Buckling and dynamic instability analysis of stiffened shell panels

The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.     

Buckling of compression-loaded multispan stiffened panel upon failure of joints between panel and supports

In research of stability of stiffened panels it is usually supposed that joints between panel and with supports do not fail at buckling. However, these joints can turn out to be insufficiently strong, and buckling of the panel can be accompanied with their destruction in limited areas. Thus the separated fragments become buckled (with finite amplitude of out-of-plane deflection) and the work for destructing the joints is dispersed.Examples include buckling of a compression-loaded multispan stiffened panel upon destruction of attachment to transverse and/or longitudinal supports. The method proposed to solve this problem is based on the energy approach which takes into account, firstly, work for possible destruction of the joints and secondly, an overall energy balance during transition of some components, from initial in-plane compression to compression+bending with finite out-of-plane displacements in the postbuckling stage. Sizes of the area of destruction of joints are determined by minimizing the total energy of the system.     

Buckling analysis of a cable-stayed circular frame

Large parabolic dish concentrators have been widely employed in solar thermal applications. The supporting structure of a solar dish concentrator consists of a circular frame, a central post, and front and rear cables connecting the frame to the post. The tensions in the cables cause compressive stresses in the circular frame and the central post, and this support structure must be designed for stability. In this paper, the nonlinear buckling behavior of the supporting structure of a cable-stayed circular frame is studied in detail. A three-dimensional finite element model of the supporting structure is developed to predict the critical cable tensions that would cause buckling of the circular frame and to determine the associated buckling mode shapes of the supporting structural system. The results show that the buckling load of a cable-stayed circular frame depends not only upon the cross-section of the frame, but also upon the number of cables and the inclinations of the cables. In all cases, in-plane buckling modes are predominant. The concentrated torques resulting from unbalanced cable tensions tend to induce the out-of-plane buckling modes.     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

Buckling design of stiffened sheet-based inner core based on bifurcation analysis

In the structural design of the sandwich plate, the inner core plays a key role to have its maximum performance. A shaped pyramidal truss core is proposed in order to increase the strength and productivity of the sandwich core. In this paper, the design guidelines of the shaped pyramidal truss core, which is enhanced by forming a cross-section of an arc shape at the strut of the inner core, is described. The inner core is composed of a stiffened section and a transient section with a varying cross-section. The critical load for bifurcation in compressive instability is calculated using an analytical and FEM simulation. The analytical equation for the critical load of the shaped column is derived using the energy method. The various buckling modes (global, distortional, local) occur due to these effects. Therefore, complications induced by such effects must be taken into account in the design. Parametric studies for the stiffened core are conducted. The effect of geometric parameters is investigated for optimal design of the inner core and their influence have been discussed.     

Buckling of laminated composite stiffened panels subjected to in-plane shear: A parametric study

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer.     

带有开口增强的复合板在剪切荷载作用下的应力集中和屈曲性能研究

数值和试验研究是了解碳／环氧复合板在面内剪力载荷作用下开口周边补强后应力集中和屈曲性能的两种重要方法。研究了采用四种不同开口型式及材料排列模式下的补强效果。采用有限元分析方法和基于平板理论的研究方法，分析了不同补强设计中的参变量。完成了4个试验板的制造和试验，并验证了分析结果。分析结果和试验结果吻合很好。基于有效分析模型，确定了最佳的开口补强方法。     

Buckling of plates with strengthenings

This paper studies the buckling behaviour of simply supported square plates, which have weakening or strengthening bands. The weakening/strengthening bands are equally spaced and their thickness is either decreased or increased. The analysis assumes that the stress state in the plate before and during the buckling process remains in the elastic range. Two cases of plate loading are studied, one with compressive forces and one with tangential forces. The buckling coefficients are calculated for different numbers and thicknesses of strengthening/weakening bands. The thickness of strengthening/weakening bands and the thickness of the remaining plate is varied so that the volume/weight of the plate remains constant. In one case it is found that the buckling load at constant weight of the plate can be increased by 118% if an optimal ratio of the thickness of strengthening bands and the thickness of the remaining plate is used.     

真空引起的薄壁圆筒屈曲压力预测

研究均匀外压力下初始缺陷对圆柱形薄壳结构屈曲性能的影响。对缩尺薄壁圆筒的外形进行分析以测量壳体表面的几何缺陷。有限元分析时将这些初始缺陷考虑在内,并进行静态几何非线性分析。在实验室进行圆筒的倒塌试验,并将试验结果和有限元分析结果进行比较。结果表明,有限元分析能够准确预测圆筒的破坏坍塌压力和后屈曲模态。     

Buckling of thin-walled torispherical heads in water heater tanks

The buckling strength of a thin-walled torispherical head in a residential electric water heater tank was investigated by both experimental and finite element analyses. Three water heater tanks pressurized with water were tested, and the strains on the heads and the pressure variations were measured and recorded. Finite element analysis was used to predict the buckling of the torispherical head. The effect of the imperfection induced by the contact nonuniformity between the torispherical head and the shell on the buckling of the structure is included. Good agreement between the test and finite element results shows that finite element models used in this paper are viable to predict the buckling pressure of a thin-walled torispherical head in a water heater tank. The results also show that the contact between the bottom head and the shell has a reinforcing effect on the buckling strength of the head. The contact imperfection will produce a dent adjacent to the knuckle region when the head buckles. The buckling pressure of the head perfectly contacting with the shell is 6.88% higher than that without contacting with the shell. The obtained results provide reference for the design and manufacture of water heater tanks.     

轴压下薄壁圆柱形壳屈曲试验承载力的准确可靠预测方法

论述了一种能可靠并准确预测偏心荷载下薄壁圆柱形壳屈曲试验的方法。详细描述了试验装置和试件,包括用配套的设备测量试件表面的几何缺陷。为了精确地预测屈曲试验的荷载,根据不同的复杂度建立了不同的有限元模型模拟试验装置,并研究了初始几何缺陷、荷载偏心、沿柱圆周方向的荷载偏心位置和影响边界条件的不同试验装置对屈曲承载力的影响。解释了具有简单刚性支座的有限元模型会过高估计屈曲试验承载力的原因。尽管这些模型均考虑了初始几何缺陷和荷载偏心的影响。作为对比,计算了考虑实际支座条件有限元模型的结果。在有限元模型中,用弹性实体单元模拟固定装置,用面—面接触单元模拟试件与支座间的接触面,计算出的屈曲承载力与试验有着平均约-1.59%的偏离。沿有缺陷薄壁圆柱形柱圆周方向的荷载偏心位置对屈曲承载力有显著影响。     

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.     

Nonlinear viscoelastic analysis of thin-walled beams in composite material

Laminated composites of polymeric matrix show anisotropic viscoelastic behaviour, enhanced by temperature and humidity effects. The consideration of anisotropy and viscoelasticity are important for the determination of deformations and, as a consequence, of deformation-related phenomena, as elastic and creep buckling. This paper studies the behaviour of thin-walled beams of composite material under flexure and buckling, taking account of creep effects. The analysis uses a nonlinear viscoelastic finite element code with shell elements, whose basic formulation is given. The use of shell elements allows a better representation of constitutive properties and boundary conditions. Comparison with available analytical results is made for several cases like flexure of an I beam, buckling of beam columns and lateral buckling of this beams. The results show good correlation.     

Buckling analysis of skew laminate plates subjected to uniaxial inplane loads

Elastic stability of skew composite laminate plates subjected to uniaxial inplane compressive forces has been studied. The critical buckling loads of the skew laminate plates are carried out by the bifurication buckling analysis implemented in finite element program ABAQUS. The effects of skew angles, laminate layups, plate aspect ratios, plate thicknesses, central circular cutouts, and edge conditions on the buckling resistance of skew composite laminate plates are presented.     

Buckling and ultimate strength criteria of stiffened shells under combined loading for reliability analysis

The work presented in this paper forms part of a broader task in establishing a guide to serve as technical documentation for buckling and ultimate strength assessment of various types of marine structural components using the best state-of-the-art knowledge for extreme environmental loading. This paper concentrates on buckling and ultimate strength assessment of ring stiffened shells and ring and stringer stiffened shells involving various modes of buckling and under various loading like axial compression, radial pressure and combined loading. Comparisons are made with screened test data, which have realistic imperfections and various radius to thickness ratio values in the range generally used in offshore structures. The statistical data of model uncertainty factors in terms of bias and coefficient of variation (COV) are calculated and may be used in a further reliability study. Comparisons are also made with the codified rules, API BUL 2U and DNV buckling strength of shells.     

Experimental study and numerical analysis of a composite truss joint

This paper presents a model test and numerical finite element analysis (FEA) on the mechanical behavior of a composite joint in a truss cable-stayed bridge. The model test with the scale of 1:2.5 for the truss joint was conduct to fully understand the safety and serviceability. In the experiment, stress distribution, crack resistance ability and shear resistance of headed studs were carefully measured to investigate the mechanical performance, force transmission of the joint part. The maximum strain of the steel plate and concrete chord remained in the linear elastic region until 1.7 times the design load, which means there is a significant safety margin for such composites. On the basis of the experimental results of composite truss joints, three-dimensional finite element models are established. The results of the finite element analysis are in good agreement with those of the tests in terms of strength and stiffness. It is also expected that the results presented in this paper would be useful as references for the further research and the design of composite truss bridges and composite joints.     

基于广义梁理论的薄壁构件屈曲模态有限元分析

提出基于广义梁理论(GBT)的新方法,将各向同性薄壁构件通过壳体有限元分析方法(FEA)获得的弹性屈曲模态分解成整体、畸变和局部屈曲模态。其创新之处在于仅使用GBT截面变形模态,而非构件变形模态。该方法能够单独计算各屈曲模态,更好地了解各构件的后屈曲特性和强度曲线。根据GBT的经典假设,忽略剪切应变和横向张力。通过有限元方法得到的各模态与经典GBT计算结果一致。     

对轴压力作用下带有椭圆形开孔的圆柱形壳体屈曲的数值和试验研究

在圆柱形壳体的设计中,开孔对于其承载能力及屈曲性能的影响非常大。采用有限元方法对具有不同尺寸开孔的薄壁钢圆柱形壳进行模拟和分析,分析了开孔的位置、长度与直径比值（L／D）和直径与厚度比值（D／t）对圆柱形壳届曲和后屈曲性能的影响。采用INSTRON 8802液压系统对一些构件进行屈曲试验,并将试验结果与数值计算结果进行对比发现,两者具有非常好的一致性。最后,基于试验和数值分析结果,提出计算这类结构屈曲荷载的公式。     

局部屈曲或局部和畸变屈曲综合作用下冷弯型钢梁的有限元模拟

有限元法可以解决冷弯钢梁复杂的相关联屈曲问题,其中包括很多重要的关键因素:几何缺陷、材料非线性和后屈曲等。也是该方法与其他分析方法的不同之处。根据特定的冷弯Z型钢梁的材料和几何非线性建立了两类研究屈曲性能的有限元模型。其中,一个模型用于分析局部和畸变屈曲综合作用,而另一个仅用于分析局部屈曲。通过先前的四点弯曲试验证实了有限元模型的有效性。利用ABAQUS软件,模拟了一个简化的试验装置。在局部屈曲有限元模型中,通过在梁翼缘角部设置弹簧以防止畸变屈曲。由于更多的模型与试验结果相吻合,证实了对承载力和变形的预测。未来的研究将优化有限元模型,以得到侧向受约束的冷弯型钢梁不同的屈曲形式,如:局部,畸变或局部与畸变综合作用。     

Buckling analysis of thin-walled sections under localised loading using the semi-analytical finite strip method

Thin-walled sections under localised loading may lead to web crippling of the sections. This paper develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions. The paper summarises the SAFSM theory then applies it to the buckling of plates, and channel sections under localised loading. Multiple series terms in the longitudinal direction are used to compute the pre-buckling stresses in the plates and sections, and to perform the buckling analyses using these stresses. Solution convergence with increasing numbers of series terms is provided in the paper. The more localised the loading and buckling mode, the more series terms are required for accurate solutions. The loading cases of Interior One Flange (IOF) and Interior Two Flange (ITF) are investigated in this paper using simply supported boundary conditions.