某机场航站楼拱壳钢屋架稳定性分析

稳定性分析是网壳结构分析中的重要内容。文中网壳为拱梁与单层网壳形成的组合空间结构,结构形式较为复杂。利用有限元程序对该网壳进行了整体稳定分析。首先对该结构的两种模型进行了特征值屈曲分析,比较了两种模型的结果,预测结构的理论屈曲强度;然后考虑网壳的屈曲模态,考虑一致缺陷模态法并引入不同的结构初始缺陷,对结构进行非线性有限元全过程跟踪分析,初步了解该网壳结构失稳的一般规律。     

四块组合型双曲抛物面扁扭壳的稳定分析

本文用脉冲函数处理四边简支四块组合型双曲抛物面扁扭壳脊线处的曲率不连续性,根据线性稳定理论导出了与单块四边简支双曲抛物面扁扭壳具有相同形式的临界荷载计算公式,并给出了有关参数的图表。研究表明,这种壳体可能有两种失稳模态,即关于两个对称轴对称或反对称失稳。反对称失稳时,其临界荷载与单壳相同。     

Schalenbeulen von Sandwichzylindern mit einem neuen Elastomer als Verbundwerkstoff

Shell buckling of cylindrical sandwich shells with a new elastomer as composite material. Alternatively to cylindrical steel shells a sandwich shell with a new elastomer as composite material is investigated with regard to the stability. The sandwich shell has an inner and an outer steel face, which are bonded adhesively to an elastomer core between them. In cooperation with Krupp Stahlbau Hannover GmbH the institute for steel construction of University of Hannover checked, if the application of this sandwich technology is possible for towers of wind energy converters. Especially the combination with high strength steel is a point of interest. In comparison with numerical buckling analyses the validity of a laminate composites shell theory is proven. Finally the stability of the sandwich construction is investigated against shell buckling due to axial compression and torsion. The results are compared to the stability of cylindrical steel shells.     

Robust design of composite cylindrical shells under axial compression — Simulation and validation

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.     

Buckling measurement and numerical analysis of M-type ribs stiffened composite panel

A combination of methods of strategy which combines optical measurements and numerical calculations was developed to study the buckling behavior and failure modes of composite panel with M-type stiffeners under compression. Utilizing the non-contact optical means for non-destructive testing, the full-field buckling deflections/evolution and compressive failure of the panel surface were systematically collected for mechanical analysis. Based on continuum mechanics modeling, the buckling and post-buckling behaviors of the composite panel were predicted and compared with the buckling shapes that are obtained from experiments. The numerical simulation methods and experimental test technique in the work provides a useful tool to study the compressive buckling behaviors of composite panel with M-type stiffeners.     

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.     

大开孔单层椭球网壳-组合楼板混合结构设计及稳定性分析

本文以九寨沟甘海子国际会展中心展厅结构为工程背景,介绍了单层椭球网壳-组合楼板混合结构的分析设计过程。首先,采用相贯节点的计算理论,对该工程采用的鼓节点的设计进行了详细论述。此外,本文采用子空间迭代法对该混合结构进行了特征值屈曲分析;采用非线性有限元理论,结合N-R法和柱面弧长跟踪技术,对该结构进行了考虑初始缺陷的非线性全过程分析;并采用估算公式进行了校核。计算结果表明,特征值屈曲分析结果是局部失稳的极限荷载,而非线性屈曲分析结果是整体失稳的极限荷载。对于有局部刚度薄弱的结构,采用非线性屈曲分析得到的极限荷载更为合理。     

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.     

组合肋壳几何非线性分析

提出了一种球面组合肋壳截面形式，基于非线性有限元理论，采用空间梁单元和等厚曲边壳单元，考虑空间结构的几何非线性影响，推导了T．L坐标系下组合肋壳非线性单元刚度矩阵。分别讨论了在不同矢跨比、不同荷载作用、不同边界条件下组合肋壳的极限承载力和失稳形态。由大量算例得到了非线性极限承载力与线性极限承载力的比值为0．66及不同情况下结构承载力变化趋势，组合肋壳的极限承载力比混凝土壳承载力提高20％。     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

复合圆柱形壳在径向冲击荷载和轴压荷载作用下的瞬时动力响应

基于首次逼近理论,利用第一阶剪切变形理论对圆柱形壳的自由和强迫振动进行分析。边界条件（BCs）考虑为悬臂状态。分析复合壳体在横向冲击和轴向压力作用下的动力响应（轴压荷载小于临界屈曲荷载）,同时对复合柱形壳进行了建模分析。利用卷积积分对给定荷载状况下的壳体进行分析。揭示纤维方向、轴向荷载及一些几何参数对壳体时间响应的影响。结果表明：动力响应主要由结构的自振周期所控制。     

Buckling analysis of a cooling tower shell with measured and theoretically-modelled imperfections

Geometrical imperfections were measured using photogrammetric techniques on an existing reinforced concrete cooling tower shell. The imperfections, related to the radii of such a real shell, were used as input data to create a real shape of the cooling tower. Numerical analysis was carried out for three models: (P) perfect shell of revolution, (M) shell with measured imperfections, (T) shell with a theoretical imperfection corresponding to the primary buckling mode under dead load. The buckling analysis was related to the linearized eigenvalue problem of elastic shells. The shell midsurface was approximated by eight-node quadrilateral isoparametric finite elements. Computations were carried out using the ANKA computer code. Critical values of the load parameter enable confirmation of a partial correlation between existing imperfections and buckling modes under dead load. The most disadvantageous direction of the wind load application on the real shell was found, in order to evaluate the decrease in the load-carrying capacity of the cooling tower shell against buckling. Theoretically modelled imperfections give rather unrealistic values of buckling loads of the real shell.     

北京新机场装配式单层铝合金网壳结构整体稳定性能研究

以北京新机场装配式单层铝合金网壳结构作为研究对象,建立了其装配式节点——板式节点及考虑节点性能的单层铝合金网壳的有限元模型,分析了板式节点的力学性能及节点性能对单层铝合金网壳稳定性能的影响。研究表明：板式节点刚度良好,破坏表现为不锈钢拉铆钉剪切破坏、连接板拉剪破坏和杆件在螺栓孔处承压破坏;北京新机场装配式单层铝合金网壳结构的整体稳定性能良好,承载力约为刚接网壳结构的90%,满足JGJ 7—2010《空间网格结构技术规程》的要求;由于铝合金材料无明显的屈服台阶,弹性模量较小,考虑几何非线性和材料非线性的稳定承载力比仅考虑几何非线性的稳定承载力降低约30%,结构发生弹塑性失稳,结构失稳形态表现为网壳结构在靠近长轴右端出现凹陷。     

Elastic buckling of cold-formed steel columns and beams with holes

Simplified methods for approximating the global, distortional, and local critical elastic buckling loads of cold-formed steel columns and beams with holes are developed and summarized. These methods provide engineering approximations appropriate for design, but are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in industry. The simplified methods are developed as a convenient alternative to shell finite element eigen-buckling analysis, which require laborious and subjective visual identification methods as well as commercial software not generally accessible to the engineering community. Global buckling of cold-formed steel beams and columns, including the influence of holes, is predicted with approximate “weighted average” cross-section properties formulated from classical energy-based stability solutions. Distortional and local buckling of a cold-formed steel member with holes are determined with the semi-analytical finite strip method, considering appropriate modifications to the element thickness and choice of buckling half-wavelength. The proposed methods are verified with shell finite element eigen-buckling studies. Unambiguous, simple methods for elastic buckling prediction of members with holes is central to the extension of the Direct Strength Method (DSM) for cold-formed steel member ultimate strength determination.     

Shear-flexible thin-walled element for composite I-beams

A shear-flexible finite element based on an orthogonal Cartesian coordinate system is developed for the flexural and buckling analyses of thin-walled composite I-beams with both doubly and mono-symmetrical cross-sections. Using the first-order shear deformable beam theory, the derived element includes both the transverse shear and the restrained warping induced shear deformations. Governing equations are derived from the principle of minimum total potential energy. Three different types of finite elements, namely, linear, quadratic and cubic elements are developed to solve the governing equations. The geometric stiffness for the buckling analysis of axially loaded, thin-walled composite beams is developed. The resulting linearized buckling problem is solved using a shifted inverse iteration algorithm. A parametric study of the effects of the aspect ratio and the fibre orientation on the tip displacement is presented. The convergence of the elements is also investigated. The elastic buckling loads for mono- and doubly-symmetric I-beam cross-sections are compared with other results available in the literature and with solutions using shell elements in a commercially available finite element program.     

考虑杆件屈曲的网壳结构的稳定性

为了了解杆件屈曲对网壳结构稳定性的影响,关键问题就是如何区分网壳结构中的杆件屈曲并得出其辨别方法。以一个Kiewitt-8型球面网壳为实例,研究杆件屈曲的特性和传播规律。同时,应用有限元分析软件ANSYS对一个球状网壳结构模型的测试结果进行分析和比较,得出对杆件屈曲的判定结果和其对结构的影响。判定结果与试验数据完全吻合。从杆件屈曲方面考虑,对材料非线性,初始几何缺陷以及杆件型号对杆件和网壳结构稳定性的影响进行研究。结果显示,所采用的方法可以有效地判定网壳结构的杆件屈曲问题;杆件屈曲和其扩散会直接影响到整个结构的稳定性。     

Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections

Lateral buckling of thin-walled composite beams with monosymmetric sections is studied. A general geometrically nonlinear model for thin-walled laminated composites with arbitrary open cross-section and general laminate stacking sequences is given by using systematic variational formulation based on the classical lamination theory. All the stress resultants concerning bar and shell forces are defined, and nonlinear strain tensor is derived. General nonlinear governing equations are given, and the lateral buckling equations are derived by linearizing the nonlinear governing equations. Based on the analytical model, a displacement-based one-dimensional finite element model is developed to formulate the problem. Numerical examples are obtained for thin-walled composite beams with monosymmetric cross-sections and angle-ply laminates. The effects of fiber orientation, location of applied load, modulus ratio, and height-to-span ratio on the lateral buckling load are investigated. The torsion parameter and a newly-defined composite monosymmetry parameter are also investigated for various cases.     

Stability of reticulated shells considering member buckling

In order to understand the influence of member buckling on the stability of reticulated shells, a key problem of how to distinguish the member buckling for reticulated shell structures was pointed out, and judgment methods of member buckling were obtained. Using a Kiewitt-8 dome as an example, the buckling characteristic and propagation rule of member buckling were studied. Meanwhile, a reticulated dome model tested was analyzed and compared by using the finite element software ANSYS. Judgment results of member buckling and the influence of member buckling on the structure were obtained. The judgment results accorded well with the test. Then taking the member buckling into consideration, the effect of material nonlinearity, initial geometrical imperfections, and member size on the stability of the members and the reticulated shell structures were investigated. The results show that the methods adopted can judge the member buckling for reticulated shell structures effectively; the member buckling and its propagation can affect the stability of the structure directly.     

大跨度钢-混凝土组合薄壳屋盖模型试验研究

本文对一种新型的结构形式——钢-混凝土组合薄壳进行缩尺破坏试验,得出该结构在多点集中荷载作用下的非线性特征以及承载性能,对裂缝的出现与开展、单元连接螺栓处失效以及底板屈曲行为作了详细的观察分析.试验结果表明,由于螺栓节点的存在,导致壳体内部刚度的不连续,从而减弱了组合壳的整体性能.本文实验结果为后续对该结构的非线性有限元分析提供了可靠依据.     

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.