CAJ | 학술논문

研究具有随机变量的稳态热传导结构在散热弱度约束下的拓扑优化设计问题。建立了以单元相对导热系数为设计变量,导热材料体积极小化为目标函数,满足散热弱度可靠性指标为约束条件的稳态热传导结构的拓扑优化设计数学模型。基于随机因子法,利用代数综合法推导出散热弱度的数字特征的计算表达式。采用渐进结构优化方法(Evolutionary Structural Optimization,ESO)求解,并利用过滤技术消除优化过程中的数值不稳定性现象。通过两个算例验证文中模型及求解策略、方法的合理性和有效性。
연구구유수궤변량적은태열전도결구재산열약도약속하적탁복우화설계문제。건립료이단원상대도열계수위설계변량,도열재료체적겁소화위목표함수,만족산열약도가고성지표위약속조건적은태열전도결구적탁복우화설계수학모형。기우수궤인자법,이용대수종합법추도출산열약도적수자특정적계산표체식。채용점진결구우화방법(Evolutionary Structural Optimization,ESO)구해,병이용과려기술소제우화과정중적수치불은정성현상。통과량개산례험증문중모형급구해책략、방법적합이성화유효성。
Topology optimization design of a heat conduction structure with random variables under dissipation of heat transport potential capacity constraint is discussed.The mathematical model of topology optimization,based on the probabilistic reliability index with dissipation of heat transport potential capacity constraint,is constructed.The total volume of heat conductive material is to be minimized and the relative thermal conductivity of elements is regarded as the design variable here.The computational expressions for numerical characteristics of dissipation of heat transport potential capacity based on the random factor method are presented.Evolutionary structural optimization method is used in optimization.A filtering technique is employed to eliminate numerical instabilities in process of topology optimization. Two numerical examples are presented to demonstrate the feasibility and effectiveness of the optimal model and the solution.