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

The equivalent stiffness of the egg-box structure was investigated to achieve structural optimization of the structure parameters. 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 equivalent stiffness of the egg-box structure with different structural parameters. A formula for equivalent stiffness characteristics was then fitted, and the structural parameters were treated as independent variables. Finally, the fitted formula was used to optimize the dimensionless 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.