复合材料板瞬态热-力耦合动力学问题的高阶多尺度方法研究

项目名称： 复合材料板瞬态热-力耦合动力学问题的高阶多尺度方法研究

项目编号： No.11501140

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王自强

作者单位： 贵州民族大学

项目金额： 18万元

中文摘要： 复合材料因其优良性能而被广泛应用于高科技领域，且多做成板、壳形态的薄壁结构；众多学者已经对复合材料及其结构的热、力性能分析的计算方法进行了研究，并取得了重要成果，但是多限于静态的块体结构问题。本项目将围绕复合材料板的瞬态热-力耦合的动力学行为的数学模型和计算方法开展系统、深入研究，主要内容是：复合材料板的热-力耦合、阻尼的力学宏-细-微观关联模型，包括含动态阻尼项和多尺度信息的偏微分方程组及其适定性；高阶多尺度方法及其数学理论；相关的有限元算法及其软件技术；并进行典型复合材料板热-力耦合动力学行为分析，以验证模型和算法的有效性。本项目的目标是为复合材料板的热-力耦合动力学行为分析提供一套理论上可靠的高性能数学方法，为复合材料板、壳设计，性能优化提供技术支持和理论依据。申请者及其合作者已经在本项目的相关领域有一定研究基础和成果积累。

中文关键词： 动态热-力耦合问题；复合材料板；高阶多尺度方法；收敛性分析

英文摘要： Composite material is widely used in many high-tech fields due to its good physical and mechanical proprities. In practical engineering, the composite materials are usually made into plates or shelles. Many scholars have studied the computation methods for thermo-mechanic coupled performance of composite material and structure and obtained many important achievements, but many of the researches consider the static problem of the block composite structure. This project will study the thermo-mechanic coupled mathematical model and computation method for dynamic behavior of composite plate thoroughly and systematically. It includes: the thermo-mechanic coupled and macro-fine-micro associated dynamic model of composite plate, including dynamic damping and multi-scale information of partial differential equations and its well-posedness；high order multi-scale method and its mathematical theory; the finite element algorithm and software technologies of high order multi-scale method; analysising the thermo-mechanic coupled dynamic behavior of the typical composite plate to verify the validity of the multi-scale model and its algorithm. The goal of this project is: providing a set of reliable high-performance mathematical method for the thermo-mechanic coupled dynamic behavior analysis of composite plate; providing a set of theory and technical for composite plate and shell design, performance optimization. The applicant and his partners have good research foundation and the achievements in the field of similar projects.

英文关键词： dynamic thermo-mechanic coupled problems;composite plate;high-order multiscale method;convergence analysis