应力约束下点阵结构多尺度并发优化研究

发布时间：2018-12-10 08:10

【摘要】：点阵材料作为一种新型的多功能材料具有高比刚度、比强度,同时由于其内部高孔隙率,使其具有良好的防隔热、减振降噪、冲击吸能及多功能应用等优点,被广泛应用于航天航空、船舶、汽车制造等领域。但是对于点阵材料构成的结构进行力学性能分析时,由于其内部含有大量微结构,使用传统的有限元分析技术不再适用。因此,本文基于扩展多尺度有限元法(Extended Multiscale Finite Element Method, EMsFEM)对该类点阵材料进行力学分析,围绕点阵材料结构设计时的强度指标、刚度指标及稳定性指标等性能要求,开展了大量应力相关的点阵结构多尺度并发优化设计研究。针对点阵结构局部微杆件强度及稳定性的不同失效模式,建立了考虑强度约束点阵材料轻量化设计模型Ⅰ和同时考虑强度和稳定性约束点阵材料轻量化设计模型Ⅱ。计算中着重讨论了尺寸因子对优化结果的影响,计算发现随着尺寸因子n的增大,优化模型Ⅰ强度约束对点阵材料轻量化设计影响不明显,结构最小重量基本不变；而优化模型Ⅱ由于施加稳定性约束,随着尺寸因子n的增大,结构最小重量降低。针对于复杂的点阵结构分析,最大应力可能发生在任何一个构件、单元,使得应力约束和稳定性约束个数急剧增加,导致考虑局部应力约束优化模型不再适用。为此,文中提出了一种新的凝聚函数,该函数可有效的将大规模的局部约束凝聚成一个整体约束,解决了“次峰值”困难,实现了考虑全局强度及稳定性约束的点阵材料多尺度优化设计。考虑点阵材料结构微观尺度和宏观尺度相互影响,在宏观尺度上引入宏观单元的相对密度p和微观尺度上引入微杆件的截面积A,以微观杆件的强度和刚度为约束,结构重量最小为目标,构建了宏微观双尺度优化模型,实现了考虑结构强度和刚度约束下点阵材料结构并发优化设计。通过数值模拟研究了负泊松比栅格材料、加筋板结构、夹芯板结构的抗热屈曲性能,等材料用量的负泊松比栅格结构比正交栅格结构具有更高的热屈曲临界失稳载荷；而正交加筋板则比负泊松比加筋板抗热屈曲性能更好,但是负泊松比夹芯板抵抗热屈曲性能又优于正交夹芯板。因此,在热承载结构设计时,需要对结构进行合理的选择和设计,才能满足工程实际安全可靠的要求。
[Abstract]:As a new type of multifunctional material, lattice material has the advantages of high specific stiffness, specific strength, high internal porosity, good thermal insulation, vibration and noise reduction, shock energy absorption and multifunctional application. It is widely used in aerospace, ship, automobile manufacturing and other fields. However, the traditional finite element analysis technique is no longer suitable for the analysis of mechanical properties of the structure made of lattice materials because of the large number of microstructures in the structure. Therefore, based on the extended multi-scale finite element method (Extended Multiscale Finite Element Method, EMsFEM), the mechanical analysis of this kind of lattice materials is carried out, and the performance requirements such as strength index, stiffness index and stability index in the structural design of lattice materials are discussed. A large number of stress-dependent multiscale concurrent optimization design studies of lattice structures have been carried out. Aiming at the different failure modes of the strength and stability of the local microbars of lattice structures, a lightweight design model for lattice materials with strength constraints and a lightweight design model for lattice materials with both strength and stability constraints is established. In the calculation, the influence of dimension factor on the optimization result is discussed. It is found that with the increase of dimension factor n, the strength constraint of optimization model I has no obvious influence on the lightweight design of lattice materials, and the minimum weight of the structure is basically unchanged. However, the minimum weight of the structure decreases with the increase of the size factor n due to the stability constraints imposed on the optimization model 鈪，

本文编号：2370261