热磁电弹性材料层合板的半解析法

以三维弹性体的HR混合变分原理为基础,考虑熵变量,重构热磁电弹性体的本构方程,并应用Hamilton正则方程半解析法,求解热磁电弹性层合板问题,主要原因为熵变量的引入,可以将热磁电弹性非齐次的Hamilton正则方程直接齐次化,齐次的Hamilton正则方程半解析法简化热磁电弹性板问题的分析过程.     

基于可分型Hamilton正则方程的复合材料层合板自由边缘效应研究

提出一种可分型Hamilton正则方程与有限元法相结合的半解析法理论,研究辛体系下正交异性复合材料层合板自由边缘效应问题。首先根据修正后的H-R变分原理,推导可分型Hamilton正则方程,应用有限元法建立沿厚度方向的状态方程。然后,实例计算分析复合材料层合板层间应力。通过数值算例验证了方法的有效性。     

Hamilton体系下旋转刚柔耦合楔形梁有限元建模及辛算法

首先利用Hamilton原理对耦合结构进行建模,然后利用有限元方法将空间连续模型离散化,得到有限元模型,然后将模型导入到Hamilton系统中,获得Hamilton正则方程。在建模的基础上,采用半隐式辛Runge-Kutta(SRK)算法对Hamilton系统下的模型进行计算,并与传统Runge-Kutta方法进行了比较。数值仿真结果表明,采用二阶的半隐式SRK算法能够长时间保持系统的能量守恒,是一种保结构算法,而传统的Runge-Kutta方法是一种耗散算法,在求解初期具有高的精度,但是不能保持系统解的长期稳定性。从仿真过程中还可以得到一个非常有意义的结果,二阶的半隐式SRK算法对步长的要求低于传统的四阶Runge-Kutta方法。     

轴对称蠕流问题双调和方程的Hamilton描述

笔者从无穷维Hamilton系统的等价定义出发,用代数方法把轴对称蠕流问题导入到Hamilton体系.借助无穷维Hamilton正则系统的定义和偏微分方程Hamilton正则表示的一些成果,把柱坐标下轴对称蠕流问题关于流线函数的双调和方程写成Hamilton正则方程,使双调和方程形式上变成可以分离变量的问题,由此得到辛...     

基于Hamilton体系的能量释放率分析

基于Hamilton体系半解析法的分离合并技术,建立了脱层损伤层合板的半解析模型,具体分析了脱层损伤层合板结构脱层前缘节点的应力、位移及其分布规律,并进一步详细地研究了各种脱层损伤情况的能量释放率,本文的数值结果与Abaqus的数值结果进行了比较,证明了本文方法的正确性。     

Hamilton体系在电磁涡流耗散系统建模中的应用研究

电磁涡流场问题的传统求解方法是按照电磁场基本理论来建立方程,并通过各种数值计算方法来求解,其缺点是计算量大,精度难以保证。文中从能量的角度出发,给出电磁涡流耗散系统的Hamilton函数;依据分析力学中Hamilton理论,推导出系统的正则方程,建立了涡流耗散系统问题求解的新模型。该建模方法将为电磁涡流问题的求解提供一条新途径。     

EFG法在线弹性结构形状优化中的应用研究

出现在基于有限元形状优化过程中的网格畸变与扭曲问题,可通过引入无网格方法得到解决。本文首先建立了结构形状优化的数学模型,利用无网格Galerkin(EFG)法对形状优化的设计域进行了离散,采用罚函数法来施加边界条件,借助于直接微分法建立了一种离散型基于无网格Galerkin法的设计灵敏度分析算法,然后用1个具有解析解的实例对其进行了验证,所得结果显示两者是一致的。最后利用对所建立的算法完成了1个工程实例的形状优化设计,并对所得到的优化结果结合工程应用进行了讨论。     

机器人动力学计算精度的研究

分析了机器人动力学数值计算中“能量耗散”的原因,论证了机器人系统动力学系数之间的恒等关系,建立了机器人系统（非完整系统）动力学的正则方程。正则方程与辛算法密切结合,消除了动力学计算的误差累积,保证了计算精度。     

Hamilton体系下四边简支复合材料开口圆柱层合壳灵敏度分析的解析法研究

基于修正后的H-R(Hellinger-Reissner)变分原理,推导了开口圆柱单层壳的Hamilton正则方程和开口圆柱层合壳的微分控制方程。将微分控制方程和灵敏度系数控制方程耦合,得到了开口圆柱层合壳响应和响应灵敏度系数的混合控制方程。利用该混合控制方程,对均布载荷作用下四边简支三层开口圆柱壳进行了位移灵敏度分析,并将所得的灵敏度分析结果与有限差分法相比较。结果表明,笔者推导的开口圆柱层合壳的混合控制方程是正确的,并且简化了Hamilton体系下层合壳结构的灵敏度分析过程。     

金属塑性成形过程再生核质点无网格方法数值模拟

应用微可压缩材料的流动法则,采用再生核函数无网格方法,自行开发了求解方棒压缩、圆棒压缩、反向挤压和轧制等金属塑性成形过程应用程序。应用再生核质点无网格方法计算得到纯铝和铝合金材料金属塑性成形过程的速度场和应力场解析结果,并与自行开发的I-Form有限元程序得到的计算结果以及试验数据进行了分析比较,结果符合良好。再生核质点无网格方法具有求解金属大变形特点,解决了有限元法中的网格重划问题,为复杂金属变形分析提供了良好的研究手段。     

Buckling of symmetrically laminated rectangular plates under parabolic edge compressions

Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh-Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending-twisting coupling may overestimate the stiffness, thus providing higher buckling loads.     

基于高阶改进方法的层合板固有频率分析

针对一般的计算层合板振动特性的方法过于繁复的问题,采用了一种高阶改进方法来计算复合材料层合板的固有频率。建立了高阶改进方法的层合板动能和势能表达式,利用哈密顿原理构建了层合板的自由振动方程并计算了层合板的固有频率。在此基础上,通过该方法计算了铺设角度、跨厚比和弹性模量比对层合板固有频率的影响。结果表明：该算法可以有效地计算出反对称铺设层合板和正交铺设层合板的固有频率,同时也可以计算任意形式铺设的层合板的固有频率。     

Analysis of rectangular laminated composite plates via FSDT meshless method

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates.     

Thermal buckling behavior of laminated composite plates: a finite-element study

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio E _L/E _T and thermal expansion ratio α _T/α _L, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.     

Finite element analysis of stress concentrations and failure criteria in composite plates with circular holes

In this study, the stress concentration factors (SCF) in cross-and-angle-ply laminated composite plates as well as in isotropic plates with single circular holes subjected to uniaxial loading is studied. A quadrilateral finite element of four-node with 32 degrees of freedom at each node, previously developed for the bending and mechanical buckling of laminated composite plates, is used to evaluate the stress distribution in laminated composite plates with central circular holes. Based up on the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical results obtained by the present element compare favorably with those obtained by the analytic approaches published in literature. It is observed that the obtained results are very close to the reference results, which demonstrates the accuracy of the present element. Additionally, to determine the first ply failure (FPF) of laminated plate, several failure criterions are employed. Finally, to show the effect of E ₁/E ₂ ratio on the failure of plates, a number of figures are given for different fiber orientation angles.     

角铺设层合板有限变形分析的减缩基法

应用减缩基方法，对导出的反对称角钢设层合板在均匀分布横向载荷作用下有限变形问题的控制微分方程进行了求解．展合板静态响应的数值计算结果表明，该方法是有效的和准确的．     

Vibrations of rectangular plates with internal cracks or slits

This work applies the famous Ritz method to analyze the free vibrations of rectangular plates with internal cracks or slits. To retain the important and useful feature of the Ritz method providing the upper bounds on exact natural frequencies, the paper proposes a new set of admissible functions that are able to properly describe the stress singularity behaviors near the tips of the crack and meet the discontinuous behaviors of the exact solutions across the crack. The validity of the proposed set of functions is confirmed through comprehensive convergence studies on the frequencies of simply supported square plates with horizontal center cracks having different lengths. The convergent frequencies show excellent agreement with published accurate results obtained by an integration equation technique, and are more accurate than those obtained by a previously published approach using the Ritz method combined with a domain decomposition technique. Finally, the present solution is employed to obtain accurate natural frequencies and mode shapes for simply supported and completely free square plates with internal cracks having various locations, lengths, and angular orientations. Most of the configurations considered here have not been analyzed in the previously published literature. The present results are novel, and are the first published vibration data for completely free rectangular plates with internal cracks and for plates with internal cracks, which are not parallel to the boundaries.     

铺设角度对层合板结构声功率的影响分析*

针对层合板结构铺设角度对前二阶声辐射模态幅值和辐射声功率的影响进行分析。利用分层理论结合有限元模型求解层合板的铺设角度与振动速度信息之间关系。通过声辐射模态理论,以某12层层合板结构为例,研究固定边界条件下的层合板辐射模态数、对称铺设角度、单向铺设角度以及激励力位置对声辐射模态幅值和辐射总声功率的影响。计算结果表明,在相同角度下,对称铺设层合板结构最大声功率值要小于单向角度铺设层合板结构最大声功率值;另外在低频时,对层合板结构辐射声功率起主要贡献的是前两阶辐射模态。并以某16层零度铺设的固定边界条件下的层合板结构为例,对复合材料层合板结构的声辐射模态幅值及声功率进行试验分析。