连续体结构动力响应下的拓扑优化方法研究

项目名称： 连续体结构动力响应下的拓扑优化方法研究

项目编号： No.U1330124

项目类型： 联合基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 高彤

作者单位： 西北工业大学

项目金额： 80万元

中文摘要： 连续体结构动力响应下的拓扑优化是有效开展航天武器装备复杂结构研发、实现其轻量化和创新设计的重要技术支撑。设计方法的先进性与否直接影响结构布局的合理性、动力学固有特性与响应。本项目以导弹武器结构动力学工程设计需求为背景，旨在拓展拓扑优化先进理论，建立简谐和随机振动激励下连续体结构拓扑优化方法。主要研究内容包括：结构动力学属性匹配插值模型、动力学拓扑优化模态参与因子和激励频率的影响机理分析、简谐激励下加速度响应峰值和功率谱载荷下加速度均方根响应的高效灵敏度求解策略。通过建立刚度、质量、预应力等的匹配插值模型，消除局部模态和材料分布不连续的孤立岛现象；采用模态参与因子表征振型对动力响应的影响，揭示固有频率特性优化和动力响应优化的差异；通过引入动力修改重分析方法，提高动力学拓扑优化灵敏度计算效率。以上工作结合应用单位导弹武器典型结构研制，对深入认识结构设计机理、提高工程设计水平具有重要的指导作用。

中文关键词： 拓扑优化；动力响应；简谐激励；随机激励；

英文摘要： Continuum structural topology optimization with dynamic responses is the key fundament of the lightweight and innovation design of the complex aerospace structures. Reasonability of the structural layout and the dynamic inherent characteristics and responses of the structure significantly depend upon the advanced design methods. Based on the engineering requirements of the dynamic performance design of the missile structures, this project is to expand the topology optimization theories and establish the continuum structural topology optimization method under harmonic and random excitations. The main research contents are as follows, i.e. matched interpolation models of structural dynamic properties, influence of the modal participation factor in dynamic topology optimization and efficient sensitivity calculation method of the acceleration response amplitude under harmonic excitation and the mean-square-root of the acceleration response under random excitation. By developing the matched interpolation models of stiffness, mass, pre-stress etc., the local mode and non-connection in optimization configurations can be eliminate. The modal participation factor is further introduced to indicate the influences of the mode shape upon the dynamic response and clarify the difference between the optimization with the struct

英文关键词： topology optimization；dynamic response；harmonic excitation；random excitation；