非轴对称载荷作用下任意弹性边界圆板弹性动力响应

利用模态迭加法得出了任意弹性边界圆板在非轴对称横向集中阶跃载荷作用下弹性动力响应的精确解，作为算例，给出简支圆板在非轴对称载荷作用下板上典型点的挠度与时间的关系曲线。     

用边界元法求双参数地基上正交异性板的动力响应

本文利用功的互等定理导出了双参数地基上正交异性板动力弯曲的边界积分方程，通过拉普拉斯变换，将问题转换到拉 普拉斯空间中求解，然后利用拉普拉斯数值逆变换得到在自然空间中的解。     

色噪声激励下Duffing—Rayleigh—Mathieu系统的稳态响应

基于广义谐和函数与随机平均原理,研究了具有强非线性的Duffing-Rayleigh-Mathieu系统在色噪声激励下的稳态响应.通过van der Pol坐标变换,将系统运动方程转化为关于幅值与初始相位角的随机微分方程.应用Stratonovich-Khasminskii极限定理,作随机平均,得到近似的二维扩散过程.在此基础上,考虑共振情形,引入相位差变量,做确定性的平均,得到关于幅值与相位差的It(o)随机微分方程.建立对应的Fokker-Planck-Kolmogorov(FPK)方程,结合边界条件与归一化条件,用Crank-Nicolson型有限差分法求解稳态的FPK方程,得到平稳状态下系统的联合概率分布.用Monte Carlo数值模拟法验证了理论方法的有效性.     

基于粘性流模型刚性物体撞水响应的边界元分析

基于二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，在线性化条件下，对于刚性物体撞水作用下的粘性流场分析，提出一个边界元－Ｌａｐｌａｃｅ数值闻变换混合方法。     

求解圆柱壳稳态谐响应的微分求积单元法

本文以Donnell经典壳体振动微分方程为基础,研究微分求积单元法(DQEM)在圆柱壳稳态谐响应计算中的应用。研究结果表明：微分求积单元法可较为方便的处理多种边界条件;与有限元法相比,微分求积单元法直接面向问题的微分方程,可用较少的节点获得较高的计算精度,计算效率较高。本文结果可为微分求积单元法在结构动力响应问题求解中的应用提供参考。     

非稳态环境激励下线性结构的模态参数辨识

假定任意随机激励信号由白噪声与非白噪声信号组成，由此导出线性结构响应之间的相关函数由两部分组成，一部分与脉冲响应具有相同的数学形式，另一部分为其它形式，利用模态分解法的基本原理，把相关函数分解为各个模态函数的叠加与余项之和，这样，第一部分信号已经分解为不同的模态函数，第二部分中的周期信号也变成了模态函数，这就把非稳态环境激励下多自由度线性结构系统的模态参数辨识问题转化为类似于已知各个单自由度系统的脉冲响应进行模态参数辨识问题，理论和模拟实验表明，本文成功地利用模态分解法进行非稳态环境激励下多自由度线性结构系统的模态参数辨识，其主要优点是，无论是白噪声激励，稳态随机激励还是非稳态随机激励，仅根据结构的响应不仅能辨识线性结构的模态参数，而且能有效地识别出环境激励中的周期成分。     

用样条边界元计算振动体的三维稳态声辐射

本文采用三次Ｂ样条边界单元计算振动体的三维稳态声辐射。实际计算表明：采用样条边界元可获得较好的数值计算结果。此外，本文在计算声场内点声压的Ｈｅｌｍｈｏｌｔｚ边界积分公式的基础上，导出了计算声场内点质点振速和声强的边界积分公式。文中还给出了应用本文方法计算的算例结果。     

换热边界下变物性梯度功能材料板稳态热应力

用非线性有限元法分析了由ZrO2和Ti-6Al-4V组成的变物性梯度功能材料无限自由长板在对流换热边界下的稳态热应力问题,检验了方法的正确性,给出了该材料板的稳态热应力场分布,并与不考虑变物性时的结果进行了比较.结果表明当M=1.0时,考虑变物性的最大拉应力比不考虑变物性减小70.5%,最大压应力减小62.5%;此外,材料组分的分布形状系数M、环境介质温度、对流换热系数和孔隙度P的变化对变物性梯度功能材料板的稳态热应力场分布均有明显的影响;在本研究相同条件下,当孔隙度系数A=3.99时,陶瓷侧拉应力最大.此结果为梯度功能材料的设计制备提供了准确的理论计算依据.     

任意激励作用下变厚度Reissner板的动力响应

本文提出了一个分析中厚度矩形板动力响应的一般方法。文中借助Laplace 变换和传递矩阵法,并引进节线的相关矩阵,较简便地求得了响应在象空间中的一般解,然后再利用拉氏逆变换的数值解求出板的瞬时位移场和内力场。列举的实例和以往的结果作了比较。     

桩—土系统稳态激励的响应分析

本文将桩的波动方程考虑为线性的，而将埋入土中一端的边界条件考虑为非线性的，用摄动法对稳态激励进行响应分析。求出了桩—土系统动力学方程的近似解析解，对桩基的无损检测和地震分析均有参考价值。     

阻尼材料对环肋柱壳稳态响应影响的分析

利用Ｆｌｕｇｇｅ壳体理论，讨论了敷设自由层粘弹性阻尼材料的环肋柱壳受周期性径向激励的稳态响应，用复模量形式计及基壳和粘弹性阻尼材料的损耗因子，并计入流固耦合作用，讨论了粘弹性阻尼材料的物理参数和厚度对其稳态响应的影响。     

结构动应力分析的FEM-BEM耦合方法

本文提出了利用结构的有限元结点位移响应(或结点力)的计算值作为子域的边界条件,然后利用边界元方法计算子域内各瞬时的动应力的FEM-BEM耦合方法.文中给出了薄板在简谐激励下动应力响应的计算实例并与分析解进行了比较,结果表明,FEM-BEM耦合法比常规有限元法对结构动应力的计算精度有大幅度的提高.     

用边界元法计算声辐射时高次奇异积分的处理方法

边界元法应用于计算辐射声场时，由于奇积分的存在，会影响以计算结果的精度，本文描述了处理带有１／ｒ奇异积分和１／ｒ＾２二次奇异积分处理方法，包括数学证明和数值积分方法，计算结果表明这种方法能提高精度。     

A generalization of BEM by Fourier transform

 To overcome the restriction of actual boundary element methods (BEMs) to cases where fundamental solutions are known we present here an alternative BEM-approach. It is based on new boundary integral equations (BIE) for the computation of the entries of the standard BEM matrices which are obtained by a spatial Fourier transform of the traditional BIE. In these equations, we only need the transform of the fundamental solution and not the fundamental solution itself. The former is always available as long as the underlying differential operator is linear and has constant coefficients. Non-linear problems can be solved by an iterative linear procedure. First applications for problems of isotropic and anisotropic Kirchhoff or Reissner plates are given. Due to the limited space, more complex examples will be presented in an additional paper. Received 6 November 2000     

双向地震动作用下刚度偏心单层体系弹性反应谱研究

目前的工程抗震设计方法是建立在弹性单自由度反应谱的基础上，然而实际地震动的多维性和结构偏心引起的空间耦合性使得基于单自由度反应谱的设计方法存在着局限性。为此，研究并建立了双向地震作用下结构刚度偏心层体系弹性反应谱模型，定义弹性位移比值谱和加速度比值谱。通过对硬土、中硬（软）土、软土3类场地60条双向地震动的弹性比值谱统计平均结果，分析3类场地比值谱的谱值分布特征及相对刚度偏心距、扭转频率比对谱值及谱值分布的影响。结果表明，各类场地的比值谱都具有独特的谱值分布特征，并且这些分布特征受相对刚度偏心距和扭转频率比的影响较小。在每种场地类型的谱值分布特征下，弹性比值谱随相对刚度偏心距和扭转频率比的变化也具有一定的规律性。     

A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity

In this paper, a new and simple boundary‐domain integral equation is presented for heat conduction problems with heat generation and non‐homogeneous thermal conductivity. Since a normalized temperature is introduced to formulate the integral equation, temperature gradients are not involved in the domain integrals. The Green's function for the Laplace equation is used and, therefore, the derived integral equation has a unified form for different heat generations and thermal conductivities. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the normalized temperature using a series of basis functions and polynomials in global co‐ordinates. Numerical examples are given to demonstrate the robustness of the presented method. Copyright © 2005 John Wiley & Sons, Ltd.     

Static and harmonic BEM solutions of gradient elasticity problems with axisymmetry

An advanced boundary element method/fast Fourier transform (BEM/FFT) methodology for treating static and time harmonic axisymmetric problems in linear elastic structures exhibiting microstructure effects, is presented. These microstructure effects are taken into account with the aid of a simple strain gradient elastic theory proposed by Aifantis and co-workers [Aifantis (1992), Altan and Aifantis (1992), Ru and Aifantis (1993)]. Boundary integral representations of both static and dynamic gradient elastic problems are employed. Boundary quantities, classical and non-classical (due to gradient terms) boundary conditions are expanded in complex Fourier series in the circumferential direction and the problem is decomposed into a series of problems, which are solved by the BEM by discretizing only the surface generator of the axisymmetric body. The BEM integrations are performed by FFT in the circumferential directions simultaneously for all Fourier coefficients and by Gauss quadrature in the generator direction. All the strongly singular integrals are computed directly by employing highly accurate three-dimensional integration techniques. The Fourier transform solution is numerically inverted by the FFT to provide the final solution. The accuracy of the proposed boundary element methodology is demonstrated by means of representative numerical examples.The authors acknowledge with thanks for the support provided by I.K.Y. through the program IKYDA 2002 (scientific cooperation between the University of Patras, Greece and the Ruhr-University Bochum, Germany).     

Symmetric‐Galerkin BEM simulation of fracture with frictional contact

A symmetric‐Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary elements) and enables the determination of two important quantities for the problem, namely the local normal tractions and sliding displacements on the crack surfaces. An effective iterative scheme for solving this non‐linear boundary value problem is proposed. The results of test examples are compared with available analytical solutions or with those obtained from the displacement discontinuity method (DDM) using linear elements and internal collocation. The results demonstrate that the method works well for difficult kinked/junction crack problems. Copyright © 2003 John Wiley & Sons, Ltd.     

三维强化抛光振动台的谐响应分析

应用有限元软件(ANSYS)对三维强化抛光振动台进行谐响应分析,根据谐响应分析结果对三维强化抛光振动台的结构进行改进。在此基础上对改进的模型进行谐响应分析,并比较改进前后的结构在共振状态下的谐响应,证明改进的合理性。