Nonlinear response of laminated cylindrical panels

The geometric nonlinear responses of laminated composite cylindrical panels subjected to (i) axial compression and (ii) central concentrated load are investigated in this work. The parameters considered are: number of layers, symmetric/antisymmetric laminate constructions, cross-ply/angle-ply fibre orientation, boundary conditions and central angle of panel. An eight-node degenerated layered shell element with an efficient explicit through-thickness integration scheme is employed. It has been observed that the cylindrical panels under axial compression exhibit stable post-buckling paths and the number of layers in the laminate for a given total thickness has considerable influence on the load–deflection behaviour. The strength of shallow panels with longitudinal edges hinged, curved edges free and subjected to a central concentrated load is controlled by the limit point load, whereas for deep panels with other parameters remaining the same, the strength is controlled by the bifurcation load. The boundary conditions have significant influence on the load-carrying capacity. The panels with longitudinal edges hinged and curved edges free should be avoided in construction, as they undergo either limit point or bifurcation failure at very low load levels compared with other edge conditions.     

Response of stiffened and unstiffened plates subjected to blast loading

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. For unstiffened panels with inplane restraint along their edges, the dynamic response of an imperfect panel was predicted using a large displacement elastic analysis based on Lagrange's equation, with the panel being treated as a shallow shell. For stiffened panels, the finite element (FE) technique was used to establish the validity of using the simplified technique to predict the inter-stiffener panel displacements for a simply supported panel. A parametric study has been carried out to analyse the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response. The significant effect of boundary conditions is demonstrated by including the actual boundary conditions of a test frame in the finite element modelling of a large-scale stiffened floorplate panel used in an experimental test series.     

板肋加劲板整体稳定数值模拟与受力机理研究

分别采用梁单元与板壳单元建立同时考虑初始几何缺陷和焊接残余应力的受压板肋加劲板整体稳定分析有限元模型,并以相应试验结果进行验证,得到梁与板壳单元模拟受压板肋加劲板整体稳定的异同。采用经验证的数值模拟方法,对不同弯曲失稳方向板肋加劲板的受力机理进行了研究。结果表明:采用板壳单元可以较好还原板肋加劲板整体稳定受力性能,板壳有限元模型与试验试件的承载力最大相对误差为4.2%,平均相对误差为1.48%; 梁单元模型与长(中长)柱试验试件的承载力最大相对误差为5.4%,平均相对误差为1.92%,与短柱试件的承载力相对误差虽仅为0.7%,但由于不能考虑板件发生的塑性失稳,其应力-位移曲线拟合情况相对较差; 不同弯曲失稳方向板肋加劲板整体稳定构件的破坏特征不同,其中对于板肋侧弯曲的板肋加劲板整体稳定构件,被加劲板边缘部分受压达到材料屈服强度且板肋边缘受拉达到屈服强度时,构件整体达到其承载极限; 对于被加劲板侧弯曲的板肋加劲板整体稳定构件,当板肋边缘部分受压达到材料屈服强度时,构件整体达到其承载极限; 对于实际工程中组成钢箱梁顶板的板肋加劲板,制作时应避免朝向板肋侧的变形。     

Dynamic stability analysis of composite skew plates subjected to periodic in-plane load

Here, the dynamic stability characteristics of simply supported laminated composite skew plates subjected to a periodic in-plane load are investigated using the finite element approach. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia. The boundaries of the instability regions are obtained using the Bolotin's method and are represented in the non-dimensional load amplitude-excitation frequency plane. The principal and second instability regions are identified for different parameters such as skew angle, thickness-to-span ratio, fiber orientation and static in-plane load.     

The computational post-buckling analysis of fuselage stiffened panels loaded in shear

Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements.     

悬索桥静动力特性分析的有限板壳单元法

本文提出一种基于正交异性板壳单元悬索桥静动力分析方法，以实际工程为例。分别按梁单元模型与正交异性板壳单元模型对其进行了静力与动力分析，并对计算结果进行了详细的比较分析。计算表明，正交异性板单元模型克服了梁单元模型中存在的问题，对大跨度悬索桥整体动力性能与局部的静力性能都能做出更加精确的模拟计算。     

The computational post buckling analysis of fuselage stiffened panels loaded in compression

Fuselage panels are commonly fabricated as skin–stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the finite element method and employing non-linear material and geometric analysis procedures, it is possible to model the post buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Investigation of element, mesh, idealisation, imperfection and solution procedure selection has been undertaken, with results validated against mechanical tests. The research undertaken has demonstrated that using a commercial implicit code, the finite element method can be used successfully to model the post buckling behaviour of flat riveted panels. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform axial compression.     

Buckling analysis of stiffened plates subjected to non-uniform biaxial compressive loads using conventional and super finite elements

This paper presents the buckling analysis of stiffened plates, using both conventional and super finite element methods. Mindlin plate and Timoshenko beam theories are utilized so as to formulate the plate and stiffeners, respectively. The arbitrary oriented stiffeners can be positioned anywhere within the plate element and are not limited to be placed on nodal lines. Therefore, any configuration of plate and stiffeners can be modeled. Furthermore, extensive boundary conditions as well as general in-plane loading conditions can be considered using the proposed method. As the applied in-plane loads are not uniform, the buckling load is evaluated in two steps. First, the elasticity problem is solved to determine the stress distribution in prebuckling stage. Applying the principle of minimum potential energy, based on derived stress distribution, yields to the buckling equation of stiffened plates. Numerical examples are proposed to study the accuracy and efficiency of the developed super elements. Effects of various combinations of biaxial loads along with different boundary conditions on buckling characteristics of stiffened panels are also investigated.     

A numerical investigation into the effects of slamming impulsive loads on the elastic–plastic response of imperfect stiffened aluminium plates

Nowadays stiffened aluminium panels have been widely used for marine applications such as building high speed vessels. The panels of high speed vessels are subjected to different in plane and out-of-plane loads. One of the most important out-of-plane loads is the impulse caused by bottom slamming. In the present study, the transient large deflection elastic–plastic responses of a number of stiffened aluminium panels subject to slamming impulsive loads are investigated. The impulsive loads are exerted on the finite element models of aluminium panels proposed by Ultimate Strength Committee of ISSC 2003. Several impact conditions are considered to study the influence of several structural factors such as heat affected zone (HAZ) arrangement, boundary conditions, thickness of plating, number of transverse frames and in-plane fixation. Based on these studies, several design-oriented conclusions are issued. Moreover, this paper outlines the various aspects of the influence of the HAZ presence on the strength of the slam-loaded panels with respect to loading time ratio.     

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.     

Experimental studies on stiffened plates under in-plane load and lateral pressure

An experimental study on stiffened plates subjected to combined action of in-plane load and lateral pressure is described in the paper. Details of the experiments and finite element analyses of the specimens tested are presented along with the results. Measurements of initial imperfection in the specimens have been made and included in the analyses. Results show that lateral load carrying capacity of stiffened plate drops with increase in axial load and vice-versa. It is found that plate slenderness ratio has significant influence on the ultimate load capacity of stiffened plates subjected to both in-plane load and lateral pressure. Increase of plate slenderness ratio results in a decrease of ultimate load capacity of stiffened plate. The accuracy of the finite element modelling is established by comparing the results with the corresponding experimental values.     

The in-plane shear failure of transversely stiffened thin plates

This paper examines the response of stiffened plates with plain flat outstands when subjected to in-plane shear loading in the form of applied in-plane shear displacement. The buckling and post-buckling failure capabilities of thin plates subjected to in-plane shear, can, of course, be improved through the introduction of stiffening elements whose flexural and torsional rigidities can contribute significantly towards a more stabilised structural system. This paper details appropriate suitable finite element modelling strategies and procedures to enable the determination of the post-buckled failure response of the stiffened shear panels and to highlight the significant influence of the stiffeners. The modelling procedures are able to describe the complete loading history of the stiffened panel structures from the onset of initial buckling through the elastic post-buckling phase of behaviour involving the considerable interaction between plate and stiffener and then through initial material yielding and yield propagation to ultimate conditions and elasto-plastic unloading.     

Dynamic elastic instability of long circular cylindrical shells under pure bending

The present paper studies the responses and instabilities of long circular cylindrical shells subjected to dynamic pure bending. The dynamic instability characteristics of the shells subjected to a sudden step bending load of infinite duration are explored. Analysis is performed using nonlinear finite element numerical methods. Critical dynamic moments are determined through the use of Budiansky and Routh's stability criterion. Numerical predictions for the dynamic instability are compared with those static results given earlier by Brazier. The effects of shell geometry on the dynamic stability of the shells are shown. It is found that the dominating factor to affect the shell stability is the ovalization of the shell cross-section in the centre of the shell.     

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.     

箱梁桥自振分析的非协调实体退化壳元法

桥梁结构的自振特性对研究其在风荷载和地震荷载作用下的动力响应具有重要意义,其分析精度取决于结构质量和刚度分布特性的准确计算。根据质量等效原理推导了非协调实体退化板壳元的一致质量矩阵,并采用逆迭代法求解了箱梁桥的固有频率和振型。实体退化板壳元可精确描述箱梁桥质量分布,便于同实体单元连接,对不同板厚的箱梁桥均适用。非协调位移的引入使其更适合描述箱梁桥各构件的变形特性。算例表明:单元可显著提高箱梁桥动力特性分析的效率,可获得满意的计算精度。     

Numerical and experimental investigations on the compression behaviour of stiffened plates

The main objective of this paper is to present the results of the finite element method for non-linear analysis of stiffened plates subjected to axial compression load considering post-buckling behaviour up to collapse. For this purpose two series of well executed experimental data on longitudinally stiffened steel plates with and without transversal stiffeners subjected to uniform axial in-plane load carried out to study the buckling and post-buckling up to final failure have been chosen. The first series are those of Ghavami where the influences of stiffener cross-section of the type rectangular (R), L and T, their spacing and the presence of rigid transversal stiffeners have been studied. The second series of Tanaka & Endo, where the behaviour of stiffened plates having three and two flat bars for longitudinal and transversal stiffeners respectively were analysed. For the purpose a well-established commercially available Finite Element program ANSYS has been chosen. The selected element was SHELL43, which can trace the full-range, elastic-plastic behaviour of the stiffened plates. It is seen that the simulated results of FEM are in good consistency with the test results.     

球面网壳结构在强震下的失效机理

研究了球面网壳结构在地震等动力荷载作用下两种可能的失效机理 :由于几何非线性起主要作用导致的动力失稳和由于塑性变形过度发展导致的强度破坏。提出了统一的基于响应分析的关于网壳结构失效机理的理论框架。对单层球面网壳在简谐荷载和地震荷载作用下的失效机理进行了较系统的分析 ,提出了具体的动力失稳和强度破坏判别准则 ,求得了相应的极限荷载。取得的结果具有良好的规律性 ,验证了所提出的理论框架的合理性和实用性     

Free vibrations of fluid-filled cylindrical shells on elastic foundations

The free vibration characteristics of fluid-filled cylindrical shells on elastic foundations are presented by a semi-analytical finite element method. A shell is discretized into cylindrical finite elements where shell governing equations based shape functions in the longitudinal direction are used instead of the usual simple polynomials. Non-uniformities of the foundations in the circumferential and longitudinal directions are handled by the Fourier series and an element mesh strategy, respectively. The fluid domain is described by the potential flow theory. The hydrodynamic pressure acting on shells is derived from the condition for dynamic coupling of the fluid-structure. The effect of fluid in a shell, shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells is investigated. Numerical results based on the present method converge more rapidly than those obtained by the simple polynomial formulation. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.     

Simple and combination resonances of rectangular plates subjected to non-uniform edge loading with damping

The effects of damping on the behaviour of simple and combination resonances of simply-supported rectangular plates subjected to non-uniform in-plane periodic loading are studied. Finite element formulation is applied to obtain the equilibrium equation for the plate. The relations for the boundaries of parametric instability regions are obtained by using the method of multiple scales. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. For nearly uniform loading, the combination resonance zones are very small in width and may disappear in the presence of slight damping. The effects of damping show that there is a finite critical value of the dynamic load factor for each zone below which the plate cannot become dynamically unstable. It is also shown that the effects of damping on the combination resonances may be destabilizing under certain conditions.     

Behavior of beam web panel under opposite patch loading

Elastic buckling is studied for a panel with various boundary conditions including simple supports, fixed supports and elastic restraints. The panel is subjected to opposite patch loading. Following a review of existing work on the effects of localized compression, also known as patch loading, a study is conducted to take into account the restraints provided by the flanges of the I beam in a realistic manner. This study is based on a finite element model implemented in the CAST3M software. A new equation is proposed to calculate the buckling critical coefficient for a beam web panel considering the rotational stiffness provided by the flanges. The model is then applied to longitudinally stiffened web panels which are subjected to opposite patch loading.A parametric analysis is performed to determine the transition from a global buckling mode to a local buckling mode where the sub-panels on each side of the stiffener behave separately. The numerical results show that the flexural rigidity of the stiffener is the appropriate parameter that governs the buckling mode. From these results, a formula is proposed to calculate the buckling critical coefficient of stiffened web panels.