波在考虑热载荷和转动惯量效应的非线性大变形多层压电层合壳内的传播研究

研究了非线性大变形、层合壳的铺设形式、转动惯量及热载荷效应对波在压电层合壳中传播的影响。首先利用Hamilton最小势能变分原理推导了波在大变形压电层合壳内传播的非线性动力学平衡方程;通过求解方程特征值得到了波传播特征曲线;数值算例表明波在压电层合壳内传播与壳体大变形、转动惯量以及热载荷有关,并与线性小变形理论(Cooper-Naghdi壳体理论)进行了比较。     

复合材料大变形任意加筋壳单元

构造了用于复合材料偏心加筋壳形结构大变形分析的任意加筋壳单元。在此模型中,肋骨连同壳的整体被视为一个单元偏心加筋壳单元。肋骨可放在壳单元内的任意位置和任意方向。所构造单元的特点是在网格划分时,可不必考虑肋骨的位置,这就给网格划分带来了很大的灵活性。在壳和肋骨的方程中,引用Von-Karman大变形理论计及几何非线性的影响,按照Mindlin-Reissner一阶剪切变形理论考虑横向剪切变形。     

热环境中的功能梯度扁球壳非线性稳定性分析

基于经典壳理论和von Karman几何非线性理论,导出了功能梯度圆底扁球壳的位移型几何非线性控制方程及简支边界条件,推导过程考虑了均匀变温场及均布外侧压力。用打靶法计算了由控制方程和边界条件提出的两点边值问题,得到了壳体轴对称变形的数值结果。考察了壳体几何参数、材料横向梯度特性、组份材料体积分数指数和弹性模量以及均匀变温场对壳体屈曲平衡路径、上/下临界荷载和平衡构形的影响。数值结果表明:随组分材料体积分数指数的增加和弹性模量的减小,壳体上临界荷载均会显著减小;体积分数指数对壳体下临界荷载影响规律较复杂;均匀升温使壳体上/下临界荷载显著增加/减小。材料横向梯度特性对简支边功能梯度圆底扁球壳屈曲平衡路径和后屈曲稳态构形有显著影响。该文末给出了便于工程设计的两个数表和一些数值曲线。     

玻璃/环氧圆柱壳的冲击响应与稳定性分析

应用Love的壳体理论得到了非轴对称变形的复合材料圆柱壳的控制方程。对扰动状态的非轴对称变形,位移函数采用复Fourier级数形式,得到了Mathieu形的扰动方程,由此给出了静态临界载荷和固有频率。本文中对层合壳在轴向冲击载荷下的动态稳定性研究考虑了几何非线性,这是以往在该问题的研究中所未涉及的问题。研究表明,考虑几何非线性得到的临界载荷较线性几何关系计算结果要高5 %左右。因此,考虑几何非线性是必要的。      

磁场中简支矩形薄板的非线性稳态随机振动

根据电动力学理论、板壳磁弹性理论和结构随机振动理论,导出电磁场中矩形薄板的磁弹性非线性随机振动方程,然后利用伽辽金法对四边简支矩形薄板的非线性随机振动方程进行整理,得到伊藤型状态方程;在外界激励是平稳高斯白噪声的条件下,利用稳态的FPK方程法求解得到薄板的稳态随机振动位移和速度响应的多个数字特征;通过具体数值算例分析,讨论了电磁参数对各数字特征的影响。     

圆柱壳几何大变形非线性频率求解的渐近摄动法

为解决圆柱壳在工作状态中由几何大变形而引起的弱非线性振动问题，将渐近摄动法引入求解考虑几何非线性的薄壁圆柱壳振动频率。首先，应用Donnell＇s简化壳理论获得了考虑几何大变形情况下具有位移三次项的非线性频率方程，把位移及频率以非线性参数的幂级数形式展开，并令同次幂的非线性项系数相等，由此得到非线性频率一次近似值与初始振幅的一系列耦合代数方程，引入Galerkin＇s方法对非线性频率方程进行解耦正交并忽略其中的永年项，考虑了对应实数根，各阶频率对应的振幅间不存在相互耦合的内共振现象，最终在引入小参数后用摄动法求出了非线性频率的一次近似解。计算结果表明，几何非线性使薄壁圆柱壳产生硬化，其非线性频率升高，并同时讨论了线性、非线性频率与节径数及初始位移之间的关系。     

湿热环境下反对称正交铺设双稳态扁壳的建模与非线性振动响应研究EI北大核心CSCD

对湿热环境下的反对称正交铺设双稳态扁壳进行了非线性动力学建模。在经典壳理论的基础上,考虑温度和湿度的影响,在本构方程中加入热膨胀系数和湿膨胀系数;联立相容方程和动力平衡方程以建立模型,得到了反对称正交铺设双稳态扁壳的偏微分运动控制方程;应用Galerkin方法对系统偏微分运动控制方程进行三阶离散,得到了三自由度的常微分运动控制方程。通过双稳态系统在主共振Ω接近于ω,内共振为1∶2∶2条件下的六维极坐标系和直角坐标系下的平均方程,得到了外激励幅值变化对反对称正交铺设条件下双稳态系统的非线性动力学特性的影响规律。     

考虑几何非线性的旋转薄壁圆柱壳进动响应分析

选取悬臂旋转薄壁圆柱壳作为研究对象,利用能量法推导了其振型进动因子,并考虑了阻尼以及几何非线性的影响.应用Donnell's简化壳理论建立考虑几何非线性以及振型进动的非线性波动方程,使用Galerkin法对非线性波动方程进行离散化,获得模态坐标上的非线性微分方程组,分别应用Runge-Kutta法和谐波平衡法对其进行数值求解和近似解析求解,并分析了近似解析解的稳定性.结果表明,几何非线性不影响振型进动因子,但使系统的频率响应曲线具有多值性和跳跃性.     

四边简支钢筋混凝土矩形薄板的热屈曲

基于刚性板和小挠度理论,考虑混凝土的材料非线性,推导了热载作用下钢筋混凝土矩形薄板的平衡方程和稳定方程。给出了四边简支钢筋混凝土矩形薄板在横向变温和温度均匀变化时临界屈曲温度变化的封闭解,并对工程中常见的钢筋混凝土矩形薄板在温度均匀变化时的临界屈曲温度变化进行了计算,讨论了板的材料常数、长宽比和相对厚度对临界屈曲温度变化的影响,从而为工程结构中钢筋混凝土矩形薄板的临界屈曲温度变化的计算提供了理论计算依据。     

被动约束层阻尼圆锥壳振动和阻尼分析的新方法

该文基于Donnell薄壳理论,考虑各层锥顶点的水平偏移,分别建立了基壳和约束壳的控制方程。仅考虑粘弹性层剪切变形的影响,由线粘弹性理论,结合基壳、约束壳的控制方程和粘弹性层的法向平衡方程,导出了PCLD圆锥层合壳的整合一阶常微分矩阵方程。该方程的系数矩阵不是常数矩阵,各元素的表达式较PCLD圆柱壳复杂。然后,借助基于精细积分技术的传递矩阵法提出了一种分析PCLD圆锥层合壳振动和阻尼特性的半解析、半数值方法。通过与文献值的对比,证明了该文方法的有效性。该文还讨论了各种参数对系统固有频率和损耗因子的影响。     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥壳非线性稳定性的基本方程中增加横向转动惯量项并引入三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells

A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis–Lagrange (M–L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.     

考虑横向剪切效应时圆柱型正交各向异性球面扁壳在横向载荷作用下的非线性压屈

本文应用参考文献所介绍的修正迭代法探讨了横向载荷作用下,圆柱型正交各向异性圆底球面扁壳的非线性稳定同题,得出了这一同题的解析解。在求解过程中,本文放弃了经典板壳理论的Kirchhoff假定,从而考虑了横向剪应变对于弯曲变形的影响, 计算结果表明:本文的分析方法和结论是正确的;对于正交各向异性复合材料板壳而言,横向剪切效应是值得注意的。     

An improved zig-zag model for the bending of laminated composite shells

A simple layerwise higher-order zig-zag model is proposed for the bending of laminated composite shells. The model provides a cubic variation of both the in-plane displacements and the transverse shear stresses within each layer. As the displacement model satisfies the zero transverse shear stress conditions at the free surfaces, there is no need for the use of shear correction factors. By imposing the continuity of the in-plane displacements and the transverse shear stresses at the interfaces, the number of variables is shown to be the same as that given by the first-order shear deformation shell theory, irrespective of the number of layers considered. For the sake of consistency, all terms of the order of the thickness coordinate-to-radius ratio have been retained in the derivation of the governing equations. Numerical results for the cylindrical bending of thick, symmetric homogeneous orthotropic and three-layer laminated shells under sinusoidal loading show that the maximum transverse deflections and in-plane stresses are in good agreement with available exact elasticity solutions for radius-to-thickness ratios greater than or equal to four.     

Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical shallow shells using vertically reinforced 1-3 piezoelectric composite (PZC). The constraining layer of the ACLD treatment is considered to be made of this 1-3 PZC material. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type non-linear strain displacement relations and the first-order shear deformation theory (FSDT) are used for deriving this electromechanical coupled problem. A three dimensional finite element (FE) model of smart composite shallow shells integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of thin laminated cylindrical shells, in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patch significantly improves the damping characteristics of the shells for suppressing the geometrically nonlinear transient vibrations of the shells. The effect of variation of fiber orientation in the PZC material on the control authority of the ACLD patch has also been investigated.     

开小圆孔圆柱壳在内压力作用下的应力集中

用一组简化的扁壳方程,分析了受内压作用下的圆柱壳在小圆孔边上的应力集中问题。类似于用薄扁壳方程分析柱壳圆孔附近应力集中的方法,求出了考虑横向剪切效应的应力集中系数的近似解析解及数值结果,由此得出了横向剪切效应对应力集中影响的一个新的特性。     

Nonlinear flexural analysis of laminated composite plates using RBF based meshless method

The paper presents the nonlinear flexural response of laminated composite plates. The mathematical formulation of the actual physical problem of the laminated composite plate subjected to mechanical loading is presented utilizing higher order shear deformation theory and von-Karman nonlinear kinematics. These nonlinear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. A meshfree technique based on multiquadric RBFs is used for analysis of the problems. Isotropic, orthotropic and laminated composite plates with immovable simply supported and clamped edges are analyzed.     

层壳考虑横向剪切效应的自由振动分析

本文采用一个分层的剪切变形理论分析层壳的自由振动。假定层壳各层横向剪切应变彼此线性相关,从而未知函数个数与一阶剪切变形理论相同,但控制微分方程的阶数为十二阶,且不含剪切修正因子。文中计算了一个短圆柱壳与两种扁壳的自由振动频率,数值结果与经典层合理论、一阶剪切变形理论及其他剪切变形理论的计算结果进行了比较。      

A higher-order shear deformation theory of laminated elastic shells

A higher-order shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. The theory is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces of the shell. The Navier-type exact solutions for bending and natural vibration are presented for cylindrical and spherical shells under simply supported boundary conditions.     

Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories

The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory.