考虑瞬态效应的承载隔热多功能结构拓扑优化

Topology optimization for multi-functional structure with both load-bearing and thermal insulation capability considering transient effect

同时满足承载和隔热要求的多功能结构在高超飞行器热防护结构设计中倍受关注。实际隔热材料通常承载能力弱,而高承载材料隔热性能差,如何在有限空间内协同结构的承载与隔热成为关键问题。高超飞行器气动加热时间有限,存在加热时间短、热荷载变化大的特点。因此结构设计需要考虑时间因素和瞬态效应,而现有稳态传热与承载的多功能协同优化设计模型无法解决上述问题。为此,本文建立了考虑瞬态效应的承载隔热多功能结构拓扑优化的设计模型和求解方法,给出了目标和约束的解析敏度计算格式。该方法以密度法为基础,考虑体积约束,通过以结构柔顺性最小为设计目标,同时以区域温度控制函数为设计约束,实现结构刚度与隔热多功能设计要求。具体的算例表明,本文提出的优化模型能够准确考虑结构的瞬态效应,实现在给定许用温度和工作时间条件下隔热和承载的多功能协同设计。

A multi-functional structure, which can meet the requirements of load-bearing and thermal insulation simultaneously, has attracted much attention in the design of hypersonic thermal protection structures.The load-bearing capacity of thermal insulation materials is weak, while the thermal insulation capacity of load-bearing materials is poor.How to balance the load-bearing and thermal insulation requirements in a limited space has become a key problem.The aerodynamic heating time of hypersonic aircraft is limited, which has the characteristics of short heating time and large variation of thermal load.Therefore, the influence of time and transient effect needs to be considered in structural design, but the existing multi-functional collaborative optimization design model of steady heat conduction and load-bearing cannot solve the above problems.In this paper, the design model and solution method of topology optimization for multi-functional structures with both load-bearing and thermal insulation capability considering transient effects are established, and the analytical sensitivity calculation format of the objective and constraints is given.Based on the density method and considering the volume constraint, this method takes the minimum structural compliance as the design objective and the regional temperature control function as the design constraint to achieve the multi-functional design requirements of structural stiffness and thermal insulation.Numerical examples show that the proposed optimization model can accurately consider the transient effect of the structure, and realize the multi-functional coordination of load-bearing and thermal insulation design under the given allowable temperature and working time.