结构拓扑优化中变量连接算法研究与软件实现

摘要

In structural topology optimization ,variable connection means that topology variables are connected with constrains in order to obtain specific configuration ,and to meet the requirements of engi‐neering design and restrictions of manufacturing technology .The formula with variable connection con‐cept for several filtration methods and sensitivity analysis is presented .Meanwhile based on the software integration platform SiPESC and topology optimization software SiPESC .TOPO ,a new algorithm design framework for variable connection concept of topology optimization is constructed .The core idea of software design is that algorithmic class and data model class are designed individually using object oriented methods and software design patterns .The mechanism of variable connection and the interfaces of software modules are discussed in detail .Finally ,the feasibility of variable connection concept and algorithm framework on static problems ,dynamic problems and heat conduction problems were verified by numerical examples .%结构拓扑优化的变量连接，是通过对设计变量之间添加约束关系，从而得到特定的拓扑优化构型，使得优化结果能够满足工程上的特殊要求和工艺制造技术的限制。针对拓扑优化中的几类过滤形式及灵敏度分析，给出了考虑变量连接的计算公式；基于自主研发的SiPESC软件集成化平台，在SiPESC ．TOPO拓扑优化模块上进行二次开发，构建了拓扑优化的变量连接算法框架，其核心思想是基于面向对象设计方法和软件设计模式，实现算法与数据分离。详细阐述了变量连接的作用方式，以及软件框架通用接口设计方案，并通过数值算例验证了其在静力问题、动力问题和热传导问题上的可行性。