热载荷及热-力载荷耦合作用下功能梯度板壳结构优化设计研究

项目名称： 热载荷及热-力载荷耦合作用下功能梯度板壳结构优化设计研究

项目编号： No.11202075

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 郑娟

作者单位： 湖南大学

项目金额： 26万元

中文摘要： 功能梯度材料(Functionally Graded Material, FGM)在航空航天、核反应堆、内燃机等领域中具有广阔的应用前景，是当前材料科学研究的前沿课题之一。本项目拟将结构优化设计方法引入到功能梯度材料结构的设计中，基于无网格数值技术对热载荷及热-力载荷耦合作用下的功能梯度板壳结构优化设计进行研究。主要的研究内容如下：1) 提出一种最适宜于求解功能梯度材料结构拓扑优化问题的新型无网格方法；2) 提出一种适宜于热-力载荷耦合作用下功能梯度材料结构拓扑优化的方法；3) 基于所提出的新型无网格方法研究热载荷及热-力载荷耦合作用下的功能梯度板壳结构尺寸、形状和拓扑优化设计，包括柔度最小化优化设计、自由振动频率优化设计和稳定性优化设计、拓扑优化问题的数学模型、灵敏度分析方法以及求解方法。本项目的研究结果将对于功能梯度材料板壳结构的设计和制造提供理论依据和参考。

中文关键词： 拓扑优化；无网格数值方法；功能梯度材料；板壳结构；

英文摘要： Functionally Graded Materials (FGM) have broad application prospect in aeronautic and astronautic, nuclear reactor and internal combustion engines, etc. For its potential application, FGM is one of the most attractive subjects in the materials science field. In the project structural optimal design is introduced in the FGM structural design, and the optimal design of FGM plates and shells under thermal loading and thermal-mechanical loading based on meshless method is resesrched. The main contributions may be summarized as follows: 1) A new meshless method is proposed to solve the topology optimization problem of FGM structures. 2) A optimization method is proposed to suit the topology optimization of FGM structures under thermal-mechanical loading. 3) Size optimization, shape optimization and topology optimization of FGM plates and shells under thermal and thermal-mechanical loading based on the proposed new meshless method are researched, incluing compliance design, frequency design and stability design.And mathematical model of topology optimization problem, sensitivity anslysis and solution method of the optimization problem are also studied. The research results of the project can provide theoretical reference value for design and manufacture of FGM plates and shells.

英文关键词： Topology optimization；Meshless Method；Functionally graded material (FGM)；Plate and shell structures；