Design of self-supporting lattices for additive manufacturing

Lattice truss structures fabricated by additive manufacturing (AM) technique are highly desired in the aerospace science and technology field for their ultra-light and multi-functional properties. However, AM constraints are seldom considered in the mechanical design of lattice units, resulting in noteworthy discrepancies between the actual mechanical performance and designed property of lattice structures. In this work, an innovative design strategy for self-supporting lattice units that considers the geometric constraint of AM is proposed. Inspired by the multi-fold rotational symmetry of crystallography in solid physics, three classes of self-supporting lattices for AM, namely, with three-, four-, and six-fold rotational symmetry, are designed. Each class of lattices can be divided into four hierarchical levels, enabling a structure to change from one with bending-dominated lattices to stretching-dominated lattices in stepwise mode. The elastic constitutive relation of the self-supporting lattices is derived using the nodal displacement method. The constitutive relation is verified by comparing with finite element calculations and mechanical experiments. This work provides the equivalent relation of stiffness properties in the design of complex structures composed of self-supporting lattices, which has been employed in the design of novel ultra-light spacecraft structures.