentially cracked cylindrical shells. A critical crack length for each crack orientation and loading condition is defined as the shortest crack causing the local buckling to precede the global buckling of the cylindrical shell. Some insight into the effect of internal pressure on this critical crack length is provided.     

A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution

An improved hybrid semi-analytical method for calculating elastic buckling load of a thin plate with a central straight through-thickness crack subject to axial compression is proposed. In the study, the actual non-uniform in-plane stress distribution is firstly conducted by using Muskhelishvili's complex variable formulation in conjunction with boundary collocation method. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of the crack edges, is obtained by using domain decomposition method. Finally the buckling load of a cracked plate using Raleigh–Ritz energy method is calculated based on the actual in-plane stress distribution and the reasonable deflection shape function obtained. The effects of crack length, plate's aspect ratio are studied for thin plates with different boundary conditions. Results obtained from the proposed method are in good agreement with the existing numerical results and experimental ones. It is finally shown that the proposed method, based on a correct non-uniform in-plane stress distribution, is more accurate than the few existing analytical methods based on a uniform in-plane stress distribution.     

Vibration, buckling and dynamic stability of cracked cylindrical shells

The presence of cracks in a structure can considerably affect its behaviour. This paper presents a finite element study on the vibration, buckling and dynamic stability behaviour of a cracked cylindrical shell with fixed supports and subject to an in plane compressive/tensile periodic edge load. The effects of crack length and orientation are analysed. Under tension load, the results show that the frequency of the shell initially increases with the load, but then decreases as the load further increases leading to buckling due to tension load. The size and the orientation of the crack and the loading parameter can all have a significant effect on the dynamic stability behaviour of the shell under both compressive and tensile loading. The effects of these parameters are discussed in detail.     

Analysis on local thermal critical buckling of square concrete filled steel short tubular under axial compression

基于薄板小挠度理论，采用能量法对方钢管混凝土中钢板局部热屈曲性能进行了理论分析。推导了热力耦合作用下钢管混凝土中钢板的临界屈曲系数，并给出了相应的钢板临界屈曲温度计算公式；推导了钢管混凝土外包钢板在热力耦合作用下外荷载、热荷载与常温临界屈曲荷载的关系。结果表明：钢管的弹性模量对临界屈曲温度没有影响；宽厚比对临界屈曲系数及临界屈曲温度有较大影响,并建议了宽厚比限值；通过热屈曲临界系数求得构件屈曲时长宽比的最小值，可用于钢板热屈曲设计。     

某体育馆楼板裂缝原因分析

针对一座受洪水侵袭的体育馆赛场楼面开裂现象,采用有限元程序,分别在两种最不利荷载组合情况下,对结构进行内力分析。根据楼面的位移场、应力场、弯矩和轴力值,对楼板开裂进行了综合分析。结果表明,水浮力过大,部分桩抗拔作用不足,导致楼板混凝土拉应力超过抗拉强度标准值,能很好地解释赛场楼板开裂现象。最后给出了防止和解决这一问题的方法,并在实践中证明了该分析方法正确性。     

Optimum design of laminated composite plates to maximize buckling load using MFD method

This paper presents optimal design of simply supported laminated composite plates subject to given in-plane static loads for which the critical failure mode is buckling. The objective function is to maximize the buckling load capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used for the finite element analysis. In this paper, the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used as an optimization method. Also, computer programs are coded in MATLAB and Golden Section method is adapted in this program for the optimal design of laminated plates for maximum buckling load. The effect of width-to-thickness ratio, aspect ratio, number of layers, material anisotropy, load ratios (N_y/N_x), uncertainties in material properties and functionally graded materials on the results is investigated and compared.     

非均匀受压矩形钢管混凝土局部弹性屈曲分析

应用不同的特征函数描述了矩形板在非均匀压力作用下的屈曲形态,解决了采用三角级数为屈曲函数模拟非均匀受压荷载作用下单侧表面约束矩形板件屈曲模态的不对称问题;通过伽辽金法建立屈曲控制方程组,分析了非均匀荷载作用对矩形钢管混凝土构件局部弹性屈曲性能的影响。结果表明:钢管屈曲系数随着不均匀荷载梯度α增加而增大,纯弯作用下（α=2）的板件弹性屈曲荷载特征值约为轴压作用下的6倍;钢板的宽厚比限值随不均匀加载梯度α的增大而增加;非均匀荷载作用下非加载边固支约束板件的屈曲系数明显大于简支约束的板件。     

薄钢板剪力墙结构水平反复荷载试验研究

给出了薄剪力墙板拉力带对周边框架梁、柱产生的作用力计算公式,以此设计了试件的原型结构。薄墙板采用建筑结构胶和高强度摩擦型螺栓固定在焊于框架梁柱的角钢连接板上。对三层薄钢板剪力墙结构进行水平反复荷载作用下的试验研究,结果表明:墙板先屈曲,后屈服,屈曲后能继续承受荷载,并形成多条非常明显的斜拉力带;二层墙板最先出现屈服,底层墙板屈服时间最晚;试件破坏时,钢框架柱脚及梁柱连接部位形成了塑性铰,柱脚翼缘严重扭曲,腹板向外鼓曲。墙板发生很大的平面外凹凸变形,并有多个裂口,且在靠近角部梁端处出现撕裂。     

Ultimate strength of cracked plate elements under axial compression or tension

In addition to corrosion, fatigue cracking is another important factor of age related structural degradation, which has been a primary source of costly repair work of aging steel structures. Cracking damage has been found in welded joints and local areas of stress concentrations such as at the weld intersections of longitudinals, frames and girders. Fatigue cracking has usually been dealt with as a matter under cyclic loading, but it is also important for residual strength assessment under monotonic extreme loading, because fatigue cracking reduces the ultimate strength significantly under certain circumstances.In this paper, an experimental and numerical study on the ultimate strength of cracked steel plate elements subjected to axial compressive or tensile loads is carried out. The ultimate strength reduction characteristics of plate elements due to cracking damage are investigated with varying size and location of the cracking damage, both experimentally and numerically. Ultimate strength tests on cracked steel plates under axial tension and cracked box type steel structure models under axial compression are undertaken. A series of ANSYS nonlinear finite element analyses for cracked plate elements are performed. Based on the experimental and numerical results obtained from the present study, theoretical models for predicting the ultimate strength of cracked plate elements under axial compression or tension are developed. The results of the experiments and numerical computations obtained are documented. The insights developed will be very useful for the ultimate limit state based risk or reliability assessment of aging steel plated structures with cracking damage.     

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.