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基于柔顺性与热变形双目标的多孔材料与结构几何多尺度优化设计

ISSN号：0254-7805
期刊名称：固体力学学报
时间：0
页码：119-132
分类：O223[理学—运筹学与控制论;理学—数学]
作者机构：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024
相关基金：国家自然科学基金重点项目（90816025 10902018 90816018）; 科技重大专项基金（2009ZX04014-034）; 高等学校博士学科点专项科研基金资助课题（200801411052）; 大连理工大学理学学科研究基金和973项目（2011CB610304）资助
相关项目：基于点阵材料微观临界应力的几何多尺度拓扑优化方法研究

关键词：多目标优化, 多孔陶瓷, 几何多尺度, 夹层结构, 热结构, multi-objective optimization, porous ceramic, multi geometrical scale, sandwich structure, thermal structure

中文摘要：

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.

英文摘要：

A new multi-objective optimization formulation is developed for the multi geometrical scale topology optimization of the load carrying spacecraft structures composed of porous ceramic materials,which combines high stiffness with low thermal expansion in a predefined domain.The objective function is composed of two items.One is to minimize the structural compliance when only the mechanical loads are applied on structures,while the other is to minimize the thermal expansion of the outer spacecraft structure surface when only the thermal loads are applied.The two items are both normalized and then jointed through weighted coefficients to form a multi-objective function.The independent macro and micro densities are introduced as the design variables and penalization approaches are adopted in both scales,i.e.SIMP（Solid Isotropic Material Penalization） in micro material scale and PAMP（Porous Anisotropic Material Penalization） in macro structure scale.Optimizations of the two geometrical scales are integrated into one system through homogenization theory.The volume preserving nonlinear density filtering based on Heaviside step function is used to prevent checkerboard patterns and to obtain a clear design.We apply the proposed multi-objective optimization model to a sandwich elliptically curved shell to investigate the concurrent multi-scale design of structure configuration and microstructure of porous ceramic.The numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performances of curve shell structure when the available amount of material is insufficiently given.And an ＂optimum＂ material volume fraction is observed for the multi-objective optimization problem.The influence of thickness of surface sheets on the optimal design is investigated at last.

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