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.

在航空航天科学技术领域，通过增材制造（AM）技术制造的晶格桁架结构因其超轻和多功能特性而迫切需要。但是，在晶格单元的机械设计中很少考虑AM约束，从而导致实际机械性能与晶格结构的设计性能之间存在显着差异。在这项工作中，提出了一种创新的自支撑晶格单元设计策略，该策略考虑了AM的几何约束。受固体物理学中晶体学多重旋转对称性的启发，设计了三类AM的自支撑晶格，即具有三，四和六重旋转对称性。每类格子都可以分为四个层次，使结构可以逐步控制方式从具有弯曲为主的晶格转变为以拉伸为主的晶格。利用节点位移法推导了自支撑晶格的弹性本构关系。通过与有限元计算和力学实验进行比较，验证了本构关系。这项工作在由自支撑晶格组成的复杂结构的设计中提供了刚度特性的等效关系，该关系已被用于新颖的超轻型航天器结构的设计中。通过与有限元计算和力学实验进行比较，验证了本构关系。这项工作在由自支撑晶格组成的复杂结构的设计中提供了刚度特性的等效关系，该关系已被用于新颖的超轻型航天器结构的设计中。通过与有限元计算和力学实验进行比较，验证了本构关系。这项工作在由自支撑晶格组成的复杂结构的设计中提供了刚度特性的等效关系，该关系已被用于新颖的超轻型航天器结构的设计中。