脱层梁屈曲的高阶剪切理论

脱层的存在将会大大降低层合结构的屈曲载荷。该文将含任意位置脱层的两端固支梁分成多段子层,用厚度的三次多项式模拟脱层梁屈曲时子层的轴向位移,利用变分原理和欧拉方程导出了脱层梁的屈曲方程和定解条件,并用状态空间方法进行求解。通过与一阶剪切理论和经典理论的比较,指出了它们各自的适用范围;考虑了脱层梁三种不同的屈曲模态。分析了脱层长度、深度、位置和材料的铺层方向对脱层梁屈曲载荷的影响;最后给出了多处简单脱层的屈曲分析。     

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。     

具任意脱层复合材料梁的非线性谐波响应

研究了具任意脱层复合材料梁的非线性谐波响应问题。基于弹性理论，建立了考虑剪切变形时的复合材料梁脱层的基本方程式。在空间上采用B样条函数和Galerkin积分法，在时间上采用增量谐波平衡法进行计算。通过实例计算，得出了简谐力作用下的非线性动力响应曲线。认为基谐波振动仍是非线性振动的主要部分。     

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．     

具脱层轴对称层合圆柱壳的振动模态分析

对具环向贯穿脱层的轴对称层合圆柱壳进行振动模态分析.首先,采用Heaviside阶梯函数,构造了一种适合于脱层壳的位移模式.通过对脱层壳的能量分析,应用瑞利--里兹法后,得到用时间函数表示的系统振动控制方程,然后对其求解,得到脱层壳模态分析的特征方程式.算例中,讨论了不同的脱层位置、脱层大小和脱层深度对脱层壳振动模态的影响.     

层合梁在线性载荷下脱层的有限元分析

运用Hamilton正则方程对层合梁的脱层扩张进行了分析。结合弹性材料修正后的Hellinger-Reissner变分原理和插值函数,构建了八节点层合梁每一层的线性方程;考虑到脱层梁连接界面上应力和位移的连续性,将脱层板离散成上下两层,采用"分离合并"技术建立了脱层情况下梁的控制方程;最后应用Griffth准则,导出了固定载荷情况下梁元脱层前缘的能量释放率。数值算例验证了该模型的正确性,并研究了不同边界、不同脱层深度、不同脱层长度、不同角铺层工况下梁的脱层问题。结果表明:层合梁在脱层过程中,固支边界和简支边界情况区别不大,但在同种边界情况下,脱层的深度越深,脱层能量释放率变化越剧烈;层合梁的不同铺层角度会产生不同的能量释放率,为避免层合梁发生脱层,应尽量使层合梁的铺层角度沿着22 11C/C最大处。     

含纤维搭桥的正交各向异性材料非线性矩形脱层屈曲分析

本文基于用挠度和应力函数表示的考虑含纤维搭桥影响的正交各向异性材料矩形脱层屈曲非线性方程组,采用伽辽金法获得了非线性矩形脱层屈曲的理论解,给出了屈曲载荷随脱层中心挠度、纤维搭桥因子及脱层几何和材料参数变化的解析关系式.通过理论计算与有限元数值结果的对比,验证了解的正确性.本文解可有效用于分析材料参数和几何参数以及纤维搭桥作用对结构非线性脱层屈曲行为的影响,对于复合材料抗压屈曲强度设计具有重要参考价值.     

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。     

拱屈曲荷载分析的三维退化曲梁单元有限元法

在三维块体等参元及１６结点相对位移板壳元的基础上,引入梁的基本假定,考虑几何非线性,构造出三维退化曲梁单元,计算了梁、拱线弹性屈曲临界荷载。     

含脱层层合板分叉屈曲的宏微观失效机制分析

根据板壳理论并考虑层合板脱层处的接触效应影响,推导了层合板的控制方程,借助量纲归一化分析建立了该问题的八次特征方程。通过对特征方程各参数进行定性分析,建立了求解八次方程根的解析表达式,发现了层合板的宏微观变形模态。利用MATLAB软件进行算例分析,获得了在不同脱层情况下层合板的屈曲模态参数和临界屈曲荷载。研究表明:层合板的屈曲模态包含整体一致的宏观变形和界面处的微观变形。研究结果与ABAQUS的有限元解进行了对比,结果表明:理论解与有限元分析的结果非常一致。论文从理论分析的角度研究了复合材料矩形层合板的屈曲问题,从理论上剖析了分层层合板的宏微观失效模态。     

Analytical solution for buckling of asymmetrically delaminated Reissner’s elastic columns including transverse shear

The exact analytical solution of buckling in delaminated columns is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. In the paper, we limit the studies to linear elastic columns with a single delamination, but with arbitrary longitudinal and vertical asymmetry of delamination and arbitrary boundary conditions. The studies of quantitative and qualitative influence of transverse shear are shown in detail and extensive results for buckling loads with respect to delamination length, thickness and longitudinal position are presented.     

Buckling analysis of two layer delaminated beams with bridging

Stitching has been used as through-thickness reinforcement to reduce the effects of delamination. In stitching, the delamination will be held by stitches in the form of crack/interface bridging. In the present work, the reinforcement of stitching threads is assumed to provide continuous linear restoring tractions opposing the delamination opening. A generalized mathematical model is developed to study the buckling analysis of two layer delaminated beams with bridging by using Rayleigh–Ritz energy method. The delaminated beam is analyzed as four interconnected beams using the delamination as their boundary. Lagrange multipliers are used to enforce the boundary and continuity conditions between the junctions of the interconnected beams. The developed mathematical model is solved as an eigenvalue problem in which the lowest eigenvalue gives the buckling load. Effective-bridging modulus, a new nondimensionalized parameter, is introduced to study the influence of bridging on the delamination buckling. It is shown that bridging strongly influences the buckling load of the delaminated beams and a monotonic relation is observed between the buckling load and the effective-bridging modulus. Parametric studies in terms of delamination sizes and locations along spanwise and thicknesswise positions on the buckling load have been carried out. The bridging is found to be effective for shallow delaminations of moderate length, and for deep and long delaminations. Spanwise positions of delamination strongly influence the buckling loads. In addition, an analytical model for obtaining upper bounds of the buckling load is developed by using Euler–Bernoulli beam theory. Effective-slenderness ratio, a new nondimensionalized parameter is defined and it is found to be controlling the buckling mode configurations, i.e., local, global and mixed modes.     

Coupled bending-torsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments

Delaminations in structures may significantly reduce the stiffness and strength of the structures and may affect their vibration characteristics. As structural components, beams have been used for various purposes, in many of which beams are often subjected to axial loads and static end moments. In the present study, an analytical solution is developed to study the coupled bending-torsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments. Euler–Bernoulli beam theory and the "free mode" assumption in delamination vibration are adopted. This is the first study of the influences of static end moments upon the effects of delaminations on natural frequencies, critical buckling loads and critical moments for lateral instability. The results show that the effects of delamination on reducing natural frequencies, critical buckling load and critical moment for lateral instability are aggravated by the presence of static end moment. In turn, the effects of static end moments on vibration and instability characteristics are affected by the presence of delamination. The analytical results of this study can serve as a benchmark for finite element method and other numerical solutions.     

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.     

The effect of a centrally located midplane delamination on the instability of composite panels

The buckling loads of eight-ply graphite-epoxy cylindrical panels with midplane delamination were determined experimentally. The study included two different ply orientations, two different aspect ratios, two different delamination sizes, and one set of boundary conditions; clamped along the top and bottom edges and simply supported along the vertical sides. The experimental test results are compared to the linear bifurcation and nonlinear collapse loads of panels with square cutouts obtained from the STAGSC-1 finite-element computer code. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

The growth simulation of circular buckling-driven delamination

Some closed-form equations for the coupling problem of buckling and growth of circular delamination are derived by recourse to the moving boundary variational principle. The axisymmetric buckling of a circular delamination subjected to an equal bi-axial compression is analysed by using high-order perturbation expansion. The axisymmetric buckled delamination has the following properties : under a certain residual pressure, there exist two characteristic radii, namely the critical radius R_c and growing radius R_g; for a certain interface toughness, the blister has three configuration of stationary, stable growth and unstable growth with increasing the loads. Under a higher edge thrust, the nonaxisymmetric secondary buckling will occur on the base of axisymmetric buckling and then the toughness and the driving force of the interface crack will be different along the delamination front. So the growth of circular delamination will not be self-similar. Without any assumption regarding the delamination front, the configurations of the blister with several nonaxisymmetric buckling modes n = 2, 3, 6, 8 are simulated. The nonaxisymmetric growth process for the nonaxisymmetric buckling mode n = 2 is simulated also under a sequence of loads.     

ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams.     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根 据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论,引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性,研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的,利用能量法推导了矩形截面梁的控制微分方程和边界条件,并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明,对称材料模型下,固支梁与简支梁均显示出了典型的分支屈曲行为特征,而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下,固支梁仍显示出分支屈曲行为特征,但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化;而对于两端简支梁,发生了弯曲变形,弯曲挠度随载荷的增大而增大．