层合圆柱壳的振动与横向应力

应用分层壳理论并在壳厚方向彩二次插值函数推导出正交层合圆醉壳的动力学方程,并得出了简支层合圆柱壳自由振动方程的解,所给出的振动频率与三维分析的结果吻合良好,计算了前四阶模态对应的壳中应力,与第三、四阶模态对应的横向正应力与面内应力的比值远高于第一、二阶模态的应力比,计算结果说明,很高的横向正应力是高频动力响应中导致分层壳脱层破坏的一个主要因素。     

三参数粘弹性地基上层合板的自由和强迫振动

基于三参数粘弹性地基模型及Reddy高阶剪切变形板理论,用双重Fourier级数形式解求得粘弹性地基上四边简支对称正交及反对称斜交层合板的各模态自由振动频率的解析解,以及这两种层合板在任意横向动荷载作用下动力响应的半解析解。通过参数分析讨论了粘弹性地基参数、边厚比等因素对自振频率及动力响应的影响。结果表明,地基的剪切刚度和压缩刚度提高了板的自振频率而降低了板的振动幅值,地基的粘性作用不可忽略。     

粘-弹层合悬臂板瞬态响应的近似解析解

采用双向梁函数组合级数逼近的方法构造粘-弹层合悬臂板的横向位移函数,用里兹法得悬臂板在集中力作用下的弯曲变形。用拉格朗日方程求出了板自由振动的频率和结构损耗因子;给出粘-弹层合悬臂板在集中力突然撤去以后瞬态响应的近似解析解。另外,分析了阻尼层损耗因子、弹性模量及厚度对响应的影响。     

用高阶位移模式分析复合材料层合板的自由振动

建立一种新的高阶位移模式：分层假设复合材料层合板的位移场，利用各层间应力及位移的连续性条件，导出了作为整体的层合板控制微分方程。最后，采用这一高阶剪切理论来分析复合材料矩形层合板的自由振动。数值计算采用有限差分法，并编制了计算程序，计算得出了六种不同边界条件、不同铺层、不同宽厚比工况下的矩形层合板的自振频率。同经典理论解进行比较，可以看出本文方法简便易行，且精度较高，可以在微机上实用。     

约束阻尼层合板的稳态响应

基于Reddy分层理论推导出约束阻尼层合板的稳态振动方程,得到了约束阻尼层合板的振动频率和损耗因子;分别分析了约束阻尼层合板的粘弹性夹层厚度、模量对固有频率和损耗因子的影响;得到了稳态振动时振幅和频率曲线以及横向应力与面内应力。数值计算结果表明所采用的算法是可靠的。     

用加权残数法分析纤维增强复合材料层合板的屈曲及自振频率

纤维增强复合材料层合板的屈曲及自振频率,用加权残数法分析,属于二次特征值的问题,迄今尚未有解。本文通过转换,把二次特征值的问题变化为标准一次特征值问题,从而获得解。通过四边简支矩形特殊正交各向异性层合板承受面内轴压的屈曲及横向自振频率的算例,所得结果与解析解吻合较好。     

变角度纤维复合材料环扇形层合板的自由振动分析

与传统的直线纤维增强复合材料相比，变角度纤维复合材料具有更强的可设计性，为改善结构性能提供了更大的可能．鉴于此，本文将研究纤维的变角度铺设对复合材料环扇形层合板的自振频率及振动模态的影响．假设纤维的方向角沿环扇形板的径向线性变化，基于经典的层合板理论，采用微分求积法获得了环扇形层合板自由振动问题的数值解．通过与现有文献及ABAQUS有限元结果的比较验证了本文模型及方法的正确性和收敛性，并详细分析了纤维起始角和终止角的变化对层合板的自振频率及振动模态的影响．研究结果表明：与常刚度层合板相比，变角度纤维复合材料层合板的基频具有更大的调整空间，通过合理选择纤维起始角和终止角可有效提高层合板的基频．研究结果可为该种新型复合材料结构的优化设计提供一定的参考．     

中间弱层对层合板性能影响分析

对于夹胶玻璃等结构,由于中间胶层很弱,层合板结构的层间剪切效应占主导地位。此时经典层合板理论以及整体高阶剪切位移场理论所预测的结果可能导致很大的实际误差,应采用更加精细的力学模型来分析弱层的效应。本文建立了分层位移场假设下的浅柱面层合板静力计算模型以及自振周期计算模型,并同经典层合板理论计算结果对比,分析了中间层的剪切模量、弹性模量、层合板曲率半径对层间剪切效应的影响。计算结果表明:中间层的剪切模量对层合板的受力性能有着决定性的影响,相对来说中间层的弹性模量对层合板性能的影响不太显著;当中间层与面层的剪切模量比值小于0.2时,随着中间层剪切模量的减小,两个模型的计算误差急剧增大。     

上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动分析

基于弹性层和饱和土半空间轴对称弹性波动方程，运用Hankel积分变换方法，得到它们在变换空间内的解．进而由层间完全接触条件及圆板底面的混合边值条件，构造一组描述上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动的对偶积分方程．将该对偶积分方程化为易于数值计算的第二类Fredholm积分方程，求得地基表面动力柔度系数随无量纲频率的变化曲线及弹性圆板的相对位移幅值．     

四角点简支双稳态层合板振动特性研究

双稳态层合板作为一种柔性可变体结构,为实现振动状态下的构型调控,将对其开展固有振动特性的 研究．本文以四角点简支约束的矩形非对称铺设双稳态板作为研究对象,运用最小势能原理、一阶剪切变形理 论、以及冯卡门几何非线性位移应变关系,得到双稳态板的两种稳态构型．首次给出了适合于四点简支的6参 数构型函数与17参数构型函数,研究对比发现对于稳态构型采用17参数的构型函数结果相对更精确;对于应 用线性位移应变关系的基于任一稳态构型下振动固有特性而言,这两种构型函数得到的结果基频相差2 %,其 它阶次频率相差也不大．随后采用6参数构型函数得到的稳态构型研究了几何尺寸、铺层数分别对两种稳态构 型固有振动特性的影响．本研究对于进一步研究该类结构动态跳变机理具有重要意义．     

Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method

The interlaminar stresses in a thin laminated rectangular orthotropic plate with four sides simply supported edges under bending was determined by using the generalized differential quadrature (GDQ) method involving the effects of thermal expansion strain and transverse load. The approximate stress and displacement solutions are obtained under the effects of thermal expansion force and uniform pressure load for eight-layer unidirectional laminates, symmetric cross-ply laminates. Numerical results on the dominant interlaminar stresses and displacement of bending analysis are compared to the Navier solution. The thermal induced forces have significant effect on the bending of plates.     

粘弹层合板的自由振动和横向应力

Based on Reddy＇s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress＇s maximum value and the in-plane stress＇s maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable.     

An advanced higher-order theory for laminated composite plates with general lamination angles

This paper proposes a higher-order shear deformation theory to predict the bending response of the laminated composite and sandwich plates with general lamination configurations.The proposed theory a priori satisfies the continuity conditions of transverse shear stresses at interfaces.Moreover,the number of unknown variables is independent of the number of layers.The first derivatives of transverse displacements have been taken out from the inplane displacement fields,so that the C 0 shape functions are only required during its finite element implementation.Due to C 0 continuity requirements,the proposed model can be conveniently extended for implementation in commercial finite element codes.To verify the proposed theory,the fournode C 0 quadrilateral element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate.Numerical results show that following the proposed theory,simple C 0 finite elements could accurately predict the interlaminar stresses of laminated composite and sandwich plates directly from a constitutive equation,which has caused difficulty for the other global higher order theories.     

A C<Superscript>0</Superscript>-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

In order to conveniently develop C⁰ continuous element for the accurate analysis of laminated composite and sandwich plates with general configurations, this paper develops a C⁰-type zig–zag theory in which the interlaminar continuity of transverse shear stresses is a priori satisfied and the number of unknowns is independent of the number of layers. The present theory is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. On the premise of retaining the merit of previous zig–zag theories, the derivatives of transverse displacement have been taken out from the displacement fields. Therefore, based on the proposed zig–zag theory, it is very easy to construct the C⁰ continuous element. To assess the performance of the proposed model, the classical quadratic six-node triangular element with seven degrees of freedom at each node is presented for the static analysis of laminated composite and sandwich plates. The typical examples are taken into account to assess the performance of finite element based on the proposed zig–zag theory by comparing the present results with the three-dimensional elasticity solutions. Numerical results show that the present model can produce the more accurate deformations and stresses compared with the previous zig–zag theories.     

Boundary-layer hygrothermal stresses in laminated, composite, circular, cylindrical shell panels

Free-edge effects in laminated, circular, cylindrical shell panels subjected to hygrothermal loading are studied by utilizing displacement-based technical theories. Starting from the most general displacement field of elasticity for long, circular, cylindrical shells, appropriate reduced displacement fields are determined for laminated composite shell panels with cross-ply and antisymmetric angle-ply layups. An equivalent single-layer shell theory is used to analytically determine the constant parameters appearing in the reduced displacement fields. A layerwise shell theory is then employed to analytically determine the local displacement functions and the boundary-layer interlaminar stresses in cross-ply and antisymmetric angle-ply shell panels under hygroscopic and/or thermal changes. Several numerical examples for the distributions of transverse shear and normal stresses in various shell panels under a uniform temperature change are presented and discussed.     

Nonlinear dynamic response of piezoelastic laminated plates considering interfacial damage effects

This paper presents a nonlinear model for cross-ply piezoelastic laminated plates containing the damage effect of the intralayer materials and interlaminar interfaces. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement, and electric potential on the interfaces are depicted by three shape functions, which are formulated according to solutions about three equilibrium equations and conservation of charge. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage are presented. Then using the finite difference method and the Newmark scheme, an analytical solution is presented. In numerical examples, the effects of different damage models, damage evolution, amplitude and frequency of electric loads on the nonlinear dynamic response of piezoelectric laminated plate with interfacial imperfections are investigated.     

Enhanced first-order theory based on mixed formulation and transverse normal effect

An accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first-order plate theory based on the mixed variational theorem (EFSDTM) developed in this paper. In the mixed formulation, transverse shear stresses based on an efficient higher-order plate theory (EHOPT) developed by Cho and Parmerter [Cho, M., Parmerter, R.R., 1993. Efficient higher-order composite plate theory for general lamination configurations. AIAA Journal 31, 1299–1306] are utilized and modified to satisfy prescribed lateral conditions, and displacements are assumed to be those of a first-order shear deformation theory (FSDT). Relationships between the modified EHOPT and the FSDT are systematically derived via both the mixed variational theorem and the least-square approximation of difference between in-plane stresses including the transverse normal stress effect. It is shown that the transverse normal stress effect should be considered in predicting the in-plane stresses when the Poisson effect is dominant. The developed EFSDTM preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure. The accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three-dimensional exact solutions for thick laminated and sandwich plates.     

NONLINEAR THREE-DIMENSIONAL ANALYSIS OF COMPOSITELAMINATED PLATES

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考虑横法向热应变的C~0型Reddy板理论和三角形板单元

考虑横法向热变形,建议了C0型Reddy理论,并用于分析复合材料层合/夹层板热膨胀问题。虽然考虑了横法向热应变,但不增加额外的位移变量。此理论位移场不含有横向位移一阶导数,构造有限元时仅需C0插值函数。基于这一模型,运用虚位移原理推导了复合材料板平衡方程以及构造了6节点三角形板单元,并分析了简支复合材料层合/夹层板的热膨胀问题。数值结果表明,建立的模型能准确分析复合材料层合/夹层板热膨胀问题,而忽略横法向热应变的理论分析热膨胀问题误差较大。