小周期结构区域中热力耦合问题的三重尺度渐近分析

发布时间：2018-11-13 17:09

【摘要】：随着复合材料在应用上广泛地应用于土木工程、航空运输和日常生活各个领域,对于复合材料的热学性质和力学性质的研究不断趋于成熟.对具有周期孔洞结构的热力耦合复合材料,通过研究等效性能去分析复合材料所具有的性能特点,进一步优化材料性能.这类复合材料问题,数学上可借助局部具有剧烈振荡系数的偏微分方程边值问题进行刻画,具有小周期性和强耦合性.此类问题的多尺度渐近分析对于预测这类复合材料的等效性能具有重大影响和深远意义.首先,本文考虑微观、介观、宏观之间的联系,利用三重尺度方法,通过构造恰当的单胞函数,对复合材料中具有周期孔洞结构的热力耦合问题构建了形式的三重尺度渐近展开.其次,基于均匀化方法和多尺度方法,讨论了问题的均匀化解与均匀化常数.最后,分析了所构造的形式渐近解的渐近误差及收敛性.
[Abstract]:With the application of composite materials in civil engineering, aviation transportation and daily life, the research on thermal and mechanical properties of composite materials is becoming more and more mature. In order to optimize the properties of thermo-mechanical coupled composites with periodic voids, the properties of the composites are analyzed by studying the equivalent properties. This kind of composite material problem can be described mathematically by means of the partial differential equation boundary value problem which has strong oscillation coefficient and has small periodicity and strong coupling. The multi-scale asymptotic analysis of such problems has great influence and far-reaching significance in predicting the equivalent properties of this kind of composite materials. First of all, this paper considers the relationship among micro, mesoscopic and macro, and constructs proper unit cell function by using triple scale method. A triple scale asymptotic expansion is constructed for the thermal-mechanical coupling problem with periodic pore structures in composite materials. Secondly, based on the homogenization method and the multi-scale method, the uniform solution and homogenization constant are discussed. Finally, the asymptotic error and convergence of the constructed formal asymptotic solution are analyzed.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33;O175.8

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