基于中空单元的夹层平板结构设计方法研究（英文）

Design procedure for thin three-layer plates made of a depleted material

目的:大型的桁架结构或空间刚架结构可以认为是用中空单元组合而成的宏观结构,在结构初步设计时,如何设计排布中空基本单元以满足结构的性能要求是设计的关键。本文旨在探讨夹层平板结构,在给定竖向变形控制指标后,如何使用简化的方法快速设计各层中空基本单元的尺寸和空隙程度。创新点:1.对于水立方这种复杂的空间多面体网格结构,本文将其理想化为连续的中空介质,利用微观力学中的均质化分析方法,将结构分解为多个基本单元(RVE)进行分析,从而推导出结构性能指标与单元参数之间的关系。2.对于大跨度平板结构,本文提出一种基于RVE重复叠加组合的设计方法,并利用有限元法对该方法进行检验。方法:1.对夹层平板结构的弯曲特性进行理论分析,根据Kirchhoff-Love理论,得到板弯曲刚度与各层的截面惯性矩之间的关系;2.通过理论推导出结构弯曲刚度(图3)、材料使用量(图4)随层厚度和层密度的变化关系;3.从基本单元出发,利用均质化分析方法分别对中空立方体(图5)和空间桁架结构(图6)进行分析,得到结构抗弯刚度随单元中空程度和距截面中性轴距离的函数关系(图7和8),进而推导出结构参数化设计的拟合公式;4.利用该设计公式,针对一个90 m×90 m×2.5 m的平板结构,以跨中挠度为跨度的1/500为设计指标,分别设计由两种基本单元组成的夹层平板结构,并将结构挠度的有限元计算结果与设计指标进行比较(图12)。结论:1.本文提出的利用中空单元组成的夹层平板结构的设计方法,通过优化设计中空单元的各项参数,可以在保证性能指标的同时最大化降低结构质量,得到最优刚度质量比。2.本设计方法和有限元法得到的结果之间差异非常小,说明该设计方法准确可靠。

The efficiency of a long-span structure relies on how material is locally distributed within a fixed structural shape. In this paper a design procedure for thin plates made of three layers of a depleted material subject to a distributed vertical load is proposed. The investigation is driven by the idea of the optimal material organization and has the objective of maximizing the overall stiffness/weight ratio of the structure. Two microstructural architectures of the media are considered： a porous solid structure and a truss arrangement. For each type of microstructure the flexural stiffness has been correlated to the level of deple- tion by the use of a power law function by setting very few parameters. Finally, invoking the principles of structural homogeni- zation theory, the global flexural response of the plate has also been calculated. The validity of the method is demonstrated by comparing the analytical results with those obtained by a numerical finite element simulation of the structure based on a detailed model of the media.