复合材料板瞬态热-力耦合弯曲行为分析的高阶多尺度方法

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-力耦合的弯曲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：复合材料板的瞬态热-力耦合的宏-细-微观关联的弯曲模型，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瞬态热-力耦合弯曲行为分析，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瞬态热-力耦合弯曲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。

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 bending behavior of composite plate thoroughly and systematically. It includes: the thermo-mechanic coupled and macro-fine-micro associated bending 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 bending 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 bending 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.