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。     

带脱层的复合材料层板屈曲分析中的接触问题

用基于Mindlin板理论的有限元方法进行了带脱层损伤复合材料层板的屈曲载荷分析．为了处理在屈曲模态中上下脱层之间的接触问题，我们提出了一种有效的算法．在这种算法中，首先用一阶灵敏度分析和二次规划方法相结合的选代算法算出接触区域的虚拟力，然后将这种虚拟力转化成一些假想弹簧的刚度系数，并对原始刚度矩阵进行修正．数值算例表明本算法可以有效地克服屈曲模态中上下脱层之间的相互贯穿．同时，还对脱层的大小，形状和位置对屈曲载荷的影响进行了研究．     

含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法

提出了一种分析含内埋矩形脱层正交各向异性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Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。     

受弯脱层层板后屈曲有限元分析

脱层是复合材料层板结构中主要的缺陷形式之一。当脱层层板受到压力载荷的作用会造成脱层的局部屈曲和扩展,从而使结构的强度和刚度大为降低。含脱层层板的弯曲问题包含了脱层的压缩问题,却比压缩问题更加复杂。本文对含穿透脱层层板在纯弯载荷作用下的后屈曲问题进行了基于一阶剪切层板理论的几何非线性有限元分析,运用虚裂纹闭合技术求解了纯弯载荷作用下的脱层尖端的能量释放率各型分量,并用脱层扩展判据求解了脱层起始扩展载荷。     

轴压层合结构脱层屈曲及其扩展研究进展

脱层及其进一步扩展可以降低层合结构的强度．首先简单介绍了脱层的一般概念、起因及其分类．从一维脱层、二维脱层和柱壳脱层三个方面介绍了脱层问题的研究概况．指出拉弯耦合和横向剪切效应对脱层结构的屈曲载荷和后屈曲特性影响很大;对于不同的材料特性和尺寸比率,脱层结构的屈曲模态和最终承载能力也不同．最后提出了需进一步深入研究的问题      

复合材料脱层梁的屈曲分析

本文研究了具有任意位置透型脱层的复合材料梁的屈曲问题。基于弹性理论建立了复合材料脱层梁的基本方程式。对脱层梁进行了分区处理,利用B样条函数作为位移型函数的基函数,方便地描述了脱层长度、脱层位置。考虑边界条件、区间位移连续性条件和弯矩剪力的平衡条件以及纵向内力的附加条件,对基本方程式进行了求解。得出了脱层位置不同,脱层长度不同的屈曲荷载的变化规律,并与轴对称脱层时的屈曲荷载进行了比较,认为层合梁考虑脱层对屈曲的影响是非常必要的。     

压电体表面金属电极脱层的屈曲分析

基于弹性有限变形理论和电弹性体偏场理论,对半无限压电体及其表面电极层间存在穿透脱层的屈曲问题进行了分析. 采用平面应变模型,在脱层远处作用有平行于脱层的应变载荷. 使用Fourier积分变换,应用脱层界面的连续条件和电极表面的边界条件将问题归为第2类Cauchy型奇异积分方程组. 利用Gauss-Chebyshev积分公式将奇异积分方程组变为齐次线性代数方程组,以确定临界应变载荷. 通过数值算例,给出了底层为PZT-4材料、电极为金属Pt在不同的脱层长厚比时的临界应变载荷和屈曲形状,分析了压电体的压电、介电效应对屈曲载荷的影响. 另外给出了脱层屈曲时,脱层尖端奇异性振荡因子随不同脱层长厚比的关系曲线.      

脱层屈曲的高阶摄动解

本文用摄动法求解了三维复合材料中有纤维搭桥的圆形脱层的屈曲问题。搭桥纤维被简化为连续分布于脱层面上的线性弹簧。用Taylor级数展开法确定了每一级摄动方程用Bessel函数表达的解析解．给出了脱层屈曲临界载荷、挠度曲线与脱层半径、搭桥因子等的封闭关系式。根据这一结果并考虑脱层只能向一个方向挠曲的约束条件，可以进一步探讨脱层屈曲的特征。     

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。     

含内埋圆形或椭圆形脱层复合材料层合板的屈曲分析

用瑞里-李兹方法来建立含内埋圆形或椭圆形脱层板的屈曲分析模型．首先利用Heaviside阶梯函数，假定一种适合于脱层板的位移模式．然后由变分原理并进行线性化得出了含内埋圆形或椭圆形脱层板的屈曲特征方程．最后通过将含表面脱层的各向同性和各向异性板的屈曲载荷与其它文献进行比较，验证了该文分析方法的正确性，并分析了含内埋圆形或椭圆形脱层的各向同性、正交各向异性和角铺层层合板各种参数对屈曲载荷的影响．     

BUCKING AND FREE VIBRATION OF PIEZOELECTRIC/PIEZOMAGNETIC LAMINATED NANO-BEAM 1)

针对压电/压磁层合纳米梁屈曲、自由振动问题，基于非局部理论与正弦剪切型变形梁理论，建立了力学模型；利用哈密顿原理推导出层合梁运动方程与边界条件；通过数值解法求得层合梁临界屈曲载荷与自由振动频率。对数值结果分析可知：磁电弹夹层对压电/压磁层合纳米梁屈曲和自由振动的影响不能忽略；磁电弹夹层中压电或压磁材料的体积分数和夹层厚度为主要影响因素；分析得到的影响规律可为此类材料在工程中的应用提供理论参考。     

含初缺陷裂纹损伤梁的冲击动力屈曲

由Hamilton原理导出考虑初始缺陷及横向剪切变形时裂纹梁的动力屈曲控制方程;应用断裂力学中常用的线弹簧模型将裂纹引入到屈曲控制方程中;基于B-R动力屈曲判断准则,采用数值方法求解了受轴向冲击载荷作用时裂纹梁的动力屈曲;对比讨论了不同冲击速度、初始几何缺陷大小以及分布形式等因素对梁冲击动力屈曲的影响。     

THERMAL POST-BUCKLING OF FUNCTIONALLY GRADED MATERIAL TIMOSHENKO BEAMS

Analysis of thermal post-buckling of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrical nonlinear governing equations including seven basic unknown functions for functionally graded beams subjected to mechanical and thermal loads were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko beams with fixed-fixed edges were obtained. Characteristic curves of the buckling deformation of the beam varying with thermal load and the power law index are plotted. The effects of material gradient property on the buckling deformation and critical temperature of beam were discussed in details. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the transversely non-uniform characteristic of materials.     

粘贴压电层功能梯度材料Timoshenko梁的热过屈曲分析

研究了上下表面粘贴压电层的功能梯度材料Timoshenko梁在升温及电场作用下的过屈曲行为。在精确考虑轴线伸长和一阶横向剪切变形的基础上,建立了压电功能梯度Timoshenko层合梁在热-电-机械载荷作用下的几何非线性控制方程。其中,假设功能梯度的材料性质沿厚度方向按照幂函数连续变化,压电层为各向同性均匀材料。采用打靶法数值求解所得强非线性边值问题,获得了在均匀电场和横向非均匀升温场内两端固定Timoshenko梁的静态非线性屈曲和过屈曲数值解。并给出了梁的变形随热、电载荷及材料梯度参数变化的特性曲线。结果表明,通过施加电压在压电层产生拉应力可以有效地提高梁的热屈曲临界载荷,延缓热过屈曲发生。由于材料在横向的非均匀性,即使在均匀升温和均匀电场作用下,也会产生拉-弯耦合效应。但是对于两端固定的压电-功能梯度材料梁,在横向非均匀升温下过屈曲变形仍然是分叉形的。     

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite(PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes(CNTs) and nanoclay(NC) simultaneously. The governing equations are derived based on the first shear deformation theory(FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams,as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.     

Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory

In this research, thermal buckling of circular plates compose of functionally graded material (FGM) is considered. Equilibrium and stability equations of a FGM circular plate under thermal loads are derived, based on the higher order shear deformation plate theory (3rd order plate theory). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. A buckling analysis of a functionally graded circular plate (FGCP) under various types of thermal loads is carried out and the result are given in closed-form solutions. The results are compared with the critical buckling temperature obtained for FGCP based on first order (1st order plate theory) and classical plate theory (0 order plate theory) given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of FGCP, whereas the first order and classical plate theory overestimates buckling temperature.     

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions and plate thickness. As expected, the natural frequencies and the critical buckling load of the plates with delaminations decrease with increase in delamination length. Increase in delamination length also causes instability regions to be shifted to lower parametric resonance frequencies. The effect of edge delamination on the static and dynamic stability as well as of delamination growth is investigated.     

Buckling of short beams with warping effect included

A beam theory for the stability analysis of short beam that includes shear deformation and warping of the cross-section is developed. The warping of the cross-section is taken to be an independent kinematics quantity and corresponding force resultants are defined. For the beam subjected to the external loading only at the ends of the beam, equilibrium equations have been obtained by the principle of virtual work. The variations of lateral displacement, rotational angle of the cross-section and the multiplier of the warping shape along the beam axis are solved in closed form and expressed in terms of deformation quantities at the ends of the beam. Based on this beam theory, the lateral stiffness of the beam sustained an axial compression force and a lateral shear force at one end is explicitly derived, from which the equation of the buckling load is established and the buckling load can be solved. When the effect of cross-section warping is neglected, the derived lateral stiffness and buckling load converge to the solutions of the Haringx theory.