Hamilton体系下层合板弱粘接模型的应用

层合板的层间粘接模型对整个层合板的结构有重要影响．运用Hamilton正则方程对层合板层间的不同类型的粘接模型进行了分析．结合弹性材料修正后的Hellinger Reissner变分原理和插值函数,构建了直角坐标系下8节点层合板的每一层的线性方程;考虑到脱层板的连接界面处应力和位移的关系,改进了现有的常用弱粘接模型,建立不同粘接模型的控制方程;最后通过求解整个板的控制方程,得到层合板的层间应力和位移．数值算例验证了该模型的正确性,并研究了层间界面为线性和非线性时的问题．结果表明:应用改进后的弱粘接模型,能够更好地模拟层合板的弱界面失效过程．     

考虑阻尼的状态向量方程和层合板的振动分析

基于考虑弹性体粘滞阻尼的修正后的Hellinger-Reissner (H-R)变分原理,推导了相应的状态向量方程．结合精细积分法和Muller法为四边简支矩形层合板的简谐振动分析提出了新的方法．依据线性阻尼振动理论,简要地给出了复合材料层合板欠阻尼、临界阻尼和过阻尼3种自由运动的通解公式．通过数值实例研究了粘滞阻尼对复合材料层合板振动的影响．丰富了状态向量方程的理论体系和应用领域．     

受弯层合板边缘效应数值-摄动分析*

本文将分析一个受弯复合材料层合板的计算模型.首先利用无量纲变量将层合板任一层的平衡方程变成以位移表示的摄动型微分方程式;然后利用合成展开法,将求解区域分成内部区域和边界层区域,并推导出求解外部解和内部解的数学模型.为突出边缘效应,最后用边界积分方程表示内部解.     

复合材料层合板的分析

在复合材料层合板静力和动力分析方面,本文提出了一个层合板理论.此理论从板的总挠度中分开了由弯曲所产生的挠度W_b与由剪切产生的挠度W_s,因而使得求控制方程的解变得容易了.而且便于讨论和分析横向剪切变形对层合板弯曲,振动和稳定性的影响.     

主被动阻尼层合板结构的自由振动和阻尼特性分析

给出了含主被动阻尼非对称复合材料层合板结构的振动微分方程;得到了在压电材料和高粘弹材料作主被动阻尼层情况下,简支层合板结构自由振动的自然频率和损失因子的解析解;分析了正逆向压电效应对自然频率和损失因子的影响     

复合材料层合板低速冲击后压缩的损伤累积模型

为了分析复合材料层合板低速冲击后的压缩性能,首先用三维动态有限元素法对两种层合板进行了低速冲击损伤模拟计算,以此作为冲击后压缩（CAI）层合板的初始损伤,然后用三维静态有限元对含损伤的层合板进行压缩破坏模拟和剩余强度计算,从而实现了层合板从冲击损伤到压缩破坏损伤全过程的模拟．结果表明,损伤投影面积和CAI强度的计算值与试验结果有较好的一致性．     

复合材料层合板的三维非线性分析

本文提出了一种研究复合材料层合板壳三维问题的解析方法．该方法采用摄动方法和变分原理来满足三维弹性理论基本微分方程及限制条件，分析了受横向载荷作用的复合材料各向异性单层圆板及层合圆板的三维非线性问题．得到了高精确度的摄动级数解答．大量结果表明横向剪应力和横向正应力在层合板的三维非线性分析中是很重要的．     

含分层损伤复合材料加筋层合板的分层扩展研究

建立了复合材料加筋结构的后屈曲和分层损伤扩展行为的数值模拟方法．基于Mindlin一阶剪切理论和von-Karman大挠度理论的层合板和层合梁单元，提出了含分层损伤复合材料加筋层合板分层扩展行为的有限元分析方法；利用虚裂纹闭合技术计算分层前缘的总能量释放率，并采用总能量释放率准则分层扩展判据，结合自适应网格移动技术，对在压缩载荷作用下的具有不同加筋形式，不同初始分层面积和形状的加筋板结构分层扩展行为进行了数值模拟研究，在分析中还考虑了加筋刚度、位置和分布，分层形状和大小、边界支撑强弱和分层前缘的接触效应对结构分层扩展行为的影响．本所提出的研究方法对工程界关于复合材料结构的设计具有重要意义．     

具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

带裂纹层合板复应力强度分析

本文用经典板理论求得了复合材料层合板的界面应力强度因子.利用裂纹尖端能量释放率和复应力强度因子间的关系,给出最一般的复合材料层合板,在相应外荷载和模型混合参数下的复应力强度因子的一个封闭形式的解.然后提出确定这一模型混合参数的步骤,给出某些层合板的数值结果.并给出在相应外荷载下的小范围接触条件.特别证明了界面韧度曲线的对称性质.最后讨论振荡指数消失后,预计的断裂荷载的精确性.还通过一个实例表明β=0法的有效性和局限性.     

A method of solving three-dimensional problems of elasticity for laminated composite plates

An efficient method of solving 3D elasticity problems for thick and thin laminated composite plates is presented. It is based on a new concept of reference surfaces inside the plate. According to this concept, into each nth layer, In arbitrary reference surfaces parallel to the midsurface are introduced, and the displacement vectors of these surfaces are chosen as unknown functions. Such a choice allows one to represent the governing equations of the high-order theory of plates proposed in a very compact form and to derive strain–displacement relationships correctly describing all rigid-body motions of laminated plates.     

Nonlinear flexural response of laminated composite plates under hygro-thermo-mechanical loading

The paper deals with Chebyshev series based analytical solution for the nonlinear flexural response of the elastically supported moderately thick laminated composite rectangular plates subjected to hygro-thermo-mechanical loading. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Karman nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The elastic and hygrothermal properties of the fiber reinforced composite material are considered to be dependent on temperature and moisture concentration and have been evaluated utilizing micromechanics model. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of Winkler and Pasternak foundation parameters, temperature and moisture concentration on nonlinear flexural response of the laminated composite rectangular plate with different lamination scheme and boundary conditions are presented.     

Shape Control of Composite Plates with Distributed Piezoelectric Actuators in a Three-Dimensional Formulation

Mechanics of Composite Materials - Based on the method of sampling surfaces, a hybrid finite-element model is developed for a three-dimensional analysis of laminated composite plates with...     

Influence of nonlinear terms on dynamical behavior of graphene reinforced laminated composite plates

This research is focused on the effects of nonlinear terms on the dynamical behavior of graphene reinforced laminated composite plates. Firstly, the governing equations of the graphene reinforced composite thin plate subjected to transverse excitations are derived by using the Hamilton's principle and the von Karman deformation theory. Then numerical method is applied to investigate the nonlinear behaviors of graphene reinforced composite plates. Bifurcation diagram, waveform and phase portrait are demonstrated to analyze the nonlinear dynamics of the graphene reinforced laminated composite plates. Furthermore, the effects of nonlinear terms on the dynamical behavior are discussed in detail, where both the stronger and weaker nonlinear characteristics of lower modes of the plate are presented. Moreover, some interesting phenomena are obtained in numerical simulation.     

The postbuckling analysis of laminated circular plate with elliptic delamination

Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.     

Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces

The time-dependent behavior of a simply supported, angle-ply piezoelectric laminate in cylindrical bending with viscoelastic interfaces is investigated. The interfacial bonding in piezoelectric laminates is considered to be dielectrically weakly (or highly) conducting, and mechanically compliant characterized by the Kelvin–Voigt viscoelastic law. The state-space approach, which is directly based on the piezoelectricity equations and very effective in analyzing laminated structures, is employed. For exact analysis, a state equation of the relative sliding displacements with respect to the time variable is further presented. Comparison study shows that the numerical results by the present analysis agree well with those reported before. Numerical results also indicate that the electromechanical response of the piezoelectric laminates with viscoelastic interfaces changes remarkably with time elapsing. Thus, the bonding imperfection should be considered carefully in the practical design of piezoelectric laminates.     

Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory

The free vibration of laminated composite plates on elastic foundations is examined by using a refined hyperbolic shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on an elastic foundation is obtained through the use of Hamilton’s principle. The numerical results found in the present analysis for free the vibration of cross-ply laminated plates on elastic foundations are presented and compared with those available in the literature. The theory proposed is not only accurate, but also efficient in predicting the natural frequencies of laminated composite plates.     

初始缺陷和拉-弯耦合对于叠层板的振动、屈曲和非线性动力稳定性的影响

研究了复合材料叠层板的初始缺陷和拉伸＿弯曲耦合对于其振动、屈曲和非线性动力稳定性的影响·推导了控制方程·这是一个修正的非线性Ｍａｔｈｉｅｕ方程·进行了５种典型复合材料的数值计算,它们是玻璃环氧Ｓｃｏｔｃｈ＿１００２,芳纶环氧Ｋｅｖｌａｒ＿４９,硼环氧Ｂ４／５５０５,石墨环氧Ｔ３００／５２０８,和ＡＳ／３５０１·结果表明：由于初始缺陷耦合效应的存在,使叠层板对于进入参数共振更加敏感,并且其振幅大于无初始缺陷或者无耦合效应的叠层板·对于不同复合材料的叠层板,尤其是层数较少的板,耦合效应是不相同的·在板结构的屈曲和动力稳定性设计中,如果忽略了耦合效应的影响,其不安全性将超过１０％以上