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论文采用拓扑优化技术针对由具有均一微结构的多孔陶瓷材料构成的结构,从结构和材料两个方面进行优化设计,在轻量化的同时使得结构具有较高的刚度和特定区域较小的热变形.以机械载荷下的结构柔顺性和热载荷下结构特定区域的热变形为目标,以宏观密度和微观密度为两类独立的设计变量,对两个目标进行归一化处理,建立多目标优化模型.采用体积守恒的Heaviside密度过滤函数获得清晰的最优拓扑构型.在微观层次上采用SIMP惩罚策略,在宏观层次上采用带惩罚的多孔各向异性材料法(PAMP),借助均匀化方法建立两个尺度间的联系.以机械载荷与热载荷作用下的夹层结构为例,给出了不同体积份数下的最优夹层结构及构成此夹层结构的多孔陶瓷微结构的最优构型.数值算例表明,给定材料用量较少时,多孔材料的使用可以使结构特定区域的热变形显著减小,同时保证结构具有一定的刚度.同时算例发现对此双目标优化问题存在一个“最优材料用量”.最后讨论了夹层结构上下面板的不同壁厚对优化结果的影响.
In this paper, the topology optimization technology is applied to the structure composed of porous ceramic material with homogeneous microstructure. The optimal design is made from the aspects of structure and material, which makes the structure have higher rigidity and less thermal deformation in a specific area Taking the structural flexibility under mechanical load and the thermal deformation in the specific area under the thermal load as targets, macroscopic density and microscopic density are two kinds of independent design variables, the two targets are normalized to establish multi - objective optimization Model.Using volume conservation Heaviside density filter function to obtain a clear topological configuration.Using the SIMP penalty strategy at the micro level, PAMP with penalty at the macro level, by means of homogenization method The relationship between the two scales was established.With the sandwich structure under the action of mechanical load and thermal load as an example, the optimal sandwich structure with different volume fraction and the optimal configuration of the porous ceramic microstructure Numerical examples show that the use of porous materials can significantly reduce the thermal deformation in a given area of the structure for a given amount of material Structure having a certain rigidity, while this example is found a dual-objective optimization problem “optimal amount of material ”. Finally the influence of different thickness of the upper and lower panels of the sandwich structure optimization results.