Mesoscale topology optimization of lattice structures for shape control considering full-field displacement matching

Shape morphing, widely required in aerospace and aeronautical structures, utilizes embedded actuators to regulate shape changes. From a structural design perspective, the objective is to minimize the discrepancy between target and achieved displacements at certain degrees-of-freedom (DOF). This work introduces a shape control problem that considers full-field (all-DOF) displacement matching, and investigates mesoscale topology optimization of cellular lattice structures for this problem. The proposed approach models lattice structures with uniform mesostructures using a two-scale homogenization-based finite element method (FEM) and solves the optimization problem with an extended Moving Iso-surface Threshold (MIST) framework. Numerical examples are investigated for design cases considering typical desired morphing shapes in engineering practice and shapes not achievable for natural isotropic material to demonstrate the effectiveness and efficiency of the proposed method: a near-zero shear modulus mesostructure is obtained for pure shear deformation; a near-zero Poisson’s ratio design is achieved for one-dimensional extension; and a maximum shear modulus configuration is realized for trailing edge morphing, where the shape errors are 1.02%, 5.36% and 6.35% respectively. Furthermore, full-scale finite element analysis validates the performance of the optimized mesostructures, confirming the efficacy of the overall design and modeling framework. • Propose shape control problem considering full-field (all-DOF) displacement matching • Model lattice structures via two-scale homogenization-based finite element method • Moving Iso-surface Threshold (MIST) framework to solve mesostructure design problem • Achieve desired morphing shapes not attainable with natural isotropic materials