沿板平面材料梯度变化功能材料板件分析

本文发展一种功能梯度构件分析的细观元法.细观元法在构件的常规有限元内部设置密集观细单元以反映材料特性变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算.这种细观元法既能充分反映材料功能梯度沿各方向任意变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法.现有功能梯度板件分析中无论对不同形状还是不同边界的功能梯度构件,其材料特性均沿板厚度方向梯度变化,本文用细观元法进行计算与分析,给出了目前尚未得到的沿板平面方向功能梯度变化构件的力学量三维分布形态.     

空隙分布对功能梯度板件宏观响应的影响

提出了一种新的功能梯度结构分析的细观元法. 细观元法对结构的常 规有限单元内部设置密集细观单元以反映材料细观构造,又通过协调条件将各细观元结点自 由度转换为同一常规有限元自由度. 此方法实现了材料细观结构到构件宏观响 应的直接过渡分析. 用细观元法来分析细观构造上空隙存在对宏观响应影响,给出了含 有不同分布与形状、位置空隙的功能梯度板件的力学量三维分布形态,实现功能梯度材料结 构宏、细观间跨尺度分析.     

具有不同功能梯度分布函数的板件的三维分析

发展了一种新颖的功能梯度结构分析的细观元法。细观元法对结构的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法。文中通过细观元技术进行计算、分析,给出了具有不同功能梯度分布函数板件的力学量三维分布形态。     

基于金相图片识别功能梯度材料参数的梯度分布函数

功能梯度材料具有复杂的细观结构.其内部构造远比匀质材料复杂.以目前的实验条件,测量功能梯度材料参数分布函数一般是十分困难的.该文提出一种细观元方法,直接利用功能梯度材料金相图片信息,来进行功能梯度构件宏观响应的跨尺度力学分析.另在功能梯度材料结构静、动力正演分析基础上,根据正演所求得的挠度或固有频率值,采用混和罚函数法来反演识别功能梯度材料参数的宏观梯度分布函数.     

功能梯度材料构件三维分析的细观元模型

提出一种新颖的功能梯度构件分析的细观元法,给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度及组分变化特性,而其计算单元与自由度又与常规有限元一样,是一种针对功能梯度构件分析的有效数值方法。算例表明了细观元法对不同情况下功能梯度构件分析的适应性与精度。     

反映材料微观结构效应的宏观动力特性分析

探讨了实现复合材料细观结构与构件宏观动力特性直接关联的细观元法。细观元法先进行宏观单元剖分，然后分析细观结构，将微结构力学量转化为宏观结点量计算。该方法不增加自由度，但使得微结构层次上任意铺设方式和任意微小变化均能在宏观动力特性上得到反映。     

非匀质材料板的微结构优化设计

探讨具有微结构构造的非匀质材料构件在微结构层次上的优化设计,即寻求满足构件宏观性能要求的最佳微结构材料与构造参数。文中采用细观元法确定非匀质材料构件宏观性能与材料微结构参数间定量关系,建立起微结构优化设计数学模型,具体分析了复合材料板件满足强度、刚度要求的最佳微结构参数。有关方法可适用于复合材料、功能梯度材料、智能材料等新材料构件。     

基于Haar小波方法的功能梯度材料矩形板三维力学分析

利用Haar小波方法对任意材料梯度分布的四边简支功能梯度材料矩形板进行了三维力学分析.由于小波方法在求解局部奇异性问题上的优越性,对于任意材料梯度变化,甚至材料性质存在局部剧烈变化的情况,各分量的Haar小波级数解都有较好的收敛性.通过算例得到了矩形板在机械荷载作用下,平板上下表面材料性质差异以及材料不同梯度形式对其结构响应的影响.     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

材料细观结构与构件宏观响应间直接关联关系

本文探讨一种用于材料细观结构与构件宏观响应之间的直接关联分析方法，该方法应用宏观计算，给出细观力学量，并可反映材料细观结构特征，适用于具有细观结构材料制成构件的力学分析。     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

Development and design of new methods of measurement of state of strain of structures

The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect.     

Calculation of aerodynamic characteristics of arrays of profiles of arbitrary shape

It is well known that the problem on nonseparating potential flow of an incompressible fluid about an array of profiles reduces to an integral equation for a certain real function, determined on the contours of the profiles of the array. As such a function one can take, as was done, for instance, in [1–5], the relative velocity of the fluid on the profiles of the array. For arrays of profiles of arbitrary shape it is necessary to solve the corresponding integral equation numerically. In the particular examples of the calculation of aerodynamic arrays that are available [1–3] the numerical methods used were based on the approximate evaluation of contour integrals by rectangle formulas. As investigations showed, sizeable errors arose thereby in the approximate solution obtained, these being especially significant in the case of curved profiles of relatively small bulk. In the present paper a method for the numerical solution of the integral equation obtained in [5] is proposed. The method is based on the replacement of a profile of the array with an inscribed N polygon, the length of whose sides is of the order N^–1 and whose internal angles are close to . Convergence with increasing N of the numerical solution to an exact solution of the integral equations at the reference points is demonstrated. Examples of the calculation are given.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–112, March–April, 1972.     

Method of constructing estimates of the solution of equations of filtration of an aerated liquid

The exact solutions of the nonlinear equations of filtration of an aerated liquid have been obtained in [1–3]. In [4] the system of equations of an aerated liquid have been reduced to the heat-conduction equation under certain assumptions. An approximate method of computing the nonsteady flow of an aerated liquid is given in [5], where the real flow pattern is replaced by a computational scheme of successive change of stationary states. In [6] the same problem is solved by the method of averaging. In the present article estimates of the solution of the equations for nonstationary filtration of an aerated liquid in one-dimensional layer are constructed under certain conditions imposed on the desired functions. These estimates can be used as approximate solutions with known error or for the verification of the accuracy of different approximate methods. We note that the use of comparison theorem for the estimate of solutions of equations of nonlinear filtration is discussed in [7–9]. The methods of constructing estimates of solutions of various problems of heat conduction are given in [10, 11]