Analysis for buckling and vibrations of composite stiffened shells and plates

This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C⁰ continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.     

复合材料加筋圆拱壳的失稳特性分析

本文应用增量形式的拉格朗日列式法对其有纵横加筋的迭层圆拱壳在均布载荷作用下的稳定性进行了非线性有限元分析。文中应用Sander 壳体理论及横向剪切的影响, 推导了矩形壳元及与该壳元变形相协调的直梁元和曲梁元的切线刚度矩阵。编制了FORTRAN 计算程序。计算并分析了加筋拱壳的局部及整体失稳过程。      

半解析有限元法分析环向加劲圆柱壳外压稳定性

采用一般有限元法分析环向加劲圆柱壳外压稳定性需要用确定的单元结点位移描述待定的各种失稳波形的变化,从而造成单元划分较多,基函数复杂,所需计算机内存大,往往使稳定性分析难于实现。本文利用半解析有限元法来分析圆柱壳的稳定性,可以利用解析的成果代替一般有限元法的离散化处理,有效地解决了用一般有限元法要遇到的难题。半解析有限元法的特点是:在位移模式中,周向引入圆环板和圆柱壳的解析函数,轴向和径向采用了离散型的内插多项式函数。由于采用了解析函数与离散函数相结合的位移模式,所以不但减少了自由度,并提高了计算精度,而且也能方便地处理各种复杂的结构及其不同的连接方式。本研究采用了几何非线性大挠度理论,据此,推导了单元的弹性刚度矩阵和几何刚度矩阵。在稳定性计算中,把求解失稳荷载和失稳变形形态的问题,转化为数学上求实矩阵的最大特征根及其特征向量的问题。本文最后给出了计算实例,计算结果与理论解吻合较好,说明此法是切实可行的,并且具有广泛的使用范围。     

圆柱薄壳在局部轴向压力作用下的屈曲

采用非线性有限元法对局部轴向压力作用下圆柱壳的屈曲进行了全过程分析,并对其进行了试验研究。有限元分析和试验结果都表明,圆柱壳在压力作用位置附近发生局部屈曲并形成局部凹陷,维持后屈曲平衡的是一个近似常量的压力。该压力即为圆柱壳的后屈曲承载力,它决定着圆柱壳的实际承载力。在其它因素相同时,该压力与壳体厚度5.2t成正比。     

An isoparametric joint/interface element for finite element analysis

A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.     

开口及边界条件对复合材料三分之一柱面壳压缩屈曲性能的影响

研究了完整、开口周边加强及开口加口盖3种型式的复合材料三分之一柱面壳的压缩屈曲性能,考查了3种典型复合材料柱面壳的轴压屈曲强度,分析了开口及口盖对柱面壳压缩稳定性的影响.结果表明:开口大大降低了柱面壳的轴压屈曲强度;口盖可以部分恢复其强度,但很难达到开口之前的水平.进行了开口加口盖经编织物铺层三分之一柱面壳轴向压缩试验,其轴压屈曲强度比用平面织物制造的相同结构的降低很多.为了探究其轴压屈曲强度比同类结构偏低很多的原因,进行了非均匀加载复合材料柱面壳模型有限元分析.结果表明:柱面壳边界不均匀加载会降低其承载能力,根据柱面壳刚度分布制定边界载荷可以提高其承载能力.     

Optimum design of the co-cured double lap joint composed of aluminum and carbon epoxy composite

Since the co-cured joint composed of composite and metallic structures has been widely used in joining process due to its simple and easy manufacturing process, the optimum design of the co-cured joint is important because the joint is usually the weakest part among the components of assembled structures.

In this work, the effect of design parameters for co-cured joint, such as fiber stacking sequence, stiffness ratio of composite to aluminum on the static tensile load capabilities and dynamic fatigue characteristics of the co-cured double lap joint composed of aluminum and carbon epoxy composite were experimentally investigated. Also, the stress distribution and energy release rate of the co-cured joint were calculated using finite element analysis with respect to design parameters.

From the experimental and finite element analysis results, the optimum values for each design parameters were obtained. Also, the optimum stiffness ratio for each stacking sequence of the carbon epoxy composite was obtained.     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

双肢冷弯C型钢斜节点抗震性能研究

针对双肢冷弯C型钢背靠背加垫板的截面形式,选取常用的屋檐斜节点作为研究对象,采用试验与有限元相结合的方法分析了15个斜节点试件,发现该类节点具有良好的抗震性能和较高的极限承载能力,得到了节点板厚度、螺栓间距、C型钢厚度和腹板高度等因素对斜节点抗震性能的影响情况。斜节点可能发生梁C型钢弯曲屈曲和节点板弯扭屈曲两种破坏形态,而节点板厚度是影响斜节点破坏形态的主要因素。随着C型钢厚度及高度、螺栓间距的增大,斜节点极限弯矩承载力和初始刚度增大,C型钢高度影响程度最大。建议设计时节点板厚度的取值不小于6mm,螺栓间距在11d₀~13d₀。最后,分析了16个斜节点正交试件,通过数值分析得到了斜节点半刚性特征值与节点参数之间的设计表达式,可供设计时参考。     

Shape optimization of reticulated shells with constraints on member instabilities

Reticulated shell structures are commonly adopted because of their large spanning capacity and novel appearance. These structures generally comprise slender beam members, which may cause the buckling of entire structures. A shape-finding method is proposed in this study to eliminate the bending moment while optimizing the member buckling capacity of reticulated shell structures. The bending stiffness of connections can be accurately considered in the topology optimization analysis. This study can systematically be adopted for designing, analysing and optimizing such structures. All of the work presented was conducted using a general finite element analysis program and can be easily mastered by engineering designers while avoiding tedious programming work.     

Post-buckling finite element analysis of composite cylindrical panels in axial compression

The post-buckling behaviour of composite cylindrical panels in axial compression is investigated using the nonlinear finite element theory. A branch switching algorithm with an ‘eigenmode injection’ is discussed. The effect of the reinforcement angle on the buckling load, as well as the post-buckling behaviour of the panels, are analysed. Examples are considered for separated and closely spaced bifurcation points.

By varying the reinforcement angle of the panels from 0 to 90°, two kinds of buckling modes are discovered for asymmetric and unstable symmetric lowest points of bifurcation. Local minima for the secondary branches of geometrically perfect panels are no less than 15% of their buckling loads, while values of the buckling loads alter more than twice in this region.

A 16-node degenerated shell element with full integration scheme is used.     

含损伤复合材料AGS 板的屈曲特性

采用有限元数值模拟方法, 研究了蒙皮内含分层损伤复合材料格栅加筋板结构(AGS) 的稳定性问题。对蒙皮和肋骨分别采用基于Mindlin 一阶剪切理论的复合材料层合板单元和层合梁单元来模拟, 推导了相应的有限元列式, 并通过坐标变换, 利用蒙皮与肋骨的几何连续条件, 形成了AGS 的单元刚度阵和几何刚度阵, 建立了含损伤AGS 稳定性分析的有限元控制方程。通过典型算例, 研究了压缩载荷作用下, 分层形状、分层大小、分层深度、肋骨的高度和宽度、布置方式等因素对AGS 的稳定性特征的影响。数值结果表明, 含分层损伤的AGS 具有十分复杂的屈曲性态。屈曲临界力和屈曲模式与分层面积、分层形状、分层深度、肋骨的高度和宽度、布置方式和位置均密切相关。      

柱面扁壳类覆盖件刚度的数值模拟研究

为更好地预测和评定板材覆盖件的刚度,进一步分析研究各影响因素对刚度的影响规律,以能代表汽车覆盖件曲面特点的柱面扁壳零件为研究对象,建立了柱面扁壳模拟件胀拉刚度的仿真分析模型.对柱面扁壳类覆盖件的成形、回弹以及刚度变形3个过程进行数值模拟研究,实验验证了本仿真系统的有效性和实用性,分析了压边力、回弹及约束形式对覆盖件刚度的影响规律.研究表明:增大压边力及回弹的减小都可以提高覆盖件的刚度;成形过程中,约束形式对刚度有重要影响,约束越大,刚度越大.     

Analysis of laminated conical shell structures using higher order models

In this paper is presented a numerical method for the structural analysis of laminated conical shell panels using a quadrilateral isoparametric finite element based on the higher order shear deformation theory. The displacement expressions used for the longitudinal and circumferential components of the displacement field are given by power series of the transversal coordinate and the condition of zero stresses in the top and bottom surfaces of the shell is imposed. The shape functions used for the transversal displacement are C¹ conforming and the finite element is a conical/cylindrical panel with 8 nodes and 40 degrees of freedom. The model presented performs static analysis with arbitrary boundary conditions and loads, as well eigenvalue problems (free vibration and buckling). Illustrative examples are presented and discussed.     

Q420焊接圆钢管轴心受压稳定性能试验和设计方法研究

该文进行了15个Q420高强度钢材埋弧焊接圆钢管柱轴心受压试验研究,基于试验结果总结了其失稳变形特征,分析比较了15个试件的稳定系数与我国规范柱子曲线计算值的关系,并验证了有限元模型的可靠性。基于有限元参数分析计算结果,对比60个试件的稳定系数与我国规范柱子曲线计算值的关系,对Q420高强度钢材埋弧焊接圆钢管的整体稳定设计方法提出两种建议:一是对于我国规范柱子曲线选择的建议,即对于Q420埋弧焊接圆钢管可以按a类截面计算其稳定承载力;二是更新我国柱子曲线整体稳定系数φ的计算参数α₁、α₂、α₃,建议了一条新的设计曲线。     

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

Symmetricability of pressure stiffness matrices for shells with loaded free edges

For the case of free edges which are loaded, follower forces remaining normal to the middle surface of a shell throughout the deformation history do not have a load potential. In finite element analysis, this results in an unsymmetric pressure stiffness matrix. Depending on the structure of the available computer program, implementation of an equation solver permitting solution of unsymmetric simultaneous systems of algebraic equations may be a tedious task. This explains the significance of the topic of symmetricability of pressure stiffness matrices, turning out to be of special importance in the case of static buckling under the assumption of a linear prebuckling path. At first, incremental equations for tracing the nonlinear load–displacement path are derived. Thereafter, the buckling condition is deduced. Then, it is demonstrated that symmetrization of the pressure stiffness matrix is admissible if the so-obtained ‘buckling pressure’ differs ‘very little’ from the ‘buckling pressure’ resulting from an alternative symmetric ‘buckling matrix’, as is shown to be the case for a simply supported cylindrical shell with a free upper edge, subjected to hydrostatic external pressure. The alternative symmetric ‘buckling matrix’ is a consequence of deleting the virtual work term, causing the unsymmetry of the pressure stiffness matrix, in the expression for the external virtual work. A mechanical interpretation of this virtual work term is given. It is shown to be equal to the difference of virtual work of the original pressure load and of a ‘substitute pressure-field’, of the form of a Fourier series of the former. This explains why, normally, the buckling coefficient resulting from the ‘substitute pressure-field’ represents a good approximation to the buckling coefficient stemming from the original pressure load.