基于累积失效法的含损伤格栅加筋板非线性屈曲状态分析

分别采用基于Mindlin一阶剪切理论八节点层合板单元和三节点层合梁单元来模拟蒙皮和肋骨,用累积失效法研究了在压缩载荷作用下蒙皮内含分层损伤复合材料正交格栅加筋板的非线性屈曲性态,分析中考虑了加载过程中蒙皮和肋骨纤维断裂、基体损伤和纤维-基体剪切失效造成的刚度退化,并采用了非线性接触单元模型处理蒙皮分层上下子板间的接触效应。通过典型算例,讨论了蒙皮铺设方式、蒙皮分层的面积和深度、肋骨与蒙皮的刚度比,累积失效行为等因素对格栅加筋板非线性屈曲性态的影响。     

具脱层的正交铺设圆柱壳的初始后屈曲分析

基于非线性弹性理论,建立了含脱层正交铺设圆柱壳的后屈曲控制方程,应用Koiter初始后屈曲理论和小参数摄动法,导出了系统的一阶和二阶摄动控制方程,以及相应的边界条件、位移连续条件和力平衡条件,然后逐阶求解．算例中,讨论了不同脱层深度和长度对脱层复合材料圆柱壳屈曲和初始后屈曲特性的影响,并与已有文献进行了比较．     

反对称铺设复合材料层合板非线性后屈曲分析

基于层合板壳理论，考虑反对称铺设层合板的拉弯耦合效应和后屈曲过程中的非线性几何变形，推导了由应力函数和挠度表示的复合材料层合板的后屈曲控制方程。引入无量纲参数对控制方程和边界条件进行无量纲化，以消除材料参数及几何尺寸对分析结果的影响。采用摄动法将无量纲的非线性控制方程及边界条件展开成一系列非齐次线性摄动方程组，分析各阶摄动方程的通解与特解的构造，并逐次求解，建立了反对称铺设复合材料层合板受单向均布压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。进而运用ABAQUS软件对复合材料层合板在面内压缩载荷作用下的屈曲和后屈曲进行有限元分析，结果表明理论解与ABAQUS结果十分接近，验证了理论解的正确性。在此基础上进一步讨论了铺设角度、铺设层数和拉弯耦合效应等对层合板后屈曲性能的影响。研究发现层合板的屈曲载荷受铺设角度与层数的影响较为显著，而拉弯耦合效应使板的屈后强度大大降低。     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系，引入沈为和Kachanov损伤演化方程，建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型；应用von Karman板理论，导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散，时间上采用增量算法和Newton-Cotes积分法离散，控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响，且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大，板后屈曲趋于稳定时的挠度就愈大，损伤的影响愈明显；而随着长宽比的增大，板后屈曲趋于稳定时的挠度愈小，损伤的影响却随之增大.     

复合材料结构的动力屈曲研究进展

本文系统地回顾了复合材料结构的动力屈曲研究进展，对周期性动载荷和瞬态动载荷作用下，复合材料结构的动力屈曲作了阐述；讨论了耦合效应，横向剪切变形、初始几何缺陷以及铺层方式等因素对动力屈曲的影响；就复合材料结构动力屈曲研究的发展前景提出了一些有益的建议     

含多个分层复合材料层合板后屈曲性态研究

基于Mindlin假定下的大变形板／壳理论，采用参考面单元和虚拟杆单元相结合的非线性有限元方法，建立了分析含多个穿透分层损伤层合板后屈曲行为的有限元计算模型，并给出了考虑接触后非线性屈曲方程的迭代算法，从而研究考虑层间接触效应的多分层层合板的后屈曲性态。文中着重讨论了分层的深度、数目和尺寸对含多分层合板后屈曲性态的影响。大量数值分析结果证明了该模型的有效性，并且得到了一些对层合板结构设计和对含分层损伤层合板评估有益的结论。     

Further discussion on the effect of shear deformation on structure displacement in structural mechanics

剪切变形对位移的影响程度,不仅取决于高跨比,截面形式对其影响也较大. 通过实例讨论了工程中广泛采用的三种形式截面：一般截面、薄壁型截面、复合材料截面. 分析表明：（1） 相较于一般截面形式,薄壁型截面梁中剪切变形对位移的影响较大,尤其是短而高的薄壁梁,剪切变形引起的位移更不能忽略. （2） 复合材料截面梁,剪切变形引起的位移受截面材料弹性模量比、不同材料截面高度比影响较大：截面材料弹性模量比越大,加强材料越厚,剪切变形对位移的影响越大. 这会导致复合材料截面,即使是细长的梁,剪切变形引起的位移有时也不能忽略.     

含脱层损伤复合材料层合梁的冲击动力屈曲

针对含初始缺陷和脱层损伤的复合材料层合梁的轴向冲击动力屈曲问题进行了分析。基于Hamilton原理导出了考虑初始缺陷、轴向和横向惯性、横向剪切变形以及转动惯性影响时含脱层损伤复合材料梁的非线性动力屈曲控制方程;基于B-R准则,采用有限差分方法求解了受轴向冲击载荷作用下含脱层损伤复合材料梁的动力屈曲问题;讨论了冲击速度、初始几何缺陷、铺层角度以及脱层长度等因素对复合材料层合梁动力屈曲的影响。     

对结构力学中“剪切变形对位移的影响”的进一步探讨

剪切变形对位移的影响程度,不仅取决于高跨比,截面形式对其影响也较大.通过实例讨论了工程中广泛采用的三种形式截面:一般截面、薄壁型截面、复合材料截面.分析表明:(1)相较于一般截面形式,薄壁型截面梁中剪切变形对位移的影响较大,尤其是短而高的薄壁梁,剪切变形引起的位移更不能忽略.(2)复合材料截面梁,剪切变形引起的位移受截面材料弹性模量比、不同材料截面高度比影响较大:截面材料弹性模量比越大,加强材料越厚,剪切变形对位移的影响越大.这会导致复合材料截面,即使是细长的梁,剪切变形引起的位移有时也不能忽略.     

基于混合变量的脱层壳屈曲分析

提出一种分析脱层圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于一阶剪切理论，通过定义广义位移变量和对应的广义力变量，建立壳的改进的混合变量能量泛函；然后引入条形单元，对混合变量在环向进行离散，从而导出超级壳单元的混合变量能量泛函，由变分原理得到控制方程，采用传递函数方法得到其形式解；最后，将含环向贯穿脱层的复合材料层合壳作为超级壳单元的组合体，得到脱层壳的屈曲方程。给出了脱层大小和深度以及脱层壳边界条件对屈曲载荷的影响。     

Post-buckling behaviour of slender structures with a bi-linear bending moment-curvature relationship

Certain classes of slender structures of complex cross-section or fabricated from specialised materials can exhibit a bi-linear bending moment-curvature relationship that has a strong influence on their global structural behaviour. This condition may be encountered, for instance, in (a) non-linear elastic or inelastic post-buckling problems if the cross-section stiffness may be well approximated by a bi-linear model; (b) multi-layered structures such as stranded cables, power transmission lines, umbilical cables and flexible pipes where the drop in the bending stiffness is associated with an internal friction mechanism. This paper presents a mathematical formulation and an analytical solution for such slender structures with a bi-linear bending moment versus curvature constitutive behaviour and subjected to axial terminal forces. A set of five first-order non-linear ordinary differential equations are derived from considering geometrical compatibility, equilibrium of forces and moments and constitutive equations, with hinged boundary conditions prescribed at both ends, resulting a complex two-point boundary value problem. The variables are non-dimensionalised and solutions are developed for monotonic and unloading conditions. The results are presented in non-dimensional graphs for a range of critical curvatures and reductions in bending stiffness, and it is shown how these parameters affect the structure's post-buckling behaviour.     

The role of plastic deformation on the impact behaviour of high aspect ratio aluminium foam-filled sections

The main objective of this work is to investigate the role of the plastic deformation of metal foams on the dynamic behaviour of aluminium foam-filled columns with respect to their energy absorbing capabilities. The influence of the cross-section shape as well as other parameters is thoroughly studied. A comparison with correspondent hollow-sections is performed concerning the dissipation of kinetic energy and the obtained deformed profiles. For this particular purpose, three-dimensional finite element modelling dynamic analyses are carried out using ABAQUS/Explicit in order to achieve an in-depth study of the structural crash behaviour, during which energy needs to be absorbed in a controlled manner. A comprehensive numerical study of the crush behaviour of aluminium foam-filled sections undergoing axial compressive loading is performed. The results obtained are also analysed with respect to the reduction in the length of the structural element and impact time, the effect of friction between the foam and the outer skin, the energy decomposition, the role of plastic deformation, the influence of the skin material and impact velocity, and the influence of the shape of the cross-section on the impact behaviour. A comparison with existing analytical expressions is made in order to corroborate the numerical results.     

A micro-mechanical homogenisation model for masonry: Application to shear walls

An improved micro-mechanical model for masonry homogenisation in the non-linear domain, is proposed and validated by comparison with experimental and numerical results available in the literature. Suitably chosen deformation mechanisms, coupled with damage and plasticity models, can simulate the behaviour of a basic periodic cell up to complete degradation and failure. The micro-mechanical model can be implemented in any standard finite element program as a user supplied subroutine defining the mechanical behaviour of an equivalent homogenised material. This work shows that, with the proposed model, it is possible to capture and reproduce the fundamental features of a masonry shear wall up to collapse with a coarse finite element mesh. The main advantage of such homogenisation approach is obviously the possibility to simulate real complex structures while taking into consideration the arrangement of units and mortar, which would otherwise require impractical amount of finite elements and computer resources.     

带旋转自由度C^0类任意四边形板（壳）单元

基于Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｉｌｉｎ板弯曲理论和Ｖｏｎ－Ｋａｒｍａｎ大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Ａｌｌｍａｎ膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点Ｃ＾０类板单元。大量算例表明：该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。     

A new theoretical approach for structural modelling of riveted and spot welded multi-spot structures

A general theoretical approach based on theory of elasticity is presented in order to define the structural behaviour of riveted and spot welded joints. The new closed form solutions lead to the definition of a joint element useful to FE models of riveted or spot welded multi-spot structures. The objective is an accurate evaluation of the local elastic stiffness of spot joints in FE analysis, which is fundamental to perform a reliable simulation of multi-joint structures and, consequently, a good estimate of loads acting on spots; this makes it possible to introduce structural stress or new general criteria allowing, for example, to predict fatigue behaviour. On the other hand, a low entry of degrees of freedom is needed when several spot joints are present in a complex structure. The goal is to reach a reliable spot region model which can be used as the basis to develop a spot element in FE analysis. In the present paper, based on new closed form solutions, a spot element is introduced, so as to precisely evaluate both local and overall stiffness both of spot welded joints and riveted joints. Based on the stress function approach and the Kirchhoff plate theory in linear elastic hypotheses, closed-form in-plane stress, displacement, moment and transverse shear force solutions are derived for a new bidimensional model, subjected to various types of loads. The capability to simulate spot welds or rivets depends on the definition of two elastic parameters intrinsic in closed form solutions, that tunes the theoretical model according to actual joint behaviour.The proposed joint element combines the precision in the simulation with a very limited number degrees of freedom in the overall finite element model of an actual multi-spot structure.The results obtained using the introduced theoretical framework and spot element approach perfectly match those obtained using very refined FE models and experimental data.     

Influence of geometrical defects on the mechanical behaviour of hollow-sphere structures

Hollow-sphere structures could represent an alternative to classical cellular materials, such as metal foams or honeycombs, for various structural applications; such stainless steel random structures are already on the market. One advantage of hollow-sphere structures unlike metal foams ensues from the possibility to stack the spheres regularly, even if in the literature there are only examples of limited size regular stackings for the moment. Higher mechanical properties than those of random cellular structures are expected for such regular structures according to modelling studies. Nevertheless, because of the difficulty in processing perfect regular stackings, it seems to be critical to study the influence of architectural defects on the overall mechanical behaviour of these cellular structures. Emphasis is on geometrical defects by introducing some dispersions on the sphere thickness and the meniscus size. Influences of both the magnitude of dispersion and the distribution of the defects on the mechanical behaviour of hollow-sphere structure are investigated. Especially, collapse mechanisms resulting from plasticity and their inhomogeneous localisation in the structure are studied in details. The case of periodic defects is addressed too in order to compare the mechanical response of infinite stackings to that of finite ones. This work highlights the significant influence of the defects on the effective mechanical behaviour of hollow-sphere structures. Most of the time, geometrical dispersion and defects are detrimental for the stacking behaviour, especially when understructures made of the defective hollow spheres or menisci are observed.     

轴向运动二维传输结构动力学有限元建模与仿真

基于物理中面概念和经典薄板理论，应用有限元法研究了机械工程中的二维传输结构作轴向运动时的面外自由振动特性．根据实际工程结构特点及设计要点，考虑受双向预张应力作用的传输薄板结构模型，由哈密顿原理出发严格导出了结构的有限元动力学方程，得到了体现轴向传输结构特性的陀螺矩阵．该矩阵具有反对称结构，这与加权余量法所得的陀螺矩阵结构不同．采用3 节点三角形单元离散求解域，且单元不受轴向运动影响，给出了单元密度对计算结果精度的影响．分析了传输结构预张应力和轴向速度与自由振动固有频率的关系；考察了不同结构的陀螺矩阵对数值结果的影响．将部分结果与ANSYS 软件模拟对比，显示出良好的一致性，证明了本文方法的有效性．研究结果可为典型传输带等结构的振动控制提供参考，建模方法可为ANSYS等计算软件添加轴向运动结构新模块提供理论依据．     

Finite element formulation for active functionally graded thin-walled structures

For the analysis and design process of smart structures with integrated piezoelectric patches, the finite element method provides an effective simulation approach. In this paper, an attempt on modeling and simulation of the behavior of hybrid active structures is carried out using developed Kirchhoff-type-four-node shell element.The finite element results are compared with reference solutions taking into account the electromechanical responses of smart structures with various geometries, and the results show very high agreement. The main aspect of the application of the proposed element is to predict the behavior of FGM shells containing piezoelectric layers. A set of numerical analyses is performed in order to highlight the applicability and effectiveness of the present finite element model, notably for smart FGM structures. A comprehensive parametric study is conducted to show the influence of material composition, the placement and the thickness of the piezoelectric layers on the deformation of the laminated structure.     

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.     

Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach

The vibration modelling of waveguide structures is considered. These structures comprise waveguides connected via joints. Traditionally, analytical models of the wave behaviour of such structures can be developed if they are simple (beams or rods connected at point joints, etc.). However, if the waveguides are of complicated constructions (truss-like, layered media, etc.) or the joints are complicated (e.g. of significant physical dimensions), obtaining the wave characteristics might be a formidable task. In this paper, such structures are modelled using a hybrid finite element/wave and finite element (FE/WFE) approach. The waveguides are modelled using the WFE method and thus their wave characteristics are obtained regardless of the complexity of their cross-section. The joints are modelled using standard FE, and the WFE and FE models are coupled to yield the scattering properties of the joints. The propagation and scattering models are assembled to describe the behaviour of the structure using relatively small models, while also providing information for other applications such as structure-borne sound, statistical energy analysis, etc. Numerical examples are presented to illustrate the approach.