基于等刚度条件的薄壁结构的一种材料替代轻量化设计分析方法

通过对板壳结构有限单元的弯曲应变能和膜应变能进行分析，得到一个采用不同材料的薄壁结构的刚度之间的近似解析关系式。将其与结构刚度的有限元计算分析过程相结合，提出一种不同材料但等刚度的薄壁结构的迭代设计方法和材料替代轻量化分析方法。分析得到的薄壁结构关于板壳的弯曲应变能占总的应变能的比例  的等刚度曲线，可用于直观地评价材料替代得到的等刚度结构的轻量化效果，可指导薄壁结构的轻量化设计。分析表明，材料替代对薄壁结构刚度的影响不仅与材料的弹性特性和板壳厚度相关，还与给定载荷下结构的  参数相关。对于铝板替代钢板的薄壁结构设计问题， 越高，则等刚度铝板结构的轻量化效果越明显。通过对一个悬臂薄壁钢板曲梁结构和一个典型车身接头结构的材料替代设计和轻量化分析，验证了提出的设计、分析方法的有效性和结论的正确性。

Analysis Method for Lightweight Material Substitution Design of Thin-walled Structures with Equal Stiffness

An approximate analytical expression for the calculation of the stiffness of thin-walled structures of different materials is developed on the basis of bending and membrane strain energy analysis of shell finite elements. The analytical expression combining with finite element analysis gives an analysis method for lightweight material substitution design of thin-walled structures with equal stiffness. The lightweight effect of material substitution can be estimated by using material density and thickness of the two structures, and an equal-stiffness curve with respect to the ratio of shell bending strain energy to the total strain energy λ of structure is presented to show the lightweight effect and to guide the lightweight design of thin-walled structures. It is also shown that the influence of material substitution on structural stiffness is related not only to the material properties and shell thickness but also the ratioλ. For design problems of substituting aluminum structures for equal-stiffness steel ones, lightweight benefit increases quickly with the ratio increasing. Two aluminum substitution designs, with equal-stiffness requirement, for a curved thin-walled steel beam and a typical car body joint are discussed, and the lightweight effects are analyzed, which demonstrates the effectiveness of the proposed design and analysis method and related conclusions.