基于渐进变分法的蛋盒型结构等效刚度分析及优化

对蛋盒型结构的等效刚度特性进行了分析并实现了蛋盒型结构参数的优化设计.首先以蛋盒型结构的单胞为研究对象,基于渐进变分法,得到了蛋盒型结构等效刚度特性的数值计算方法.随后用该方法计算蛋盒型结构不同参数情况下的等效刚度特性,并以结构参数为自变量,等效刚度特性为因变量进行拟合.最后应用拟合公式在限定泊松比或等效刚度的情况下,分别以最大化结构的屈曲载荷和最大化单位质量吸能能力的优化为例,对蛋盒型结构参数进行了量纲为一的优化设计.计算结果表明:蛋盒型结构拉伸刚度降低,弯曲刚度升高;蛋盒型结构的刚度特性与结构参数之间呈现非线性的特点,结构表现出负泊松比的特性;在给定优化目标和限定条件时应用拟合公式可以快速实现蛋盒型结构参数的主动优化设计.

Equivalent stiffness and optimized design of egg-box structure based on variational as-ymptotic method

The equivalent stiffness of the egg-box structure was investigated to achieve structural optimization of the structure pa-rameters. A unit cell of the egg-box structure was studied using the variational asymptotic method to obtain a numerical calculation method for equivalent stiffness of the whole egg-box structure. This numerical calculation method was then used to analyze the equiva-lent stiffness of the egg-box structure with different structural parameters. A formula for equivalent stiffness characteristics was then fit-ted, and the structural parameters were treated as independent variables. Finally, the fitted formula was used to optimize the dimen-sionless structural parameters to obtain maximum buckling load and maximum energy absorbed per unit weight when Poisson' s ratio or equivalent stiffness was restricted. Results show that the tensile stiffness of the egg-box structure is reduced, but the bending stiffness is increased. In addition, there is a nonlinear relationship between stiffness and structural parameters, and the structure exhibits a negative Poisson' s ratio. Furthermore, active parameters optimization design of the egg-box structure can be easily achieved with the fitted formula.