Shape and Size Optimization of Large-Scale Lattice Structures for Ultralight Auxetic Structural Designs Considering Thermal Elasticity

Metamaterials, which exhibit unconventional physical behaviors such as negative Poisson’s ratio and negative thermal expansion (NTE), have garnered significant attention for their potential applications in various engineering fields. However, conventional design methods made it difficult to systematically achieve optimal performance. This study proposes a H¹ gradient method-based shape and size optimization method for lattice structures, aiming at tailoring linear elastic behaviors. This approach treats both the geometric shape (curvature) and the cross-sectional areas of lattice members as continuous design variables. The objective function is formulated as a weighted sum of the squared error between target and actual displacements (corresponding to properties such as Poisson’s ratio or thermal expansion) and the structural compliance. Using adjoint variable methods, sensitivities are derived precisely with regard to both shape and size variations. The proposed method provides a unified and efficient framework for the systematic design of lattice metamaterials exhibiting auxetic and NTE properties.