多物理场小周期结构体双尺度有限元分析

项目名称： 多物理场小周期结构体双尺度有限元分析

项目编号： No.10801042

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 建筑科学

项目作者： 冯永平

作者单位： 广州大学

项目金额： 17万元

中文摘要： 复合材料由于具有抗腐蚀、耐疲劳、抗热震及耐高温等物理和力学性能, 故在航空航天、土木工程建筑等方面被广泛应用。大部分复合材料通常在多物理场耦合作用的环境中更能体现其自身的优点， 所以对高温、高压、高强度环境中复合材料的设计与性能分析成为目前材料学家、力学家、数学家等关注的重点。对多物理场耦合作用的小周期结构复合材料性能的分析评价和计算方法在国内外已有初步的研究，但进行系统、全面的双尺度分析和算法研究并不多见。本项目拟对多物理场耦合作用的具有孔洞结构的复合材料， 特别是热力、力电耦合作用的复合材料运用双尺度方法及相应的有限元方法进行物理性能的评价研究，建立细观、宏观相耦合的均匀化模型、双尺度模型和计算方法；分析复合材料多尺度构造的关联特征及均匀化参数；并给出相应的有限元算法设计与误差分析。通过上述的分析研究， 对多物理场耦合作用下复合材料的性能分析与评价提供一套行之有效的算法。

中文关键词： 热力耦合；压电；双尺度方法；有限元；周期孔洞区域

英文摘要： Composite materials have been widely used in civil engineering and aeronautics & astronautics because of many elegant qualities, such as high stiffness, high strength and fatigue resistance. Nowadays many mathematicians and material scientist are interested in analyzing effective physical properties and designs of these materials under condition of high temperature and high pressure etc. Up to now, there are fewer papers are applied to discuss the systematic and overall effective analysis properties and corresponding algorithms of two-scale method for multi-scale materials although a lot of researches of computational methods and analytic technology for periodic composite materials in multi-physical fields are obtained. In these methods, the two-scale method couples macroscopic scale and microscopic scale together, it not only reflects global mechanical behavior of structures but also the effects of microscopic of composite materials. In this subject, by means of two-scale method and corresponding finite element method, some effective physical properties of periodic perforated composite materials in multi-physical fields especially in coupled thermo-elasticity and piezoelectricity are analyzed. Firstly, we will present the homogenization models, two-scale models and corresponding computational methods of these coupled problems. Next, we will analyze the interaction between different physical fields and effective properties and homogenized coefficients of these materials. Lastly, some error estimates and finite element algorithms are given corresponding to mathematic problems. Our main aim in this subject is to provide an effective method for analyzing and evaluating physical properties of composite materials in periodic perforated domain under condition of multi-physical field.

英文关键词： Coupled thermoelasticity; Piezoelectricity;Two-scale method;Finite element method;Periodic perforated domain