基于哈密顿解法的矩形厚板分析

建立了分析Reissner-Mindlin厚板问题的哈密顿解法。首先,以x坐标模拟时间坐标,选用互为对偶的混合变量作为基本变量,建立哈密顿正则微分方程组。然后,采用分离变量法和特征函数展开法在相应的边界条件下求出级数解。最后,给出矩形厚板典型例题的解答,分析了级数解的收敛性质。与常用的半逆解法相比,Hamilton解法有其优点:一是求解方法严密合理、有规可循;二是应用范围广,可用于求解系列问题。     

A new iterative order reduction (IOR) method for eigensolutions of large structures

Order reduction is a computationally efficient method to estimate some lowest eigenvalues and the corresponding eigenvectors of large structural systems by reducing the order of the original model to a smaller one. But its accuracy is limited to a small range of frequencies that depends on the selection of the retained degrees of freedom. This paper proposes a new iterative order reduction (IOR) technique to obtain accurately the eigensolutions of large structural systems. The technique retains all the inertia terms associated with the removed degrees of freedom. This hence leads to the reduced mass matrix being in an iterated form and the reduced stiffness matrix constant. From these mass and stiffness matrices, the eigensolutions of the reduced system can be obtained iteratively. On convergence the reduced system reproduces the eigensolutions of the original structure. A proof of the convergence property is also presented. Applications of the method to a practical GARTEUR structure as well as a plate have demonstrated that the proposed method is comparable to the commonly used Subspace Iteration method in terms of numerical accuracy. Moreover, it has been found that the proposed method is computationally more efficient than the Subspace Iteration method. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite Element Model Updating of Complicated Beam-Type Structures Based on Reduced Super Beam Model

基于超梁降阶模型的复杂梁式结构有限元模型修正

王文胜，魏豪杰，候中华，梅群，李一帆

（河南科技大学 工程力学系，河南 洛阳 471023）

摘要：

提出一种针对复杂梁式结构的有限元模型修正方法。首先采用建立在经典梁理论中的平面截面假设和位移插值函数的超梁降阶模型方法，将复杂的梁式结构简化为具有较少自由度的超梁降阶模型。在此基础上，模型修正过程中所需要的特征值求解和特征灵敏度分析是在降阶后的小规模矩阵上进行，与传统基于全结构的模型修正方法相比，大大减少计算量。采用优化技术实现结构模态特性差异的修正，从而获得结构参数的最优值。最后以复杂加筋圆柱壳模型和一实际导弹结构的模型修正为例，证明了基于超梁降阶模型的有限元模型修正方法的有效性和高效性。

关键词：超梁降阶模型方法，模型修正，复杂梁式结构，特征方程，特征灵敏度

     

径向平方贝塞耳函数调制高斯光束的研究

在一般情况下从近轴波动方程出发直接推导出变量为径向平方的贝塞耳函数调制的高斯光束是其解,并研究了它在自由空间中的传输特性。     

Epsilon算法在结构模态重分析中的应用

基于Neumann级数和Epsilon算法,提出了一种模态重分析的新算法。在求解过程中,利用Neumann级数产生基向量,然后用Epsilon算法求出近似特征向量,最后用Rayleigh商分析,求出了修改后结构的近似特征值和特征向量。数值算例表明,所提出的算法比K irsch组合近似法精度更高,计算速度更快。     

多机电力系统中PSS配置点的合理选择

基于多机电力系统推广的Phillips-Heffron模型和模型控制原理,提出了采用一种新的模型控制分析自由特征解方法来选择多机电力系统中电力系统稳定器(PSS)的合理配置点.该方法不必计算系统传递函数的留数,所需的计算时间较少,而且适用于多种电力系统运行方式,又能满足系统对PSS效率的要求.最后以3机系统为例利用本文方法为其选择了PSS的合理配置点,验证了本文方法的正确性.     

Hamiltonian Approach to Analytical Thermal Stress Intensity Factors—Part 1: Thermal Intensity Factor

An analytic method to determine the thermal intensity factors of finite domains in two-dimensional heat conduction in the vicinity of a crack is introduced. The method first separates the variables of the heat conduction equations in polar coordinates using the Hamiltonian formalism and finds the symplectic eigenfunctions analytically. The coefficients of the symplectic series are determined from the boundary conditions. The thermal intensity factor is given by the first coefficient of the antisymmetric part of the series and no post-processing is required.     

Analysis of Electromechanical Stress Singularity in Piezoelectrics by Computed Eigensolutions and Hybrid-trefftz Finite Element Models

This paper concerns the determination of singular electromechanical stress field in piezoelectrics. A one-dimensional finite element procedure is generalized to compute the eigensolutions of the singular electromechanical field. The generalized procedure is capable of taking differently poled piezoelectrics, cracks and ultra-thin electrodes into account. To determine the strength of the singular electromechanical stress field, the hybrid-Trefftz finite element method is adopted. The independently assumed electromechanical stress modes are extracted from the eigensolutions previously computed from the one-dimensional procedure. Since the eigensolutions satisfy all the balance conditions, the hybrid-Trefftz models can be constructed by boundary integration. This feature enables the models to be interfaced compatibly with conventional finite element models. To illustrate the efficacy of the present approach, the eigensolutions and/or parameters directly related to the electromechanical stress intensity in crack, interfacial crack and bimorph with embedded electrode are considered. The predictions are in good agreement with the reference solutions reported in the literature or computed by using over 10,000 conventional finite elements.     

在热冲击下弹性梁非线性热局部屈曲

研究了弹性梁在热冲击下的热传导过程和大变形下的后屈曲行为。采用Hamilton体系下的辛本征解基描述屈曲模态,并用辛本征解展开方法对非线性的后屈曲问题进行探讨。提出了一种数值计算方法。研究结果揭示了梁后屈曲的整个变化过程。结果还表明屈曲变形过程依赖热冲击强度、热传导系数和梁的参数等。     

Eigensolution for free vibration of planar frames by weighted graph symmetry

In this paper, the method recently developed for mass‐spring systems is generalized to include the free vibration of frames. Here, the inter‐relation for the mechanical properties of elements is established using weighted graphs, enabling the calculation of the eigenvalues involved. Using graph symmetry, the models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels results in the eigenvalues of the entire model. The present method is illustrated through many simple examples of different configurations. Copyright © 2006 John Wiley & Sons, Ltd.