考虑尺寸效应的模块化结构两层级优化设计

CONCURRENT HIERARCHICAL OPTIMIZATION FOR STRUCTURES COMPOSED OF MODULES CONSIDERING SIZE EFFECTS

出于构造、美观、生产工艺、质量控制、降低成本等考虑,在很多工业应用中,整个结构或装备可被规整的分成几个相同的子区域,各个子区域的结构形式完全相同,这样的子区域称为基本设计模块.整个结构或装备可通过有限个基本设计模块重复拼装而成.针对此类模块化结构,考虑结构与模块间的耦合作用,提出了结构、模块两层级并发优化设计的模型与求解方法,研究了基本设计模块的绝对尺寸对优化结果的影响.通过在结构和模块两个层次上分别引入独立的人工密度变量,借助拓扑优化技术和惩罚策略,给出了最优的设计模块构型以及模块在结构尺度上的最优分布,通过单工况和多工况数值算例验证了该方法的有效性.

The concurrent optimization model and algorithm for modular structures are developed in this paper.The effects of actual size of the basic design module on optimization results are investigated for structures composed of periodic modules.The size of modules can greatly affect the optimization results of configuration and distribution of basic design modules.The concurrent optimizations of macro structures and design modules are implemented by introducing independent densities in macro-structure and micro-module hierarchies as design variables.The optimal designs of configurations of macro structure and modules in two hierarchies are obtained via topology optimization and penalty technique.The interactions of structures and modules can be considered automatically by the optimization model.Two numerical examples with single load and multi loads are presented to validate the proposed optimization model and algorithm.