导电薄板内电流密度分布与反平面剪切的比拟

定量分析电流密度在含裂纹载流薄板内的分布是当前利用电流热效应止裂技术中一个首先要解决的问题．由于裂纹的存在,电流密度在裂尖形成带奇异性分布的高度密集．现有的分析方法往往比较复杂或局限于特殊布置形式的裂纹．通过电流密度分布与弹性力学里反平面剪切问题的比拟,把分析含裂纹载流薄板内电流密度的分布等效于考虑相应的III型裂纹问题,并比照III型裂纹的应力强度因子来定义电流密度因子．而对于裂纹问题的处理可采用分布位错法这一断裂力学里便利有效的分析手段．由给出的算例可见,所提出的比拟解法可以方便精确地求解电流密度在裂尖附近的奇异分布,并有助于对这一奇异性在概念上的直观理解．     

倒T型环形基础的分析

本文根据实际工程中大型双曲冷却塔的基础形状和受载方式,分析了倒T型环形基础的应力和位移分布。采用加权残差法求得了问题的解析解。文中提供了一个工程实例的分析,探讨了不同荷载形式和基础与土壤的剪切模量之比对于基础内应力分布的影响。     

结构可靠性灵敏度分析的方向（重要）抽样法

方向抽样法是在标准正态空间极坐标系下,通过对矢径的方向进行随机抽样来分析结构可靠度的.但是当极限状态面接近平面时,方向抽样法就没有优势了.为了提高方向抽样法的效率,提出了三种基于方向(重要)抽样法的可靠性灵敏度分析方法.根据独立标准正态空间中基本变量的x<'2>分布特性及矢径与随机变量分布参数的关系,推导失效概率对基本随机变量分布参数的可靠性灵敏度分析的计算公式.该文所提的可靠性及灵敏度计算方法有较高的计算效率和精度,对于高度非线性极限状态方程问题亦有很强的适应性.     

对称抛物型模糊变量下的可靠性及灵敏度分析

当模糊变量的隶属函数为正态型时,可以将模糊随机可靠性及可靠性灵敏度转化为随机可靠性及可靠性灵敏度,并利用复合函数求导法则求解模糊随机失效概率对正态型隶属函数分布参数的灵敏度.对于对称抛物型隶属函数,文中提出了"改进最大最小"法和"改进等面积"法两种近似等价正态化方法,从而将模糊随机可靠性问题转换为随机可靠性问题,并利用线抽样方法分析之.算例结果表明,由于"改进最大最小"法所得的等价正态型隶属函数能在函数图形尾部更好地近似对称抛物型隶属函数,因而"改进最大最小"法更适用于模糊变量的隶属函数为对称抛物型分布时模糊随机可靠性及可靠性灵敏度的近似计算.     

直接有限元法求解广义磁热弹二维旋转问题

为了验证直接有限元法求解广义磁热弹耦合旋转问题的有效性及准确性,该文基于Lord和Shulman(L-S)广义热弹性理论,采用直接有限元方法,求解了置于磁场中的旋转半无限大体受热冲击作用的动态响应问题.文中给出了L-S型广义磁热弹耦合旋转问题的控制方程,建立了L-S型广义磁热弹旋转问题的虚位移原理,推导得到了相应的有限...     

圆弧型墙背下的主动土压力研究

基于平面滑裂面假设,采用水平层分析法计算墙背为圆弧型情况下的挡土墙主动土压力及其分布情况,分析了挡土墙与墙后填土的各参数对主动土压力大小及分布的影响。计算结果表明,随着挡土墙倾斜角的减小,土压力分布曲线由凸曲线变成凹曲线。最后通过算例将圆弧型墙背下主动土压力及分布的计算结果与平面墙背下的进行分析对比,结果表明当墙背倾斜...     

平面裂纹问题的h, p, hp型自适应无网格方法的研究

无网格方法以其独特的优点：不需“网格”（即节点间的连接信息）划分,特别适合自适应的分析,在分析中只需要高梯度域简单地插入离散点（ｈ型）或保持模型节点数、分布、覆盖大小均不变,中增加高误差覆盖上的函数的多项式阶次（ｐ型）,便可以得到更高精度的数值模型。针对平面弹性问题发展和推导一种显式后验误差指示公式,对平面裂纹实例进行了ｈ型,ｐ型,ｈｐ型三种不同类型的无网格自适应分析,数值分析结果表明了这种自适应     

界面反射超声散斑一阶统计特性

对界面反射超声斑场的一阶统计特性进行了理论和实验分析,在假设条件下,推导了超声散斑场的振幅分布和相位分布,实测数据显示理论与实验结果有很好的吻合,这表明理论假设是合理的并在实践中可行,这还表明,在B超影像分析中,超声扫描截面上散斑场统计特性的结果与该文的结果一致。     

热力藕合问题的交替算法

在极大的加热速率下,针对CV型非Fourier介质,提出一个热力耦合问题的解耦交替计算方法,即交替地计算两个解除了耦合的问题,逐步地得到足够精度的解。这两个问题分别是已知温度时空分布的热Hooke介质的应力分析问题和已知位移、应变和应力时空分布的非Fourier介质的热传导问题。这个方法也适用于Fourier介质,与每一解耦问题实施计算的方法无关。用简例说明了随交替计算次数的增加,其结果趋近于准确解;同时给出了对Fourier介质板一个瞬态问题的应用例子。     

螺杆泵动力学热力耦合分析方法研究

地面驱动螺杆泵是一种广泛应用于油田采油工程中的人工举升装置。由于螺杆泵深置地下的油管中,密封性很强,很难现场测试工作过程中定子橡胶材料的温度变化以及温度变化引起的定子变形。本文采用有限元方法分析螺杆泵定子的热力耦合效应,讨论定子橡胶材料温度变化的物理机理。用热力学单向解耦分析方法分析单螺杆泵定子橡胶材料的温度分布场以及温度分布引起的定子型线变化。讨论了过盈量、转子转速对温度分布和定子型线变化的影响。     

Homogenization-based method for bending analysis of perforated plate

Owing to the existence of distributed holes, it is difficult to solve the bending problem of perforated plates by the conventional finite element method. A homogenization-based method for this problem is presented in this paper. As an example, the bending analysis of a circular perforated plate with distributed step-wise cylindrical holes is made. The deflection and the fundamental frequency obtained by present method are in good agreement with experimental data, this implies that the method is effective. This project is supported by the National Natural Science Foundation (19602007) and National Outstanding Youth Foundation (19525206).     

Asymptotic analysis of perforated plates and membranes. Part 2: Static and dynamic problems for large holes

Static and dynamic problems for the elastic plates and membranes periodically perforated by holes of different shapes are solved using the combination of the singular perturbation technique and the multi-scale asymptotic homogenization method. The problems of bending and vibration of perforated plates are considered. Using the asymptotic homogenization method the original boundary-value problems are reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. In the present paper the perforated plates with large holes are considered, and the singular perturbation method is used to solve the pertinent unit cell problems. Matching of limiting solutions for small and large holes using the two-point Padé approximants is also accomplished, and the analytical expressions for the effective stiffnesses of perforated plates with holes of arbitrary sizes are obtained.     

Asymptotic analysis of perforated plates and membranes. Part 1: Static problems for small holes

Static problems for the elastic plates and rods periodically perforated by small holes of different shapes are solved using the asymptotic approach based on the combination of the asymptotic technique and the multi-scale homogenization method. Using the asymptotic homogenization method the original boundary-value problem is reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. The combination of the perturbation method and the technique of successive approximations is applied for the solution of the unit cell problems. Taking into the account small size of holes the method of perturbation of the shape of the boundary and the Schwarz alternating method are used. The problems of torsion of a rod with perforated cross-section; deflection of the perforated membrane loaded by a normal load; and bending of perforated plates with circular and square holes are considered consecutively. The error of the applied asymptotic techniques is estimated and the high accuracy of the obtained solutions is demonstrated.     

On the optimum shape of apertures for a perforated plate subject to bending

The problem of finding the optimum shape of the holes in a perforated plate weakened by a triangular or square lattice of holes and subject to bending is considered by methods based on the theory of functions of a complex variable. The criterion determining the optimum shape of the hole is based on the condition that no stress concentration should occur on the hole contour or, alternatively, that a plastic region should be created around the whole contour of the hole at exactly the same instant.     

Solving the problem of linear viscoelasticity for multiply connected anisotropic plates

This paper describes the method for solving the problems of linear viscoelasticity for thin plates under the influence of bending moments and transverse forces. The small parameter method was used to reduce the original problem to a sequence of boundary-value problems solved via complex potentials of the bending theory of multiply connected anisotropic plates. The general representations of complex potentials and boundary conditions for their determination are obtained. The method for determining the stress state of the plate at any time with respect to complex approximation potentials is developed by replacing the powers of the small parameter by the Rabotnov operators. The problem of a plate with elliptical holes is solved. The numerical calculation results in the case of a plate with one or two holes are given. The variation of bending moments in time until stationary condition is reached is studied, and the influence of geometric characteristics of the plate on these variable is described.     

Stresses in a perforated circular ring

This paper presents a solution for the stresses in a perforated circular ring containing a ring of uniformly distributed circular holes. The stress function is constructed by using ring-periodic biharmonic functions. Even and odd solutions are formulated separately. The solution is illustrated by numerical examples of a ring containing six holes under two types of loading.     

Nucleation of cracks in perforated solids under longitudinal shear

The problem of fracture mechanics on nucleation of cracks emanating from circular contours of holes of perforated isotropic solids under longitudinal shear is under consideration. The solution of the equilibrium problem of a perforated solid under longitudinal shear with prefracture zones is reduced to solving an infinite algebraic system and a nonlinear singular integrodifferential equation with a kernel of the Cauchy type. Forces in crack nucleation zones are found by solving these equations. The condition of crack emergence is formulated taking into account the criterion of the limiting discontinuity of material displacements.     

Dynamical bending of rigid-plastic annular plates

Dynamical bending of circular rigid-plastic annular plates, fixed along the exterior boundary and free on the interior boundary, when subjected to instantaneously applied transverse uniformly distributed blast-type load[1], is investigated in this paper.It is shown that annular plates are preferable to plates without holes, since their load capacity increases while residual deflections decrease. A so-called boundary parameter is introduced to estimate the effect of boundary conditions on the radial bending moment.A procedure for determining the residual deflections at every point of a plate is developed for use on an electronic computer. Numerical examples are given. In the end of the paper, the particularities of solution of our problem for annular plates, corresponding to the setting of Wang[2], Wang and Hopkins[3] for plates without holes are discussed.     

射孔套管弹性抗挤能力分析

套管射孔后其抗挤能力将有所降低．建立了射孔段套管弹性抗挤性能分析控制一般方程，并采用摄动理论给出了射孔段套管弹性抗挤能力降低系数一般计算公式．并与方孔精确解比较后得出，摄动法所得近似解具有足够的精度．为进一步开展射孔套管的弹塑性抗挤分析奠定了基础．     

Three-point bending of honeycomb sandwich beams with facesheet perforations

A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under threepoint bending,both analytically and numerically.Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet(perforation ratio).While for large-scale engineering applications like the decks of cargo vehicles and transportation ships,the perforations are needed to facilitate the fabrication process(e.g.,laser welding)as well as service maintenance,it is demonstrated that these perforations,when properly designed,can also enhance the resistance of the sandwich to bending.For illustration,fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs.Further,the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes:(1)bending failure,i.e.,yielding of beam cross-section and buckling of top facesheet caused by bending moment;(2)shear failure,i.e.,yielding and buckling of core webs due to shear forcing.The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios.As the perfo-ration ratio is increased,the load of shear failure increases due to thickening core webs,while that of bending failure decreases due to the weakening bottom facesheet.Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal,leading to significantly enhanced failure load(up to 60%increase)relative to that of a non-perforated sandwich beam with equal mass.