三维应力状态下高温低周疲劳寿命分析

通过带缺口的圆柱形ＬＤ８铝合金度样的高温低周疲劳试验，并应用ＴＭＦ程序，进行了轴对称问题的循环应力应变计算，探讨了应用当量应变范围评价三维低周疲劳特性，研究结果表明，三维应力状态下，当量应变范围可以作为三维高温低周疲劳的有效力学参量。     

复合材料定向管热弹动力响应特性研究

为研究复合材料定向管热弹性问题,采用求解轴对称流动Euler方程组的正格式方法对管内火箭燃气射流场进行数值模拟,得到了管内流场热力载荷。运用非线性有限元方法,建立了复合材料定向管非线性热弹性有限元模型,将定向管模态计算结果与模态试验结果作比较,验证了有限元模型的有效性,计算了复合材料定向管分别在火箭燃气动压载荷、非定常温度场和耦合状态下的动力学响应。结果表明:由非定常温度场热冲击引起的定向管内壁面热应力响应呈现脉冲形状,轴向应力对复合材料定向管定位部间管段的应力响应影响较径向应力和周向应力明显,热冲击引起的热应力在复合材料定向管的热弹性应力响应中占主导作用。     

两端简支圆柱体的轴对称振动

本文用三维弹性动力学理论研究圆柱体在两端简支约束下的轴对称自由振动问题。给出位移振型和应力振型的解析表达式，求得固有频率的精确解。研究结果表明：在圆柱体的径向还存在着不同的半波数的位移振型，这种性质在初等理论中是无法反映的     

带冠涡轮叶片的接触分析

以航空发动机动力涡轮一级带锯齿形叶冠的转子叶片为例,用有限元接触分析方法对装配和工作状态下的叶冠紧度和叶冠接触力、叶身应力进行了计算和分析,着重考察了工作载荷(温度和离心力)对叶冠接触力的影响。分析结果表明,叶冠的紧度由预扭角和工作载荷决定,离心力对紧度的变化起主要作用。     

有限长厚壁圆筒康托洛维奇应力变分解端部偏差的修正

本文指出文献[4]、[5]在用康托洛维奇应力变分法解有限长厚壁圆筒轴对称问题时存在的端部应力偏差；提出一个消除该偏差的反向端部效应的问题；通过简单计算推导出满足其全部应力边界条件与平衡微分方程的应力表达式，并用应力变分法求得其解答；数值计算结果表明，该解答较好地修正了文献[4]中端部附近应力的偏差。     

固支三维弹性矩形厚板的精确解

采用有限积分变换和状态空间理论相结合的方法推导出了固支三维弹性矩形厚板的精确解.在分析过程中摒弃以往薄板和中厚板理论中有关应力和位移函数的各种人为假定,完全从三维弹性力学基本方程出发,经过变量代换将关于应力和位移分量的六阶偏微分方程组化为2 个彼此独立的四阶、二阶矩阵微分方程,再利用有限积分变换的方法得到空间状态方程,并由Cayley-Hamilton定理求得应力和位移分量沿板厚度z 方向的传递矩阵,最后利用边界条件定解出待定常数,经过有限积分逆变换解得了固支三维厚板的精确解.通过计算实例验证了该文方法的正确性.     

轴对称条件下混凝土板的冲切强度

本文采用Hsich-Ting-Chen强度准则,对轴对称条件下混凝土板冲切强度进行了分析,推导出破坏时的冲切面上正应力和剪应力表达式;采用刚塑性模型,给出了轴对称破坏机构,再利用虚功原理求得破坏荷载的上限。计算公式形式简单,计算结果与已有结果相比符合较好。     

移动荷载下有限深度Winkler地基上梁的动力响应研究EI北大核心CSCD

基于考虑有限深度土体运动的Winkler地基梁理论,建立移动荷载作用下弹性地基上有限长梁的横向运动方程。利用模态叠加法求得移动荷载作用下有限长梁动力响应的解析解,进而以移动荷载离开时梁的响应为初值,采用分离变量法求得有限长梁自由振动的一阶近似解;通过数值计算和参数分析,揭示了移动荷载作用下有限深度Winkler地基上简支边界梁的动力学特性,分析地基深度、地基黏滞阻尼系数和荷载移动速度等对有限长梁受迫振动阶段和自由振动阶段动力响应的影响,全面揭示有限深度土体运动对临界速度的作用效应。结果表明:地基深度显著降低了临界速度,且弹性地基黏滞阻尼明显延长了自由振动衰减时间;荷载移动速度加剧了有限深度弹性地基与其支承梁的相互作用效应,系统振动的幅值和响应周期均发生显著变化。     

轴对称声学问题的有限元素法

本文应用有限元素法计算轴对称自由声场的声辐射特性,采用三角形一次元对区域离散化,通过外推加速法提高计算精度。用两个算例考察本方法:脉动球声场和无限长脉动园柱声场,计算结果与精确解比较,取得了满意的结果。     

声弹效应测量螺栓轴向应力的有限元计算分析

为促进超声技术在定量评价螺栓拧紧状态中的有效应用,结合实际检测需求,对基于声弹效应的螺栓轴向应力测量方法构建了合适的有限元模型。使用二维轴对称方式模拟M8×25的螺栓,螺栓头部安放10 MHz的超声波探头;有限元计算时,采用具有默纳汉三阶弹性常数的超弹性材料,将结构场与声场进行耦合分析,通过前后两个研究步骤,确定出螺栓在轴向拉伸状态下的超声波形信号;有限元计算结果表征了声传播时间差(ns)、轴向载荷(MPa)间的线性关系,此线性关系随螺栓夹紧长度、螺栓材料的不同而相应地改变;计算表明,对基于声弹效应的轴向应力测量方法而言,线性系数的准确测定非常重要;对有限元计算结果进行深入分析,可知螺栓内部应力状态对于超声传播声时变化存在叠加影响;因螺栓夹紧长度不同会引起声弹效应的较大变化,在实际测量时应对此足够重视。有限元计算结果与解析计算结果、实际试验测试结果对比,结果吻合性良好;所建立的超声法测量螺栓轴向应力的有限元模型,解决了对声弹效应进行数值模拟分析的难题,可为检测方法分析、专用仪器研发提供技术指导。     

动载荷下应力强度因子的边界元计算

用Ｎａｒｄｉｎｉ－Ｂｒｅｂｂｉａ边界元法计算了动载荷下的应力强度因子，与解析解及有限元解相比较，效果较好。最后对计算结果进行了分析讨论。     

Nodal sensitivities as error estimates in computational mechanics

Summary This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.     

基于水平集算法的扩展有限元方法研究

扩展有限元是一种以单位分解思想为基础,在常规有限元位移中加入跳跃函数和渐近位移场函数,以处理不连续问题的数值方法。将水平集算法应用到裂纹界面的描述及加强单元类型的判别,并与扩展有限元相结合,用于分析材料断裂问题。相比传统有限元,有限元网格与裂纹面位置相互独立,不需满足裂纹为单元边、裂尖为单元节点和在裂纹附近进行高密度的...     

Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads

In this paper, a thick truncated hollow cone with finite length made of two-dimensional functionally graded materials (2D-FGM) subjected to combined loads as internal, external and axial pressure is considered. The volume fraction distribution of materials and geometry are assumed to be axisymmetric but not uniform along the axial direction. The Finite Element Method based on the Rayliegh-Ritz energy formulation is applied to obtain the elastic behavior of the functionally graded thick truncated cone. By using this method, the effects of semi-vertex angle of the cone and the power law exponents on the distribution of different types of displacements and stresses are considered. The results show that using 2D-FGM leads to a more flexible design so that both the maximum stresses and stress distribution can be controlled by the material distribution.     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method

The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface.     

Tsallis entropy in dual homogenization of random composites using the stochastic finite element method

This work concerns an application of the Tsallis entropy to homogenization problem of the fiber‐reinforced and also of the particle‐filled composites with random material and geometrical characteristics. Calculation of the effective material parameters is done with two alternative homogenization methods—the first is based upon the deformation energy of the Representative Volume Element (RVE) subjected to the few specific deformations, while the second uses explicitly the so‐called homogenization functions determined under periodic boundary conditions imposed on this RVE. Probabilistic homogenization is made with the use of three concurrent non‐deterministic methods, namely Monte‐Carlo simulation, iterative generalized stochastic perturbation technique as well as the semi‐analytical approach. The last two approaches are based on the Least Squares Method with polynomial basis of the statistically optimized order— this basis serves for further differentiation in the 10th‐order stochastic perturbation technique, while semi‐analytical method uses it in probabilistic integrals. These three approaches are implemented all as the extensions of the traditional Finite Element Method (FEM) with contrastively different mesh sizes, and they serve in computations of Tsallis entropies of the homogenized tensor components as the functions of input coefficient of variation.     

Symmetric coupling of multi‐zone curved Galerkin boundary elements with finite elements in elasticity

The coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the efficient symmetric coupling of a Symmetric Galerkin Multi‐zone Curved Boundary Element Analysis method with a Finite Element Method for 2‐D elastic problems. Existing collocation based multi‐zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi‐zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent ‘macro finite elements’, that are symmetric, so that symmetry in the coupling is retained. This computationally efficient and fast approach can be used to solve a wide range of problems, although only 2‐D elastic problems are shown. Three elasticity problems, including one from the FEM‐BEM literature that explore the efficacy of the approach are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

三维空间杆系结构动力分析的超级元法

本文研究了超级元法在复杂杆系结构动力分析中的应用。该方法是最近提出的一种新的数值计算方法，它具有有限元法的灵活、通用性强等优点，同时解决了有限元法自由度多，计算机内存需要量大，计算工作量大等缺点，可以大大提高计算效率，并能在微机上实现复杂结构的计算。