复合材料层合板振动的边界元法

本文用边界元法分析了复合材料特殊正交各向异性层合板的振动.为了克服在用边界元法求解正交各向异性层合板振动时寻求相应的基本解的困难,本文采用了傅立叶级数形式的近似基本解.算例说明了近似基本解方法的可行性和有效性.      

复合材料边界元素法研究

边界元法是一种迅速发展的数值解法.本文研究了在复合材料层合板中运用平面二次边界元法的有关问题.首先,讨论了将层合板等效为一般正交各向异性单层板的方法;其次,给出了偏轴情况下的基本解,研究了直线型二次边界元偏轴影响系数的解析计算以及域内应力表达式;最后对算例进行了计算,所得结果与相应的解析解和有限元相符甚好.     

弯剪复合载荷作用下复合材料层合板屈曲的强度校核方法

基于复合材料各向异性板的大挠度方程，采用Ritz法和最小势能原理推导出了正交各向异性复合材料层合板在面内弯曲载荷作用下临界屈曲弯矩的解析解；给出了面内弯剪复合载荷作用下复合材料层合板屈曲的强度校核方法，并将本文方法所得结果与用有限元法（FEM）所得结果进行了比较。结果表明，本文方法与有限元方法相吻合，并且形式简洁，便于工程应用。     

含脱层纤维增强复合材料层合板在湿热环境下的屈曲分析

依据复合材料细观力学研究了含脱层的正交各向异性复合材料层合板的力学性能与温度和湿度的关系,在宏-细观力学模型框架下建立了考虑湿热效应的屈曲控制方程,利用空间上分离变量的方法求解了控制方程,得到满足连续性条件和边界条件的控制方程的解。通过含脱层的复合材料层合板的屈曲数值算例,综合讨论了几何参数、材料参数和湿热环境等多方面的参数变化对含脱层的正交对称铺设复合材料层合板的临界屈曲载荷的 影响。     

热荷载作用下正交各向异性层合板振动响应的精确解

本文从三维弹性力学出发,导出了层合板第 i 层在任意变温 T(x,y,z,t)下的状态方程,解此状态方程,可得正交各向异性层合板在热荷载作用下的振动响应。     

冲击荷载下有孔复合材料层合板的结构声强特性

研究了有孔钢板和有孔碳纤维/环氧层合板在冲击荷载作用下的结构声强特性.讨论了不同叠层顺序的正交异性碳纤维/环氧层合板的结构声强向量场和流线特性.应用有限元法计算了碳纤维/环氧层合板在冲击荷载作用下各单元的力和速度,再应用MATLAB软件自编程序得出此复合材料层合板的结构声强,再运用Tecplot软件绘制结构声强的向量图和流线图.算例表明,有孔钢板,有孔各向异性碳纤维/环氧层合板的瞬态结构声强向量图及流线图与无孔钢板,无孔各向异性碳纤维/环氧层合板的存在不同的特性;研究发现,不论是钢板,还是正交异性碳纤维/环氧层合板,孔的存在改变了能量流传播途径、结构声强向量分布及应力大小;最大应力位置并不对应最大结构声强位置.     

对称层合板复合材料的屈曲变形解析

提出了如何利用2 元多项式位移函数来分析层合板复合材料的屈曲问题。在解析中同时 考虑到层合板的面外剪切变形。解析表明屈曲载荷在多项式项数大于20 以上时趋于稳定, 可得到 高精度的解。本文并对对称角铺设层合板进行了系统地数值解析, 明确了在各种边界拘束条件下 材料的工程弹性系数, 层合板长宽比, 铺层数, 层合角对屈曲载荷的影响, 从而以达到优化设计。同 时, 验证了本解析法对任意边界条件下的层合板的屈曲解析是非常有效的。      

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。      

用样条有限点法分析正交各向异性层合板的振动与稳定问题

本文采用样条有限点法,对多种边界条件下正交各向异性层合板的振动与稳定问题,进行了系统的分析,编制了通用程度。计算结果表明:样条有限点法在分析计算正交各向异性层合板的振动与稳定问题时,具有自由度少、收敛快、精度高、计算格式简便,易于在微机上计算等优点。     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。     

Curvature effects in the buckling of symmetrically-laminated rectangular plates with transverse shear deformation

It is shown that the effect of stress discontinuities from ply-to-ply must be taken into account when curvature terms are included along with shear deformation in the buckling analysis of rectangular, symmetrically-laminated plates. Such ply-stress discontinuities lead to curvature terms in the governing equations which differ considerably from those derived for homogeneous plates. Critical buckling loads are determined for orthotropic laminates subjected to biaxial inplane loading and for cylindrical bending of anisotropic plates subjected to uniaxial compression loading. Simply-supported boundary conditions are considered in conjunction with the rectangular, orthotropic laminate, while simply-supported and clamped boundaries are considered for the case of cylindrical bending of anisotropic plates. Numerical results indicate that the curvature terms have little effect on critical buckling loads for the laminates investigated. The effect of transverse shear deformation is shown to depend on the degree of boundary constraint, laminate stacking geometry, and inplane load ratio.     

Adaptive vibration control of a cylindrical shell with laminated PVDF actuator

A generalized higher-order theory describing the mechanical behavior of multi-layered composite plates with arbitrary lamination scheme is proposed. Ritz’s method is employed to determine the kinematic unknowns expressed in a complete polynomial power series of the thickness-wise coordinate whereas the dependence on the in-plane coordinates is such that the functions satisfy all boundary conditions. The correct constitutive laws of a three-dimensional orthotropic elastic continuum are employed for each individual layer. The convergence and accuracy of the computational scheme are investigated by comparing elastic static and buckling results with analytical or finite element solutions for complex cross- and angle-ply laminates. For further validation of the theory, laminated plates under a transverse pressure are investigated for technically relevant lamination schemes and the associated deformation and stress results are compared with those obtained through FE calculations.     

含内埋矩形脱层板屈曲分析的传递函数方法

研究了含任意内埋矩形脱层复合材料层合板的屈曲问题。采用一种基于Mindlin一阶剪切理论的条形传递函数方法,将含内埋矩形脱层的复合材料层合板分成含脱层和不含脱层的两种矩形超级单元,然后由各超级单元之间连接结点处的位移连续和力平衡条件得到脱层板屈曲的特征方程,进而得到脱层板的屈曲载荷和屈曲模态。进行参数分析发现,脱层大小、深度、位置以及脱层板的边界条件和复合材料铺层方向对脱层板屈曲载荷的影响较显著。     

正交异性层板加载孔的变形与断裂分析

本文用云纹法着重对正交异性层板加载孔的变形与断裂行为进行了分析和研究,描述了加载孔的线弹性段、突然起裂段、裂纹稳态扩展段以及失稳扩展段的位移场与应变场的突变,给出了载荷—裂纹长度曲线、载荷—最大应变曲线,载荷—张开位移曲线以及裂纹张开角。在起裂以前,云纹法和线性有限元法的结果较好地吻合;起裂后,云纹法描述了材料的非线性特性。      

双模数复合材料角交铺设厚层板的弯曲特性分析

本文应用里兹法和有限层法［１］研究了简支条件下双模数复合材料角交铺设厚层板的弯曲，并研究了层板长宽比、正交各向异性比、多模数比以及铺层角对层板中心挠度的影响。     

On refined computational models of composite laminates

Finite element models of the continuum-based theories and two-dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the third-order are presented in a single theory. Results of linear and non-linear bending, natural vibration and stability of composite laminates are presented for various boundary conditions and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non-linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non-linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative.     

Single-mode solution for post-buckling analysis of composite panels with elastic restraints loaded in compression

A closed-form solution is obtained to determine the buckling and post-buckling behavior of elastically restrained composite panels under compressive loading. The approach allows to study the response of stiffened panels undergoing local buckling modes, taking into account the restraints provided by the stiffeners to the rotation of the skin edges. The panels are modeled as thin plates referring to Marguerre type equations together with classical lamination theory. The equations are written in non-dimensional form, allowing for the study of a wide class of orthotropic laminates. The problem is formulated in terms of out of plane displacement, represented with a single-mode approximation, and Airy stress function. The compatibility equation is solved exactly, while the method of Galerkin is applied to impose the equilibrium. The buckling load, the out of plane displacement at different load levels, and the post-buckling stiffness are derived and compared with finite element analyses, revealing good accuracy. Sensitivity analyses are also performed obtaining design charts.     

On buckling of orthotropic compressed plates with circular holes

Buckling and post-buckling behaviour of square plates having central circular holes is analysed with the aid of the finite element method. Four different degrees of orthotropy pertinent to real materials are examined. Both uniaxial and biaxial compression are considered for various types of boundary conditions. Also, buckling of polar orthotropic annular plates is analysed for different boundary conditions and material properties. In the case of small holes a perturbation method is applied to both kinds of plates.