复合材料层合板剪切稳定性试验及强度预测

对无损伤及含冲击损伤的复合材料层合板进行了剪切稳定性试验,基于数字图像相关方法 (Digital image correlation,DIC)对层合板屈曲后屈曲行为进行了实时测量。试验结果表明：引入冲击损伤后,复合材料层合板剪切屈曲波形、屈曲载荷无明显变化,失效模式转变,承载能力下降了9.69%。随后,基于断裂面失效理论,建立了考虑剪切非线性效应的复合材料渐进损伤失效模型,并对复合材料层合板剪切失效过程进行了模拟。模型采用软化夹杂法将冲击损伤等效简化,直接将损伤区的几何边界信息写入材料模型中,不需要对冲击损伤区进行切割,从而保证了整体网格质量。与试验结果对比发现：模型考虑剪切非线性对屈曲载荷预测无明显影响,对后屈曲承载能力的预测精度影响较大,不考虑剪切非线性效应时的误差可达20%以上;软化夹杂法可以有效地模拟冲击损伤,预测的含冲击损伤的复合材料层合板的屈曲载荷、破坏载荷误差分别为-3.17%、-1.27%。     

复合材料层合板非线性热屈曲分析

本文基于高阶变形理论和修正型Hahn-Tsai非线性本构模型,提出一种复合材料层合板非线性热屈曲分析方法.针对四边简支反对称角铺设复合材料层合板,导出了非线性热屈曲临界温度封闭解.数值结果表明:材料非线性能显著降低层合板临界温度.      

复合材料层合板非线性屈曲分析

本文基于高阶变形理论和修正型Ｈａｈｎ－Ｔｓａｉ非线性本构模型，提出一种复合材料层合板非线性热屈曲分析方法。针对四边简支反对称角铺设复合材料层合板，导出了非线性热屈曲临界温度封闭解。数值结果表明：材料非线性能显著降低层合板临界温度。     

含分层损伤复合材料层合板非线性动力稳定性

采用Reddy 的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型, 推导了考虑几何非线性和阻尼效应的Methieu 方程, 给出了该方程的解析解表达式; 研究了参数振动解的稳定性; 然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响; 研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响, 以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知, 随着复合材料层合板分层损伤的扩大, 其动力稳定性能逐渐减弱, 特别是损伤接近层合板的中面时, 分层损伤对其动力稳定性能的影响最大。      

双轴受压反对称角铺设复合材料层合板在固支边界下的后屈曲和模态跃迁

为有效分析双轴受压反对称角铺设复合材料层压板在固支边界下的后屈曲性能, 由渐近修正几何非线性理论推导其双耦合四阶偏微分方程(即应变协调方程和稳定性控制方程), 通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程, 从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题, 研究了模态跃迁前后不同复杂程度的后屈曲模式。对四层固支边界复合层合板的数值模拟结果表明: 该解析法与有限元方法在主后屈曲区域的线性屈曲荷载计算结果吻合良好; 有限元方法在解靠近二次分岔点时失去收敛性, 而解析方法可深入后屈曲区域, 准确捕捉模态跃迁现象; 对于反对称角铺设层合板, 可仅用纯对称模态来定性预测主后屈曲分支、二次分岔荷载及远程跃迁路径。      

考虑制造因素的变刚度层合板的抗屈曲铺层优化设计

与常规层合板相比,变刚度层合板的制造、有限元建模分析和铺层设计有其特殊之处。首先对设计时需考虑的制造因素进行了归纳,提出了变刚度层合板的铺层设计要求。然后给出了变刚度层合板的理想模型和考虑丝束宽度模型的建模方法。基于理想模型对ABAQUS的前处理模块进行二次开发,利用编制的参数化建模程序分析了不同铺放角的变刚度层合板的屈曲性能,并讨论了最小曲率半径对铺层的限制和变刚度设计提高屈曲载荷的机制。基于变刚度层合板的抗屈曲机制建立了一种铺层优化设计方法,使用遗传算法经两步优化得到最优铺层。对最优铺层建立考虑丝束宽度的模型以研究丝束宽度和铺层偏移对变刚度层合板抗屈曲铺层优化结果的影响。研究表明,在变刚度层合板的抗屈曲铺层优化中使用简化的理想模型通常来说是可行的。在考虑制造因素的情况下,优化后的变刚度层合板较常规层合板屈曲载荷有显著提高。     

热声载荷下C/SiC层合薄板动态响应分析及寿命预测

鉴于处在热声载荷下的薄壁结构工作条件恶劣,极易发生屈曲和声疲劳从而影响构件的稳定性和使用寿命。以四边固支C/Si C复合材料层合板结构为研究对象,运用有限元方法计算结构在不同温度和声压级组合下的振动响应,分析屈曲前后响应特性并总结了典型的非线性振动响应特性;基于复合材料层合板高比强和特殊的结构疲劳损伤机理特点,运用改进的雨流法统计了层合板在超高温度强噪声工况下的应力响应,结合材料对称循环疲劳性能试验所得数据拟合地考虑平均应力影响的等效寿命公式和Palmgren-Miner线性累积损伤准则估算层合板的疲劳寿命。     

弹性支持任意铺层加筋板的非线性稳定性分析

本文利用能量变分原理和广义傅里叶级数法对具有弹性支持的复合材料任意铺层加筋板在面内各种组合载荷作用下的非线性稳定性特性进行了研究.通过采用牛顿一梯度法数值求解,证明前屈曲压-弯耦合效应对弹性支持的复合材料加筋板的屈曲和后屈曲特性均产生了明显的影响,以致于在压、剪载荷作用的开始即产生了横向翘曲变形.只有当加筋板的四边为夹支时,这种前屈曲耦合效应才不明显.除此之外,还得到了一些与非加筋的层合板完全不同的屈曲和后屈曲特性.所得结果与文献上的相关计算或实验结果对比后均吻合很好,证明本文的理论分析和数值计算是正确有效的.     

丝束变角度层合板屈曲性能的参数化研究

通过选择合适的纤维轨迹,丝束变角度(VAT)层合板相对于直纤维层合板能拥有更好的抗屈曲特性。为研究纤维轨迹特征长度和定向坐标系偏角对VAT层合板屈曲性能的影响,首先对原始的纤维角度线性变化方法进行改进,提出了一种纤维角度分段线性变化方法,拓展了纤维轨迹的设计空间;其次,采用改进后的纤维轨迹定义方法构建了一系列变刚度层合板;最后,基于有限元方法,从内力分布角度对变刚度层合板不同承载情况下的屈曲性能进行研究和探讨。数值结果表明:单向轴压工况下,采用半边长的特征长度和90°偏角的纤维轨迹,能使层合板的稳定性最好;双向轴压工况下,应将特征长度和定向坐标系偏角作为额外的设计变量,并通过优化获得最优的纤维轨迹。     

Bezier曲线变角度层合板设计及屈曲特性分析

基于二次Bezier曲线法,开展纤维变角度层合板的屈曲特性研究。首先,对原始的二次Bezier曲线进行了扩展,提出了分段式二次Bezier曲线变化方法,重新定义了纤维变角度铺放参考路径,确定了变角度层合板的表示形式。其次,以[0±20(β)65]_(2s)和[90±20(β)65]_(2s)为例对变角度层合板的屈曲特性进行了有限元分析,并与定角度层合板对比。最后,研究了不同终止角α和连接点参数β对层合板屈曲性能的影响,结果表明:连接点参数β的增大使得两种变刚度层合板的线性屈曲载荷先增大后减小,终止角大于起始角时,层合板的一阶屈曲载荷逐渐增大,铺放角度的增大有利于层合板屈曲载荷的提高。     

求解层合板非线性屈曲问题一般方法的若干讨论

用广义傅立叶级数法建立具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组后,讨论了非齐次项对方程组性质的影响,该非齐次项包含了所有的边界条件信息、外载信息及初始缺陷信息,可直接用作层板发生屈曲与否的判据。从数学上阐明了产生前屈曲耦合挠度的原因,并进一步从矩阵理论和非线性泛函两方面证明了前屈曲解的唯一性,进而提出了求解复合材料层板非线性稳定性问题的一般方法。     

Effective widths of compression-loaded of perforated cross-ply laminated composites

In this study the influence of eccentric circular cutouts on the prebuckling and postbuckling stiffness, and effective widths of compression loaded laminated composite plates are presented. The effective-widths concept is derived based on nonlinear finite element analysis for the plates with and without cutout. Several behavioral trends are described that initially appear to be nonintuitive. The results demonstrate a complex interaction between cutout size and the degree of plate orthotropy that affects the axial stiffness and effective width of plate subjected to compression loads. Also these investigations show that the cutout dimension have a more considerable effect on prebuckling stiffness compare to postbuckling one. It will show that the stiffness ratio of the postbuckling over prebuckling is increased by cutout size. Considering the effective-width ratios concept provide a simple means for incorporating the postbuckling strength and stiffness of plate subcomponents into the design of stiffened structures.     

Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions

The concept of variable angle tow (VAT) placement is explored for enhancing the buckling resistance of composite plates subjected to axial compression loading. The problem is relatively difficult to solve because of varying stiffness properties and requires prior prebuckling analysis to determine the non-uniform stress variation followed by the buckling analysis of VAT plates. A stress function formulation for in-plane analysis and displacement formulation for buckling analysis was employed to derive the governing differential equations of VAT plates based on classical laminated plate theory. The Differential Quadrature Method (DQM) is applied to solve the differential equations. The novel aspect of the present work is the use of Airy’s stress function to model the prebuckling analysis of VAT plates which considerably reduces the problem size, computational effort and provides generality to model pure stress and mixed boundary conditions. DQM was applied first to solve the prebuckling problem of VAT plates subjected to cosine distributed compressive load/ uniform end shortening. Then, DQM was applied to solve the buckling problem of rectangular VAT plates subjected to axial compression under different plate boundary conditions. Results were validated with detailed finite element analysis and the relative accuracy and efficiency of the DQM approach is discussed.     

The nonlinear vibration of an initially stressed laminated plate

Nonlinear partial differential equations of motion for a laminated plate in a general state of non-uniform initial stress are presented in various plate theories. This study uses Lo’s displacement field to derive the governing equations. The higher-order terms in Lo’s theory can be disregarded, to obtain the equations of simpler forms and even other theories for laminated plate. These nonlinear partial equations are transformed to ordinary nonlinear differential equations using the Galerkin method. The Runge–Kutta method is used to obtain the ratio of nonlinear frequency to linear frequency. The numerical solutions of an initially stressed laminate plate based on various plate theories obtained by the Galerkin and Runge–Kutta method are presented herein. Using these equations with various theories, the nonlinear vibration behavior of laminated plate is studied. The results show that apparent discrepancies exist among the various displacement fields, which indicates the transverse shear strain, normal strain and initial stress state have great effect on the vibration behavior of laminate plate under nonlinear vibration.     

Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical thin shell of finite length subjected to compressive axial loads and in thermal environments. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of axially-loaded, perfect and imperfect, cylindrical thin shells with two constituent materials and under different sets of thermal environments. The effects played by temperature rise, volume fraction distribution, shell geometric parameter, and initial geometric imperfections are studied.     

Plate buckling loads by the boundary element method

A boundary element solution of the plate buckling problem is extended and refined to accommodate any combination of loading and support conditions. It is complemented by a similar boundary element formulation yielding the prebuckling membrane state of stress for non-uniform distributions of edge loads. Both continuous and discontinuous models of various orders of approximation for boundary as well as domain unknowns have been employed and their effect on the accuracy of the solution algorithm assessed. The computer code incorporates automatic mesh generation schemes for both the boundary and the domain through which a wide range of plate geometries can be discretized and analysed. Further, gains in both efficiency and accuracy are achieved by taking advantage of any support and loading symmetries and reducing the formulation to a standard eigenvalue problem. A large number of plate examples are solved to optimize the choice of various modelling parameters and to establish the reliability of the proposed analysis.     

变截面门式刚架结构的非线性性能

本文论述了变截面有限梁元几何非线性分析方法;研究了变截面刚架的几何非线性影响;通过非线性屈曲分析考察了屋面均布荷载对刚架柱稳定的影响;计算结果表明,刚架在屋面均布荷载作用下所产生的横梁轴力和弯曲变形对其侧向屈曲荷载的影响不能忽视。     

Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers

Nonlinear vibration analysis of thin circular pre-stressed functionally graded (FG) plate integrated with two uniformly distributed piezoelectric actuator layers with an initial nonlinear large deformation are presented in this paper. Nonlinear governing equations of motion are derived based on classical plate theory (CPT) with von-Karman type geometrical large nonlinear deformations. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed piezoelectrically actuated circular FG plate are derived. An exact series expansion method is used to model the nonlinear electro-mechanical vibration behavior of the structure. Control of the FG plate’s nonlinear deflections and natural frequencies using high control voltages are studied and their nonlinear effects are evaluated. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FG plate on the dynamic characteristics of the structure.     

复合材料加筋板的大变形有限元分析

本文将考虑横向剪切变形的Mindlin's理论应用于复合材料加筋板的大变形分析,在Total-Lagrange坐标系下推导了八结点等参弯曲板单元和三结点等参梁单元的增量平衡方程和切线刚度矩阵,非线性问题采用增量法和Newton-Raphson迭代法相结合的方法求解.本文通过一些算例,证明了所采用单元具有良好的收敛性和足够的精度,并讨论了边界条件、纤维铺设角和加筋疏密等因素对复合材加料筋板非线性解的影响.     

洛仑兹力的应力应变效应

阐述了在非定常电磁场和机械场的作用下,洛仑兹力对非线性载流薄板薄壳应力应变状态的影响。导出了在电磁场中洛仑兹力的具体表达式。通过对环形薄板在电磁场和机械场联合作用下应力应变状态的计算,指出变化洛仑兹力的作用可以得到最佳的应力应变状态。本文可供在强电磁场中工作的载流元件、防护元件及设备在设计及实际应用时作参考。