Study on Application of Homogenization Method in Structural Engineering

本文通过数值实验详细探讨了均匀化方法在结构分析中的适用性。为了用有限元法分析复合材料的应力，必须用某种方法确定材料的有效系数，如平均弹性常数等。均匀化法是求得这些常数的数学方法之一。在本研究中，纤维增强复合材料，有时用作热材料，进行了详细的分析。由于大多数纤维增强复合材料所具有的隔热性能，其在高温环境下的应用，特别是在航天飞行器上的应用越来越多。因此，建立一种科学有效的热应力分析和热传导处理方法是十分必要的。本研究的优点是均匀化方法适用于复合材料在一个方向、两个方向或三个方向以上的纤维增强情况，即不需要如此认真地考虑几何极限。因此，该方法适用于计算平均热传导率和膨胀率。给出了计算这些参数的方法。本课题的研究成果大致总结如下：(1)研究表明，对于弹性和热弹性问题，采用均匀化方法求平均弹性常数和热膨胀系数是可行的。结果表明，该方法可以较准确地得到复合材料的局部应力。(2)对于非定常热传导问题，当包涵材料的热传导率远大于基本材料的热传导率时，可以准确地求出其常数。反之，如果前者的热传导率远低于后者，则可以发现平均温度的差异。(3)对于热传导或其准训练问题，研究表明，当基元材料的热传导率远高于包套材料的热传导率时，均质化方法也是可行的。少

This research investigates the applicability of homogenization method to structural analysis by some numerical experiments, in detail. In order to analyze the stress of composite materials by means of FEM,effective coefficients of the materials, such as average elastic constants must be determined by some method. Homogenization method is one of mathematical means to obtain these constants. In this research, fiber-reinfored composite materials, sometimes used as thermal materials, is analyzed in detail. Due to the thermal insulating property that most fiber-reinforced composite materials possesses, ther application under high temperature circumstances, specially like using in space vehicles, is increasing. Consequently, it is quite necessary to establish a scientific and effective method to analyze heat stress and to deal with heat conduction. The research takes the advantage that the homogenization method is applicable to any cases that composite materials is fiber-reinforced in one, t … More wo or three directions, namely, it is not needed to consider geometrical limit so seriously. Hence this method is applicable for evaluation of average heat conduction rate and expand rate. A process to evaluate these parameters is given.In this term of project, research results gained are roughly summaried as follows :(1)The research shows that for elastic and thermal elastic problems, it is feasible to apply homogenization method to evaluate average elastic constants and heat expand coefficients. It is found that even local stress of the composite materials can also be obtained with a high degree of accuracy by this method.(2)With reference to unsteady heat conduction problems, if the heat conduction rate of inclusive materials is much higher than the one of fundamental materials, the constants can be evaluated exactly. Coversely, if the heat conduction rate of the former is much lower than the latter, the difference of average temperature can be found.(3)For heat conduction or its quasi-training problems, the research reveals that if heat conduction rate of fundamental is much higher than the one of inclusive materials, homogenization method is also feasible. Less