对于具有较低导热系数和较高生热率的热源材料(自发热体),通过优化植入内部的高导热材料的布局以降低内部温度,是实现自发热体冷却的重要措施.如何设计自发热体内部高导热材料的布局,是实现热源内部热量高效收集和温度控制的关键问题.本文研究建立植入式导热路径的拓扑优化设计方法,考虑高导热材料的植入对于热源分布的影响,以实现自发热体冷却的内置导热路径最优设计.基于固体各向同性材料惩罚模型(solid isotropic material with penalization,SIMP)拓扑描述方法,以高导热材料的相对密度为导热路径描述参数,分别选择合适的热传导系数和生热率的插值模型以建立热传导系数和生热率与相对密度的关系,并以结构散热弱度最小为目标,建立了植入式导热路径设计的拓扑优化数学模型和求解方法.该优化模型能够反映高导热材料的布局对热源布局的影响.通过具体算例,给出了贴片式散热路径与植入式散热路径的拓扑优化结果.设计结构表明,两种优化模型获得的最优散热构型存在较大不同,并且考虑植入高导热材料对热源布局影响的设计结果散热性能优于贴片式散热路径的设计结果.数值算例验证了本文所提出方法的正确性和有效性.
Auxetic materials have previously been shown to enhance various performances due to its unusual property of becoming fatter when uniaxially stretched and thinner when uniaxially compressed(i.e., the materials exhibit a negative Poisson's ratio). The current study focuses on assessing the potential of an auxetic material to enhance the buckling capacity of a rectangular plate under uniaxial compression. The in-plane translational restraint along the unloaded edges that was often neglected in open literature is taken into consideration in our buckling model proposed in this study. The closed-form expressions for the critical buckling coefficient of the rectangle are provided and the predicted results agree well with those determined by the finite element method. Furthermore, the results indicate that the buckling performance of a rectangular plate under uniaxial compression can be significantly improved by replacing the traditional material that has a positive Poisson's ratio with an auxetic material when there is in-plane translation restraint along the unloaded edges.
