A general multi-scale topology optimisation method for lightweight lattice structures obtained through additive manufacturing technology

A general framework for the multi-scale topology optimisation (TO) of lattice structures (LSs) is presented in this work. The proposed method involves: Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent pseudo-density field describing LS representative volume element (RVE) topology, Solid Isotropic Material with Penalisation (SIMP) approach and strain energy-based homogenisation (SEHM) perform scale transition. main contributions work are essentially three. Firstly, physical responses defined at different scales their gradient evaluated by exploiting NURBS local support property Dirichlet’s problem properties RVE scale. Secondly, computational efficiency SEHM based on elements energy over that averaged stresses rigorously proven. Finally, show effectiveness method, numerical analyses conducted 2D 3D problems. sensitivity analysis optimised integer parameters hyper-surface carried out. Moreover, influence initial guess macroscopic loading condition investigated. minimum length-scale requirement also integrated into formulation as a manufacturing constraint.