复合材料板壳结构性能预测的多尺度分析和数值计算

The multi-scale analysis method is one of the most important methods in the fields of science and engineering computing and numerical simulation. When considering engineering design, fabrication and applications of composite materials, it is often in the need of material performance prediction, numerical simulation of the process affecting the microstructure and the service behavior analysis for materials and structures in the complex environment. Composite engineering products is mostly constitute of plate or shells structure, but the existing literature only consider the homogenization solution, the coupling analysis results between homogenization and micro three-dimensional mechanical solution for composite plates or shells. Based on the previous work, this project is going consider the physical / mechanical behavior of composite plates and hyperbolic flat shells with 3-D periodic configuration under the condition of static and thermal elastic environment. Intending to use the coupling technologies routes between the macro and micro mechanics, starting from the micromechanics, based on the homogenization method, the method of multi-scale analysis, finite element method and the geometric characteristics of the plate or shell structure, we construct high-order multi-scale model which can capture the three-dimensional micro-mechanical behavior controlled by the three-dimensional configuration of the microstructure, analysis multi-scale models and algorithms theoretically; establish approximate relationship between the three-dimensional mathematical model of the composite plate or shell structure and two-dimensional mechanical assumptions; and finally design more efficient multi-scale numerical algorithm.

多尺度分析方法是目前科学工程计算领域最热门的数值模拟方法之一。工程中复合材料设计、制备和应用常常需要进行材料性能预测，对影响微观结构的工艺过程进行数值模拟，并对材料与结构进行多尺度性能分析。复合材料工程制品多为板壳结构，现有的文献只考虑了宏观的均匀化解，至今尚未见到复合材料板壳结构制品宏观均匀化解和细观三维力学耦合的分析结果。本项目利用多尺度分析方法和有限元计算方法，研究复合材料制品周期构型板结构和双曲扁壳结构在静力学服役环境下的力学行为，以及两种结构在瞬态热弹性环境下的性能。拟采用宏、细观相关联的技术路线，从细观力学出发，基于均匀化方法、多尺度分析方法、有限元方法以及板壳结构的几何特性，构造可以捕捉到由三维构型微结构导致的微观三维力学行为的高阶多尺度模型；并进行多尺度模型和算法的理论分析，建立复合材料板壳结构三维数学模型与二维力学假设之间的近似关系；设计高效的多尺度数值算法。

多尺度分析方法是目前科学工程计算领域最热门的数值模拟方法之一。复合材料工程制品多为板壳结构，材料设计、制备和应用常常需要进行材料性能预测，对影响微观结构的工艺过程进行数值模拟，并对材料与结构进行多尺度性能分析。本项目利用多尺度分析方法和有限元计算方法，研究复合材料制品周期构型板结构和双曲扁壳结构在静力学服役环境下的力学行为，以及两种结构在瞬态热弹性环境下的性能。采用宏、细观相关联的技术路线，从细观力学出发，基于均匀化方法、多尺度分析方法、有限元方法以及板壳结构的几何特性，构造可以捕捉到由三维构型微结构导致的微观三维力学行为的高阶多尺度模型；并进行多尺度模型和算法的理论分析，建立复合材料板壳结构三维数学模型与二维力学假设之间的近似关系；设计高效的多尺度数值算法。