压电层合板的B样条小波有限元半解析法

利用小波有限元法的优越性可方便地求解压电材料与复合材料混合层合板的某些静力学问题。根据层合结构的特点,将区间B样条尺度函数作为插值函数离散结构的平面域,应用压电材料修正后的H-R(Hellinger-Reissner)变分原理推导了压电材料的Hamilton正则方程的区间B样条小波(BSWI)元列式。该BSWI元的主要特点之一是厚度方向是解析解形式的。针对具体问题的求解,为了保证各层之间力学量和电学量的连续性,进一步应用了状态转移矩阵技术。数值算例表明所提出的区间B样条小波单元是成功的。采用推导压电材料BSWI元的方法可建立磁电弹性材料类似的BSWI元。     

压电材料的K正则方程及其层合板的显式辛算法

显式辛数值算法有一个重要的特性,即在长时间内保存Hamilton函数的指数幂,用这种方法求解可分的微分方程所得到的解逼近精确解.该文基于压电材料修正后的H-R混合变分原理,首先推导了Hamiltonian四节点有限元列式,然后通过对该列式进行行列变换,得到了K正则方程.最后将显式辛数值算法用于求解压电材料层合板的静力学...     

厚度不连续悬臂梁板的自由振动分析

将厚度不连续梁板视为层合板, 分别应用Hamilton 正则方程半解析法建立每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性, 联立各层的方程得到整个结构的特征方程, 其主要的优越性表现为: 控制方程不限制不连续梁板的厚度, 并能适合处理厚度不对称且不连续的层合板。本文中的方法可修改或扩展用来分析加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳等问题。      

壁厚不连续不对称圆柱壳和开口壳的自由振动分析

视壁厚不连续不对称的圆柱壳或开口壳为层合壳。以弹性力学中的Hamilton正则方程为基础,分别应用Hamilton正则方程的半解析法构建层合壳每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性,联立各层的方程得到系统的控制方程和特征方程。主要的优点是系统的控制方程不限制圆柱壳的厚度,数学模型和数值方法也适应分析壁厚不连续且壁厚不对称的复合材料层合壳问题。     

基于径向基点插值函数的弹性力学Hamilton正则方程无网格法

结合径向基点插值函数和弹性材料修正后的H-R(Hellinger-Reissner)变分原理,推导了Hamilton正则方程的无网格列式。以Multiquadric(MQ)、Gaussian(EXP)和薄板样条(TPS)为基函数,研究了Hamilton体系下无网格方法的收敛性、精确性以及基函数无量纲形状参数对计算结果的影响规律。该文的工作使得无网格有限元法的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合,为Hamilton正则方程提出了一种无网格半解析方法。     

压电体的混合变分原理及叠层板的自由振动分析

建立了具有机一电耦合效应的压电材料修正后的Hellinger—Reissner(H—R)混合变分原理，并推导了压电材料的Hamilton正则方程，即压电材料自由振动的控制微分方程；根据矩阵分析理论给出了带有压电材料层的叠层矩形板自由振动的精确求解方法，文中没有引入任何位移模式或应力模式假设，实例分析得到了压电混合叠层板正逆效应两种情况自由振动的低阶频率，并与已有文献结果进行了比较。本文提出的压电材料修正后的H—R混合变分原理将有利于压电材料动力问题的有限元法或半解析法的推导。     

压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程。给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的。这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析。变分原理将有利于压电材料问题相应的半解析法或有限元法的推导。     

Hamilton体系下复合材料层合板特征值灵敏度分析研究

在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固支复合材料层合板前四阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明了该文所提出方法的可靠性。另外,该方法能够方便地拓展到复杂层合板壳结构以及智能材料层合板特征值灵敏度系数的求解问题中去。     

周边固支缝合复合材料层板的小波配置精细积分法

建立了缝合复合材料面内纤维弯曲几何描述模型,将拟Shannon小波配置法和缝合单层板的刚度矩阵应用到缝合层合板的Hamilton正则方程中,构造了缝合板平面方向离散、而厚度方向解析的Hamilton正则方程,然后用精细积分法求解。用拟Shannon尺度函数表示的近似解很适于求解固支边界问题。数值算例结果表明,小波配置精细积分法在缝合复合材料层板位移、应力分析方面,较低网格密度下即可获得较精确的结果。从而为缝合层合板静力学问题分析提供了一种方法。     

敷设主动约束层阻尼圆锥壳的控制特性分析

基于压电材料的本构关系和内力位移方程,考虑压电材料的正、逆压电效应,求出了压电约束层的动力学控制方程和电学控制方程。根据圆锥壳的几何特性,将变量沿周向进行傅里叶展开,可将上述方程转化为沿母线方向的一阶常微分方程的形式。结合黏弹层的法向平衡方程和位移连续性条件,由主动约束层和基壳的力学方程导出层合结构的动力学方程,并将该方程与压电约束层的电学方程联立,建立了敷设主动约束层圆锥壳的机电耦合模型。然后,借助精细积分技术和叠加原理,采用速度反馈控制策略,提出了一种分析此类结构的半解析、半数值方法,并采用该方法分析了反馈系数、反馈点的布置等参数对敷设主动约束层阻尼圆锥壳振动特性和控制特性的影响。     

A three-dimensional semi-analytical model for the composite laminated plates with a stepped lap repair

A three-dimensional semi-analytical model of the static response and sensitivity analysis was established based on the state space methods and meshless method for the composite laminated plates with a stepped lap repair. Firstly, the meshfree formulations of Hamilton canonical equation and the linear spring-layer were deduced by the radial point interpolation method (RPIM) shape functions and the modified Hellinger–Reissner (H–R) variational principle of elastic solids. And then a three-dimensional hybrid governing equation of the static response analysis and sensitivity analysis were developed for the composite laminated plates with a stepped lap repair. The present three-dimensional semi-analytical model with no initial assumptions regarding displacement and stress accounts for the transverse shear deformation and rotary in the governing equation of structure. By using the hybrid governing equation in the response analysis and sensitivity analysis, the convoluted algorithm can be avoided in sensitivity analysis, and the response quantities and the sensitivity coefficients can be obtained simultaneously.     

Three-dimensional semi-analytical model for the static response and sensitivity analysis of the composite stiffened laminated plate with interfacial imperfections

For the stiffened composite laminated plates with interfacial imperfections, the problem of static response and sensitivity analysis was investigated in Hamilton system. Firstly, the meshfree formulation of Hamilton canonical equation for the composite laminated plate with interfacial imperfections was deduced by the linear spring-layer and the state-vector equation theory. And then, based on the equation of plates and stiffeners, governing equation of the composite stiffened laminated plate was assembled by using the spring-layer model again to ensure the compatibility of stresses and the discontinuity of displacements at the interface between plate and stiffeners. At last, a three-dimensional hybrid governing equation was developed for the static response analysis and sensitivity analysis.     

叠层厚壳动力分析的Hamilton方程及精确解

本文通过动力问题的Hellinger-Reissner变分原理,在柱坐标系下,导出了Hamilton正则方程,未采用任何有关应力或位移模式的人为假设,用状态空间法给出了薄的、中等厚度的以及强厚度的叠层闭口柱壳的精确频率,此解满足所有弹性力学基本方程,并计及了全部弹性常数,任意需要的精度均能得到.此法可通用于其它板壳的动力计算问题.     

正交异性层合厚板的混合状态Hamiltonian元

本文给出一种求解正交异性层合厚板混合状态Hamilton正则方程的半离散半解析方法。该方法沿板厚方向未作任何有关位移和应力的人为假设,采用状态控制方程给出解析解答,并采用分层迁移法进行计算,保持了层与层之间位移和应力的连续,大大地减少了未知量数目。      

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.