利用导重法进行结构轻量化设计

LIGHTENING STRUCTURAL DESIGN USING GUIDE WEIGHT METHOD

结构轻量化设计的目的是以最少的设计资源设计出性能合格的产品结构,以降低产品生产成本,提高产品性价比和市场竞争力。结构轻量化的实质是材料重量在结构几何空间内及构件间的合理分配。导重法是可用于产品结构轻量化的结构优化有效方法,它可适用于包括各类单元的各种产品结构构件尺寸优化与结构几何形状优化以及结构拓扑优化;其目标与约束可以涉及各种结构静动力性态。首先给出结构优化导重法用于结构轻量化设计的具有广泛一般性的数学模型及其求解方法。接着给出一种新的包络函数—方根包络函数,使数目庞大的应力与位移约束凝聚为单值强度约束与单值精度约束;还给出适用于多数产品结构轻量化设计的单性态约束优化实用模型与解法;最后给出两个产品结构轻量化的应用实例,验证了导重法用于轻量化设计的有效性与广泛适用性。

The lightening structural design of mechanical products aims at designing qualified mechanical products using the least design resources to reduce product costs, and to improve the performance-price ratio and capability for market competition. The essence of lightening design is the rational distribution of material mass in a geometrical space among components. The Guide-Weight method（GWM） is effective for structural optimization and can be used in lightening structural design of mechanical products. GWM is applicable to the optimization of component size for various structures, including diverse kinds of finite elements and optimization of geometrical shapes, as well as topology optimization. The objective functions and constraint functions of GWM can involve various kinds of structural static and dynamic behaviors. In this paper, firstly, the GWM＇s mathematical model and solution with abroad universality that can be used in lightening design of various mechanical products are presented. Then a square root envelope function is discussed, which converts the enormous stress or displacement constraints into single strength or precision constraint. A practical GWM model and solution with a single behavior constraint is also presented, which is suitable for the lightening design of most mechanical products. Finally, the applied lightening-design examples of two mechanical products are demonstrated, and the effectiveness and broad applicability of GWM are verified.