锅炉炉墙板梁结构随机响应的边界元方法

锅炉炉墙可简化成板，梁的组合结构，在燃烧脉动的激励下会形成随机性的振动。本文提出了一种借助于边界元方法进行随机激励作用下正交各向异性板，梁组合结构动力响应计算的一般方法。文中首先导出各向异性板，梁结构动力问题的边界积分方程，进而得到用于随机响应计算的板，梁结构的频率响应函数矩阵。在此基础上可以求出板，梁结构上任意点响应的均方值。这一方法的有效性在文中电站锅炉实际算例中得到了验证。     

Dynamic buckling of thin-walled composite plates with varying widthwise material properties

The paper deals with dynamic response of a thin-walled rectangular plate subjected to in-plane pulse loading. The plate is made of orthotropic (fibre composite) material in which the principal directions of orthotropy are parallel to the plate edges. The plate is characterised by a widthwise varying fibre volume fraction. The structures are assumed to be simply supported at the loaded ends and at non-loaded ends with five different boundary conditions (both simply supported, both fixed, simply supported fixed, simply supported free edge, fixed free edge). In order to obtain the equations of motion the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s Principle. The problem of nonlinear static stability was solved with the second order of the Koiter’s asymptotic stability theory of conservative systems. The results obtained from analytical–numerical method were compared with the results from finite element method (FEM).     

Local buckling of wide-flange thin-walled anisotropic composite beams

The present contribution deals with the onset of local buckling of compressively loaded thin-walled beams with open I, C, Z, T and L-cross-sections made of laminated composite materials. The method employs a discrete plate analysis approach in the course of which each structural subelement of interest—which presently is the flange—of the thin-walled cross-section is considered as a separate composite plate with elastic rotational restraints at those edges where an adjacent substructural element is located. While in many investigations the lamination schemes of webs and flanges are considered to be purely orthotropic, in the present paper the laminate layups are allowed to be of an arbitrary non-orthotropic nature, which also allows for the analysis of laminates with inherent bending–torsion coupling. The analysis of the buckling loads of the flanges of thin-walled composite beams is performed using the Ritz-method for which some especially adjusted displacement shape functions are employed. For the case of pure orthotropy, a novel closed-form solution is described. The accuracy of the employed approaches is established by comparison with accompanying finite element simulations of thin-walled composite beams. It is revealed that the presented methodology is highly efficient in terms of computational effort and yet performs with satisfying accuracy, which makes it very attractive for actual practical applications whenever the local stability behaviour of wide-flange thin-walled composite beams is to be considered.     

冲击作用下含孔洞纤维增强复合材料平板的动力学实验与数值研究

作为复合材料动力学实验与数值研究的应用实例 ,实验研究采用正交异性动态光弹性方法 ,数值分析运用各向异性介质的时域边界元方法。纤维增强光弹性复合材料平板被用来模拟含孔洞的正交异性半无限域 ,用小口径步枪施加与纤维方向成 0及 90两个方向的冲击载荷 ,在正交异性动态光弹性实验中记录了应力波在孔洞周围的传播、反射与绕射过程 ,此过程被进一步转换成应力分量的变化时程 ,并与相应的时域边界元方法的数值分析结果进行了比较。     

概率断裂分析的随机边界元法

应用随机边界元法分析材料弹性常数的随机性和裂纹面随机性对应力强度因子的影响。文中首先简介了随机边界元法，给出了具有随机材料或几何参数的弹性体的边界位移或面力的协方差，进而给出了材料参数和裂纹面随机时应力强度因子均值和方差的计算公式。算例中详细讨论了杨氏模量、泊松比及裂纹面的随机性对应力强度因子的影响。     

各向异性板的面导纳特性研究

目前在工程上各向异性结构中的振动问题和振动能量传递的问题越来越多,然而对各向异性结构导纳的研究还不充分,对各向异性板面导纳的研究也还处于萌芽状态。面导纳不仅反映结构的振动特性还能反映能量传递的特性,因此面导纳比点导纳在工程上更加贴合实际。本文根据理论公式获得了一般各向异性板面导纳的理论解,并与有限元模型的数值解对比发现两者有较好的一致性。作者采用有限元方法深入研究了各向异性板的弹性常数、板的尺寸大小及边界条件等对面导纳及其点导纳和面导纳差异值的影响,力求给工程测量和实际运用提供指导。研究发现增加激励面积、减小结构刚度及阻尼系数会使点、面导纳差异变大,剪切模量对板振动特性的影响远小于弹性模量,一般各向异性板模型退化为正交各向异性板模型会使点、面导纳差异变大,加大板的面积及增加阻尼系数有利于缩减导纳的波动范围,边界条件对板减振性能的影响较小。     

Boundary element analysis of anisotropic Kirchhoff plates

In this paper, the radial integration method is used to obtain a boundary element formulation without any domain integral for general anisotropic plate bending problems. Two integral equations are used and the unknown variables are assumed to be constant along each boundary element. The domain integral which arises from a transversely applied load is exactly transformed into a boundary integral by a radial integration technique. Uniformly and linearly distributed loads are considered. Several computational examples concerning orthotropic and general anisotropic plate bending problems are presented. The results show good agreement with analytical and finite element results available in the literature.     

随机有限元动力分析方法的研究进展

对随机结构动力分析方法,包括随机模拟法、摄动随机有限元法、动态随机有限元法和正交展开法等进行了评述,介绍了该领域内的研究进展,并讨论了研究中存在的问题以及发展方向．      

中厚板统计分析的随机边界元法

本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法,基于Taylor级数展开技术,分析和到广义位移的均值和一阶偏差的积分方程,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理,从而得到广义边界位移或面力的均值和协方差,并进一步求出部点广义位移和内力的均值和协方差,最后用本文方法计算了两个数例,并对所得结果进行了分析,探讨。     

空间杆系与叠层板组合结构的非线性稳定分析

本文用非线性有限元法研究一种空间杆系与复合材料叠层板组合结构的非线性稳定问题。将杆系离散成空间梁柱单元，将复合材料叠层板离散成复合材料叠层板单元，并考虑了几何非线性和板的成层正交各向异性性质。为了获得较高的计算效率并顺利通过稳定临界点，求解非线性平衡方程采用了变增量步长和柱面弧长法迭代策略。在考证了程序的正确性之后，具体分析了几个工程模型，得出了于工程设计有益的结论。     

随机有限元方法在断裂分析中的应用

在幂律非线性随机有限元基础上,以单边裂纹板为例给出计算含量钢继裂参数,J（J积分）,δ（裂纹张开位移）,Δ（由裂纹引起的裂纹板上下底面相对位移）,θ（由裂纹引起的裂纹板上下底在相对转角）及其对基本随机变量变化率的方法和分析算例。     

The coupling of stochastic BEM and stochastic FEM with application in the reliability analysis of pile foundation

The coupling theory of the stochastic boundary element method and stochastic finite element method is put forward for the reliability analysis. Its application in the reliability analysis of pile foundation is illustrated.     

二维弹性随机边界元与可靠性分析

本文利用对随机变量求偏导数的方法，推导了二维弹性随机边界积分方程及其相应的公式，考虑了随机边界条件、材料性能参数随机量以及几何尺寸随机因素等。本文还将所发展的方法用于结构静强度的可靠性分析。算例分析表明，本文数值结果与ＭｏｎｔｅＣａｒｌｏ模拟和理论解相比是十分满意的。     

正交异性光弹性应力分离的边界元法

本文对平面正交各向异性复合材料模型引入正应力线性和及边界上正应力线性和流的概念,提出从应力相容方程出发.用边界元法计算正交异性光弹性模型内任一点的正应力线性和位的方法,再与正交异性光弹性法中所给出的应力同的关系结合,即可进行正交异性光弹性应力的分离.最后,对边界元方法的精度进行了讨论.     

Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method

The work deals with the development of an effective numerical tool in the form of pseudospectral method for wave propagation analysis in anisotropic and inhomogeneous structures. Chebyshev polynomials are used as basis functions and Chebyshev–Gauss–Lobatto points are used as grid points. The formulation is implemented in the same way as conventional finite element method. The element is tested successfully on a variety of problems involving isotropic, orthotropic and functionally graded material (FGM) structures. The formulation is validated by performing static, free vibration and wave propagation analysis. The accuracy of the element in predicting stresses is compared with conventional finite elements. Free vibration analysis is carried out on composite and FGM beams and the computational resources saved in each case are presented. Wave propagation analysis is carried out using the element on anisotropic and inhomogeneous beams and layer structures. Wave propagation in thin double bounded media over long propagating distances is studied. Finally, a study on scattering of waves due to embedded horizontal and vertical cracks is carried out, where the effectiveness of modulated pulse in detecting small cracks in composites and FGMs has been demonstrated.     

复合材料箱型结构的屈曲性态研究

采用带旋转自由度参数C^0类板（壳）单元，研究复合材料箱型结构的初始屈曲性态，在推导单元几何刚度阵时，同时考虑出平面位移和面内位移对膜应变的影响；着重讨论了不同材料正方形截面梁的长细比与欧拉临界力的关系，复合材料典型盒段的截面形式和铺设角，铺设次序对初始屈曲性态的影响。     

用于正交异性材料构件应变、应力测量的OPCM传感元件研究

介绍了由压电陶瓷和树脂材料构成的正交异性压电复合材料（Orthotropic Piezoelectric Composite Material,简称OPCM）应变传感元件的构造及传感原理，推导了粘贴式和埋入式OPCM传感元件测量正交异性材料构件中应力的传感方程。对受平面应力场的作用的正交异性板的表面应力，应变进行了实测研究，并对测试误差进行了分析。     

随机有限元方法与结构可靠性

简要介绍和综合论述了随机结构的有限元分析及可靠性分析方法的研究及发展情况．包括随机结构的离散化、随机有限元控制方程的求解、随机有限元可靠性方法及随机结构的可靠性分析等．讨论了随机结构分析中存在的一些问题．概要论述了可能的发展方向．     

Analytical bending solutions of free orthotropic rectangular thin plates under arbitrary loading

This paper presents the analytical solutions for the bending of orthotropic rectangular thin plates by the double finite integral transform, which, as an effective tool in solving plate problems, should have received attention. As a representative and difficult problem in the theory of plates, free plates’ bending is successfully solved to demonstrate the accuracy of the method by comparing the present analytical solutions with those from the literature as well as those by the finite element method. With the proper integral transform kernels, the proposed solution procedure is applicable to the bending of orthotropic rectangular plates with all combinations of simply supported, clamped and free boundary conditions, which serves as an elegant approach to analytical solutions of plate bending problems.     

Large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure

Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.